AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A \( 120 V, 60 H z \) a.c. power is connected \( 800 \Omega \) non-inductive resistance and unknown capacitance in series. The voltage drop across the resistance is found to be \( 102 \mathrm{V} \), then voltage drop across capacitor is
\( A \cdot 8 v \)
B. 102v
\( c \cdot 63 v \)
D. \( 55 v \)
Subject: Physics
The angular momentum of particle of mass \( 0.01 K g \) and position vector \( \vec{r}= \) \( (10 \hat{i}+6 \hat{j}) \) meter and moving with a velocity 5 ìmetre/ sec about the origin
will be :
A. \( -0.3 \hat{k} \) Joulesec
B. \( 3 \hat{k} \) joulesec
c. \( 1 / 3 \) joulesec
D. \( 0.03 \hat{k} \) Joulesec
Subject: Maths
\( \operatorname{Matrix} \boldsymbol{A}_{\boldsymbol{r}}=\left[\begin{array}{cc}\mathbf{1} & \boldsymbol{r}-\mathbf{1} \\ -\mathbf{2} & \mathbf{1}\end{array}\right] ; \boldsymbol{r}= \)
\( \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots . . \) If \( \sum_{r=\mathbf{1}}^{\mathbf{1 0 0}}\left|\boldsymbol{A}_{\boldsymbol{r}}\right|=(\sqrt{\mathbf{1 0}})^{\boldsymbol{k}}, \) then
\( \boldsymbol{K}=\ldots . . ;\left(\left|\boldsymbol{A}_{\boldsymbol{r}}\right|=\operatorname{det}\left(\boldsymbol{A}_{\boldsymbol{r}}\right)\right) \)
A .2
B. 6
\( c \cdot 4 \)
\( D \)
Subject: Chemistry
When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is:
\( A \cdot\left(\frac{2}{5}\right) \)
B. \( \left(\frac{3}{5}\right) \)
\( c \cdot\left(\frac{3}{7}\right) \)
D. \( \left(\frac{5}{7}\right) \)
Subject: Physics
A block of mass 10 kg placed on rough horizontal surface having coefficient of friction \( =0.5, \) if a
horizontal force of \( 100 \mathrm{N} \) acting on it then acceleration of the block will be :
\( A \cdot 10 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 5 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathrm{c} \cdot 15 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 0.5 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Physics
In the nuclear reaction pictured below, what is the missing nuclide? \( _{1}^{2} \boldsymbol{H}+\mathbf{7}^{14} \boldsymbol{N} \rightarrow_{2}^{3} \boldsymbol{H} \boldsymbol{e}+? \)
B . \( _{6}^{13} \mathrm{C} \)
\( \mathbf{c} \cdot \frac{14}{7} N \)
D. \( _{6}^{1} C \)
E \( \cdot \frac{12}{6} C \)
Subject: Physics
A small, magnetized sphere A of pole strength \( m \) is counter-poised by a pan in a balance. Another magnetised sphere B of the same mass as \( A \) is placed below \( A \) so that their centres are at a distance
\( 1 \mathrm{cm} . \) If \( \mathrm{A} \) and \( \mathrm{B} \) are unlike poles of same strength and to restore counter the weight in the pan is increased by \( 500 g m \) the pole strength of each sphere is:
A \( .1 .4 A m \)
B. \( 9.8 A m \)
c. \( 0.7 A m \)
D. \( 70 A m \)
Subject: Chemistry
Which of the following compounds do
not exist?
\( N_{4}, P_{4}, P C I_{5}, N C I_{5}, P_{2} O_{5}, N O_{2}, P O_{2} \)
A. \( N_{4}, N C I_{5}, N O_{2} \)
B. \( N_{4}, N C I_{5}, P O_{2} \)
c. \( P C I_{5}, N C I_{5}, P O_{2} \)
D. All of these
Subject: Chemistry
The correct order of stability of
\( \boldsymbol{A l}^{+}, \boldsymbol{A l}^{+2}, \boldsymbol{A l}^{+\mathbf{3}} \mathbf{i s} \)
A \( \cdot A l^{+3}>A l^{+2}>A l^{+} \)
B. \( A l^{+2}>A l^{+3}>A l^{+} \)
c. \( A l^{+2}<A l^{+}>A l^{+} \)
D. \( A l^{+3}>A l^{+}>A l^{+} \)
Subject: Chemistry
Two solutions labelled as \( 3 \mathrm{M} \) HCl and 1
M HCl are mixed in the ratio of \( x: y \) by
volume and the molarity of mixture solution becomes 1.5 M. What is the
molarity of the resulting solution if they
are mixed in the ratio of \( y: x \) by volume
\( ? \)
A. 4 м
в. 3 м
c. 2 м
D. 2.5 М
Subject: Physics
A ray of light strikes a glass plate at an
angle of \( 60^{\circ} . \) If the reflected and refracted rays are perpendicular to each other, the refractive index of glass is
\( ^{A} \cdot \frac{\sqrt{3}}{2} \)
B. 3
\( c \cdot \frac{1}{2} \)
D. \( \sqrt{3} \)
Subject: Physics
A wire of initial length \( L \) and radius \( r \) is stretched by a length \( l \). Another wire of same material but with initial length \( 2 L \) and radius \( 2 r \) is stretched by a
length \( 2 l \). The ratio of the stored elastic energy per unit volume in the first and second wire is,
\( A \cdot 1: 4 \)
B. 1: 2
c. 2: 1
D. 1:
Subject: Chemistry
Assertion
Silica is added as a flux in a
reverberatory furnace, in the extraction
of copper for copper pyrites.
Reason
Silica acts as basic flux.
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 of the following pairs of homologous series is represented by the general molecular formula
\( \boldsymbol{C}_{\boldsymbol{n}} \boldsymbol{H}_{2 \boldsymbol{n}-2} ? \)
A. Alkene and alkyne
B. Alkyne and alkadiyne
c. Alkane and alkadiene
D. Alkyne and alkadiene
Subject: Chemistry
Consider the reaction \( \boldsymbol{A}_{2}+\boldsymbol{B} \rightarrow \)
products. If the concentration of \( A_{2} \) and
B are halved, the rate of the reaction decreases by a factor of 8. If the concentration of \( A \) is increased by a factor of \( 2.5, \) the rate increases by the
factor of \( 2.5 . \) What is the order of the
reaction? Write the rate law.
Subject: Chemistry
The correct relationship between free energy change in a reaction and the
corresponding equilibrium constant,
\( K_{c} \) is :
A \( . \triangle G=R T \ln K_{c} \)
B. \( -\triangle G=R T \ln K_{c} \)
c. \( \triangle G^{0}=R T l n K_{c} \)
D. \( -\triangle G^{0}=R T \ln K_{c} \)
Subject: Physics
A ray incident at a point at an angle of
incidence \( \theta \) enters into a glass sphere
placed in air which is reflected and
refracted at the farther surface of the
sphere as shown in the figure. The angle between reflected and refracted rays at
this surface is \( 90^{0} . \) If refractive index of
the sphere is \( \sqrt{3}, \) the angle \( \theta \) is :
A \( \cdot \frac{\pi}{3} \)
B. \( \frac{\pi}{4} \)
c. \( \frac{\pi}{6} \)
D. \( \frac{2 \pi}{3} \)
Subject: Physics
A convex lens of focal length \( 0.15 \mathrm{m} \) is
made of a material of refractive index 2
When it is placed in a liquid, its focal length increases by \( 0.225 m . \) The refractive index of the liquid is
A \( \cdot \frac{7}{4} \)
B. \( \frac{5}{4} \)
\( c \cdot \frac{9}{4} \)
D. \( \frac{3}{2} \)
Subject: Physics
Assume that a neutron breaks into a
proton and an electron. The energy released during this process is : (mass of neutron \( =1.6725 \times 10^{-27} k g, \) mass
of proton \( =1.6725 \times 10^{-27} k g, \) mass of
electron \( \left.=9 \times 10^{-31} k g\right) \)
\( \mathbf{A} .5 .4 \mathrm{MeV} \)
в. \( 0.73 \mathrm{MeV} \)
c. \( 7.10 M e V \)
D. \( 6.30 \mathrm{MeV} \)
Subject: Chemistry
The volume of \( C O_{2} \) produced at STP by
decomposition of \( 4.2 g \) of \( N a H C O_{3} \)
according to the reaction:
\( 2 N a H C O_{3} \rightarrow N a_{2} C O_{3}+H_{2} O+C O_{2} \)
\( \mathbf{A} \cdot 150 \mathrm{m} \)
B. \( 569 \mathrm{ml} \)
c. \( 1.68 L \)
D. \( 5.6 L \)
Subject: Maths
If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{2 \times 2} \) and \( \boldsymbol{a}_{i j}=\boldsymbol{i}+\boldsymbol{j}, \) then \( \boldsymbol{A}= \)
\( A \cdot\left(\begin{array}{l}12 \\ 3\end{array}\right) \)
в. \( \left(\begin{array}{c}23 \\ 3\end{array}\right) \)
\( c \cdot\left(\begin{array}{cc}2 & 3 \\ 4 & 5\end{array}\right) \)
D. \( \left(_{6}^{4} \begin{array}{r}5 \\ \end{array}\right) \)
Subject: Physics
Four particles each of mass \( M, \) are located at the vertices of a square with
side \( L . \) The gravitational potential due
to this at the centre of the square is
A \( \cdot-\sqrt{32} \frac{G M}{L} \)
в. \( -\sqrt{64} \frac{G M}{L^{2}} \)
c. zero
D. \( \sqrt{32} \frac{G M}{L} \)
Subject: Biology
Assertion
Copper-T is an effective contraceptive
device in human females.
Reason
Copper-T prevents passage of sperms from vagina upwards into fallopian
tubes.
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
f \( p, q, r \) are real and \( p \neq q, \) then roots of
the equation \( (\boldsymbol{p}-\boldsymbol{q}) \boldsymbol{x}^{2}+\mathbf{5}(\boldsymbol{p}+\boldsymbol{q}) \boldsymbol{x}- \)
\( \mathbf{2}(\boldsymbol{p}-\boldsymbol{q})=\mathbf{0} \) are
A. Real and equal
B. Complex
c. Real and unequal
D. None of these
Subject: Maths
The radius of a sphere is changing at the rate of \( 0.1 \mathrm{cm} / \) sec. The rate of
change of its surface area when the radius is \( 200 \mathrm{cm}, \) is.
A \( \cdot 8 \pi c m^{2} / \) sec
В. \( 12 \pi c m^{2} / \)sec
c. \( 160 \pi c m^{2} / \) sec
D. \( 200 \pi c m^{2} / \) sec
Subject: Maths
Assertion
Let equations \( a x^{2}+b x+c= \)
\( \mathbf{0}(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \in \boldsymbol{R}) \& \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}+\mathbf{5}=\mathbf{0} \) have
common root, then \( \frac{\boldsymbol{a}+\boldsymbol{c}}{\boldsymbol{b}}=\frac{\mathbf{1}}{\mathbf{3}} \)
Reason
If both roots of \( A x^{2}+B x+K_{1}=0 \& \)
\( \boldsymbol{A}^{\prime} \boldsymbol{x}^{2}+\boldsymbol{B}^{\prime} \boldsymbol{x}+\boldsymbol{K}_{2}=\mathbf{0} \) are identical
\( \operatorname{then} \frac{\boldsymbol{A}}{\boldsymbol{A}_{1}}=\frac{\boldsymbol{B}}{\boldsymbol{B}_{1}}=\frac{\boldsymbol{K}_{1}}{\boldsymbol{K}_{2}}\left(\text { where } \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{K}_{1}\right. \)
and \( \left.A^{\prime}, B,^{\prime} K_{2} \in R\right) \)
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, Reason is correct
Subject: Maths
Prove that \( (\boldsymbol{a}+\boldsymbol{b})^{5}-\boldsymbol{a}^{5}-\boldsymbol{b}^{5}= \)
\( \boldsymbol{5} \boldsymbol{a b}(\boldsymbol{a}+\boldsymbol{b})\left(\boldsymbol{a}^{2}+\boldsymbol{a} \boldsymbol{b}+\boldsymbol{b}^{2}\right) \)
Subject: Chemistry
The following reaction is an example of
\( a: \)
\( \mathbf{4} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+\mathbf{5} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{4} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
(i) displacement reaction
(ii) combination reaction
(iii) redox reaction
(iv) neutralisation reaction
\( A \). (i) and (iv)
B. (ii) and (iii)
c. (i) and (iii)
D. (iii) and (iv)
Subject: Maths
A plane which passes through the point (3,2,0) and the line \( \frac{x-3}{1}=\frac{y-7}{5}= \)
\( \frac{z-4}{4} \) is?
A. \( x-y+z=1 \)
в. \( x+y+z=5 \)
c. \( x+2 y-z=1 \)
D. \( 2 x-y+z=5 \)
Subject: Physics
In the equations below, \( A, B, \omega \) and \( \phi \) are
constants; \( y \) and \( t \) are variables; \( t \)
represents time. Only one of the following equations does not represent SHM. Which one is that?
A. \( y= \) Asinwt
B. \( y= \) Bcoswt
c. \( y= \) Asinwt \( +B \) coswt
D. \( y= \) Asinwt \( +B \cos (2 \omega t) \)
Subject: Chemistry
One mole of \( S O_{3} \) was placed in a two
litre vessel at a certain temperature. The following equilibrium was established in the vessel :
\[
\mathbf{2} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g})
\]
The equilibrium mixture reacted with
0.2 mole \( K M n O_{4} \) in acidic medium.
Hence, \( \boldsymbol{K}_{c} \) is :
A. 0.50
в. 0.25
\( c \cdot 0.125 \)
D. None of these
Subject: Physics
5 kilomoles of oxygen is heated at
constant pressure. The temperature of the oxygen gas is increased from \( 295 \mathrm{K} \) to 305 K. If the molar heat capacity of oxygen at constant pressure is 6.994 kcal/kmole K. The amount of heat
absorbed in kcal,
A . 249.7
B. 44
c. 349.7
D. 539.7
Subject: Chemistry
Equilibrium constant for the following
reaction is \( 1 \times 10^{-9} \)
\( \boldsymbol{C}_{5} \boldsymbol{H}_{5} \boldsymbol{N}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightleftharpoons \)
\( \boldsymbol{C}_{5} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q} \cdot) \)
Determine the mole of pyridinium
chloride \( \left(C_{5} H_{5} N . H C I\right) \) that should be
added to \( 500 \mathrm{mL} \) solution of \( 0.4 \mathrm{M} \)
pyridine \( \left(C_{5} H_{5} N\right) \) to obtain a buffer
solution of \( \mathrm{pH}=5 \)
A. 0.1 mole
B. 0.2 mole
c. 0.3 mole
D. 0.4 mole
Subject: Chemistry
Write the name, the structure and the
magnetic behavior of each of the
following complexes:
(i) \( \left(\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right) \boldsymbol{C l}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right] \)
(ii) \( \left(\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right] \boldsymbol{C l} \)
(iii) \( \boldsymbol{N} \boldsymbol{i}(\boldsymbol{C O})_{4} \)
Subject: Physics
An electron, \( \alpha \) - particle and a proton
have the same kinetic energy. A comparison of their de Broglie wavelengths yields:
A \( \cdot \lambda_{p}>\lambda_{a}<\lambda_{c} \)
B . \( \lambda_{e}>\lambda_{a}<\lambda_{p} \)
c. \( \lambda_{a}<\lambda_{p}<\lambda_{e} \)
D. \( \lambda_{p}<\lambda_{e}<\lambda_{a} \)
Subject: Physics
Displacement x of a particle moving in one dimension is related to time \( t \) by the equation \( t=\sqrt{x}+2 . \) The displaclcement of the particle when its velocity is zero, is (Here \( x \) is in metre
and \( t \) is in second
\( A \cdot 4 \)
B. 2
\( c \)
\( D \)
Subject: Chemistry
Assertion
A reaction between \( F e \) and \( I_{2} \) occurs,
but a reaction between \( F e^{2+} \) and \( I^{\ominus} \)
does not occur.
Reason
Fe is a better reducing agent than \( \boldsymbol{I}^{\ominus} \)
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
A ball is thrown vertically upward with
speed \( v_{1}, \) and it returns to ground with
speed \( v_{2} . \) If air resistance is not ignored,
then, choose the correct alternative:
\( \mathbf{A} \cdot v_{1}=v_{2} \)
B. \( v_{2}>v_{1} \)
\( \mathbf{C} \cdot v_{1}>v_{2} \)
D. Nothingcanbesaid
Subject: Maths
If \( f(x) \) is differentiable in the interval
\( [2,5], \) where \( f(2)=\frac{1}{5} \) and \( f(5)=\frac{1}{2} \)
then there exists a number \( c, 2<c< \)
5 for which \( f^{\prime}(c)= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{1}{10} \)
D. None
Subject: Maths
The random variable \( x \) follows normal
distribution
Then the value of \( C \) is
A \( \cdot \sqrt{2 \pi} \)
в. \( \frac{1}{\sqrt{2 \pi}} \)
c. \( 5 \sqrt{2 \pi} \)
D. \( \frac{1}{5 \sqrt{2 \pi}} \)
Subject: Maths
The value of the intgral \( \int_{-\pi / 2}^{\pi / 2} \log \left(\frac{a-\sin \theta}{a+\sin \theta}\right) d \theta, a>0 \) is?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 5
Subject: Maths
ABCD is a parallelogram as shown in figure. If \( A B=2 A D \) and \( P \) is mid-point of
\( A B, \) then \( \angle C P D \) is equal to
\( A \cdot 90^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 135^{\circ} \)
Subject: Physics
A resistor, an indicator and a capacitor are connected in series with a \( 120 \mathrm{V}, 100 \) \( \mathrm{Hz} \) ac source. Voltage leads the current
by \( 35^{\circ} \) in the circuit. If the resistance of
the resistor is \( 10 \Omega \) and the sum of
inductive and capacitive reactance is \( 17 \Omega, \) calculate the self-inductance of
the inductor.
Subject: Maths
The length of the chord of a circle is \( 8 \mathrm{cm} \) and perpendicular distance between centre and the chord is \( 3 \mathrm{cm} \). Then the
radius of the circle is equal to?
A. \( 4 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( \mathrm{c} \cdot 6 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)
Subject: Physics
If \( g \) is acceleration due to gravity on the
earth's surface, the gain in the potential energy of an object of mass \( m \) raised from the surface of the earth to a height equal to the radius \( R \) of the earth is:
A. \( 2 m g R \)
в. \( m g R \)
c. \( \frac{m g R}{4} \)
D. \( \frac{m g R}{2} \)
Subject: Maths
Suppose a continuous function \( \boldsymbol{f} \) \( [0, \infty) \rightarrow R \) satisfies \( f(x)= \)
\( 2 \int_{0}^{x} t f(t) d t+1 \) for all \( x \geq 0 \)
Then \( \boldsymbol{f}(\mathbf{1}) \) equals
\( A \)
B \( \cdot e^{2} \)
\( c \cdot e^{4} \)
D. \( e^{6} \)
Subject: Maths
Assertion \( f(x)=\frac{2}{\pi} x \sin x+x^{3}, \) where \( x \in \)
\( \left[0, \frac{\pi}{2}\right] \)
Statement-1: \( f(x)=\frac{\pi}{2} \) has exactly one solution in \( \boldsymbol{x} \in\left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right] \)
and
Reason
Statement-2: \( \boldsymbol{f}(\boldsymbol{x}) \geq \mathbf{0} \) for all \( \boldsymbol{x} \) in
\( \left[0, \frac{\pi}{2}\right] \)
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
c. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.
Subject: Physics
Assertion
Kirchhoff's junction rule can be applied to a junction of several lines or a point in a line.
Reason
When steady current is flowing, there is no accumulation of charges at any junction or at any point in a line.
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
\( \operatorname{Let} f(x)=\int \frac{x^{2} d x}{\left(1+x^{2}\right)(1+\sqrt{1+x^{2}})} \)
and \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} . \) Then \( \boldsymbol{f}(\mathbf{1}) \) is
A \( \cdot \log (1+\sqrt{2}) \)
B \( \cdot \log (1+\sqrt{2})-\frac{\pi}{4} \)
\( c \cdot \log (1+\sqrt{2})+\frac{\pi}{4} \)
D. none of these
Subject: Physics
\( \vec{B}=-(0.31 T) \hat{i} \) what will be the angle between \( \hat{\text { iand }} \) B. (length of wire is 0.01m)
A .
в. \( (0.01085 N) \hat{k} \)
c. \( (-0.01085 N) \hat{k} \)
D. \( (0.01085 N) \hat{i} \)
Subject: Physics
The reactance of a condenser of
capacity \( 50 \mu \mathrm{F} \) for an \( A C \) of frequency
\( 2 \times 10^{3} \) Hertz will be
\( A .5 \) ohm
B. \( \frac{2}{\pi} \)
\( c \cdot \frac{3}{\pi} \)
D. \( \frac{5}{\pi} \)
Subject: Physics
Two block masses \( m_{1} \) and \( m_{2} \) are
connected with the help of a spring of spring constant \( k \) initially the spring in its natural length as shown. A sharp
impulse is given to mass \( m_{2} \) so that it
acquires a velocity \( v_{0} \) towards right. If the system is kept on smooth floor then find:
(a) the velocity of the centre of mass
(b) the maximum elongation that the spring will suffer?
Subject: Maths
Range of \( f(x)=\tan ^{-1}\left[\frac{2}{\pi}\left(2 \tan ^{-1} x-\right.\right. \)
\( \left.\left.\sin ^{-1} x+\cot ^{-1} x-\cos ^{-1} x\right)\right] \) contains
A. Only one integer
B. More than 2 integers
c. only two integers
D. No integer
Subject: Chemistry
lonisation potential values of noble gases decrease down the group with increase in atomic size. Xenon forms
binary fluorides by the direct reaction of elements. Identify the correct statement(s) from below.
This question has multiple correct options
A. Only the heavier noble gases form such compounds
B. It happens because the noble gases have higher ionisation energies
c. It happens because the compounds are formed with electronegative ligands
D. octet of electrons provide the stable arrangements
Subject: Chemistry
The wave number of the first line of
Balmer series of H atom is \( 15200 \mathrm{Cm}^{-1} \)
What is the wave number of the first
line of Balmer series of \( L i^{2+} \) ion?
A. \( 15200 \mathrm{Cm}^{-1} \)
B. \( 6080 \mathrm{Cm}^{-1} \)
c. \( 76000 C m^{-1} \)
D. \( 136800 C m^{-1} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \) and \( \boldsymbol{f}(\boldsymbol{x})= \)
\( 1+(\sin 2 x) g(x) \) where \( g(x) \) is
continuous, then \( f^{\prime}(x) \) equals
A \( . f(x) g(0) \)
B \( .2 f(x) g(0) \)
D. \( 2 f(0) \)
Subject: Chemistry
The uncertainty (in meters) in the position of an insect weighing \( 0.68 g \) and traveling at a velocity of \( 0.85 \mathrm{m} / \mathrm{s} \) (the uncertainty in the velocity is 0.1 \( m / s), \) is:
A. \( 8 \times 10^{-21} \mathrm{m} \)
В. \( 4 \times 10^{-25} \mathrm{m} \)
c. \( 8 \times 10^{-31} m \)
D. \( 8 \times 10^{-34} m \)
Subject: Maths
Simplify \( (2 a+b)(c-2 d)+(a- \)
\( \boldsymbol{b})(\boldsymbol{2} \boldsymbol{c}+\boldsymbol{3} \boldsymbol{d})+\boldsymbol{4}(\boldsymbol{a} \boldsymbol{c}+\boldsymbol{b} \boldsymbol{d}) \)
A. \( 8 a d+a c b-c-b d \)
B. \( 8 a c-a d-b c-b d \)
c. \( 8 c-a d+b c-d \)
D. \( 8 a c+a d-b c d \)
Subject: Chemistry
Which of the following reagents will
best convert nitrobenzene into \( 2,4,6- \)
trichlorobromobenzene?
A. \( \operatorname{SnCl}_{2} / \mathrm{HCl}, \mathrm{Cl}_{2}(a q), \mathrm{NaNO}_{2} / \mathrm{HCl}-0^{\circ} \mathrm{C} ; \mathrm{CuBr} \)
B . \( C l_{2} / A l C l_{3}, S n C l_{2} / H C l, N a N O_{2} / H C l-0^{o} C ; C u B r \)
c. \( \operatorname{SnCl}_{2} / \mathrm{HCl}, \mathrm{Br}_{2}-\mathrm{H}_{2} \mathrm{O}, \mathrm{NaNO}_{2} / \mathrm{HCl}-0^{\circ} \mathrm{C} ; \mathrm{CuCl} \)
D. \( \operatorname{SnCl}_{2} / \mathrm{HCl}, \mathrm{NaNO}_{2} / \mathrm{HCl}-0^{\circ} \mathrm{C}, \mathrm{H}_{2} \mathrm{O}, \mathrm{Cl}_{2}(\mathrm{aq}) ; \mathrm{HB} \)
Subject: Physics
Two points \( \mathbf{P} \) and \( \mathbf{Q} \) are maintained at
the potentials of \( 10 \mathrm{V} \) and \( -4 \mathrm{V} \) respectively. The work done in moving
100 electrons from \( \mathbf{P} \) to \( \mathbf{Q} \) is :
В \( \cdot 9.60 \times 10^{-17} \mathrm{J} \)
c. \( -2.24 \times 10^{-16} \mathrm{J} \)
D \( .2 .24 \times 10^{-16} \mathrm{J} \)
Subject: Chemistry
Assertion
Solubility of sparingly soluble salt decreases due to common ion effect
Reason

Solubility product constant does not
depend on common ion effect.
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
In an A.C. circuit, the current flowing in
inductance is \( \boldsymbol{I}=\mathbf{5} \sin (\mathbf{1 0 0} \boldsymbol{t}-\boldsymbol{\pi} / \mathbf{2}) \)
ampers and the potential difference is \( =200 \sin (100 \mathrm{t}) \) volts. The power
consumption is equal to
A. 1000 watt
B. 40 watt
c. 20 watt
D. zero
Subject: Physics
Car \( A \) and car \( B \) start moving simultaneously in the same direction along the line joining them. Car \( A \) with a
constant acceleration \( \boldsymbol{a}=\mathbf{4} \boldsymbol{m} / \boldsymbol{s}^{2} \)
while car \( B \) moves with a constant
velocity \( \boldsymbol{v}=\mathbf{1} \boldsymbol{m} / \boldsymbol{s} . \) At time \( \boldsymbol{t}=\mathbf{0}, \) car \( \boldsymbol{A} \)
is \( 10 m \) behind car \( B \). Find the time
when car \( A \) overtakes car \( B \)
Subject: Maths
The points \( A(-1,3,0), B(2,2,1) \) and
\( C(1,1,3) \) determine a plane. The distance of the plane \( A, B, C \) from the
point \( D(5,7,8) \) is
A . \( \sqrt{66} \)
B. \( \sqrt{71} \)
c. \( \sqrt{73} \)
D. \( \sqrt{76} \)