AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The range of the function
\( f(x)=\sin \cos \left(\ln \left(\frac{x^{2}+1}{x^{2}+e}\right)\right) \) is
A \( \cdot[\sin \cos 1,1) \)
B. \( [\sin \cos 1, \cos 1) \)
c. \( [\sin \cos 1, \sin 1) \)
D. \( (\sin \cos 1, \sin 1] \)
Subject: Maths
If \( l^{2}+m^{2}+n^{2}=5, \) then \( (l m+m n+ \)
\( (n) \) is
\( \mathbf{A} \cdot \geq(-5 / 2) \)
B \( \cdot \geq(-1) \)
\( c \cdot \leq 5 \)
\( D . \leq 3 \)
Subject: Maths
\( a, b, c \) are in A.P. and the points \( \boldsymbol{A}(\boldsymbol{a}, \mathbf{1}), \boldsymbol{B}(\boldsymbol{b}, \mathbf{2}) \) and \( \boldsymbol{C}(\boldsymbol{c}, \boldsymbol{3}) \) are such
that \( (O A)^{2},(O B)^{2} \) and \( (O C)^{2} \) are also in A.P; \( O \) being the origin, then This question has multiple correct options
A \( \cdot a^{2}+c^{2}=2 b^{2}-2 \)
B. \( a c=b^{2}+1 \)
c. \( (a+c)^{2}=4 b^{2} \)
D. \( a+b+c=3 b \)
Subject: Physics
A particle projected from 0 and moving
freely under gravity strikes
the horizontal plane passing through 0 at a distance \( R \) from the starting
point 0 as shown in the figure. Then
This question has multiple correct options
A. there will be two angles of projection if \( R g<u^{2} \)
B. the two possible angles of projection are complementary
c. the product of the possible times of flight from 0 to \( A \) is \( \frac{2 R}{g} \)
D. there will be more than two angles of projection if \( R g=u^{2} \)
Subject: Chemistry
\( H F \) can be prepared by the action of
\( H_{2} S O_{4} \) on \( N a F . \) Choose the correct
statement(s) for action of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) on
Na Br.
This question has multiple correct options
A. \( H_{2} S O_{4} \) cannot react with \( N a B r \)
B. \( H B r \) cannot be prepared by the action of \( H_{2} S O_{4} \) on \( _{N a B r} \)
c. \( H_{2} S O_{4} \) oxidises \( H B r \) to form \( B r_{2} \)
D. \( S O_{2} \) gas is evolved
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{M} \boldsymbol{g}-\boldsymbol{B r}+\boldsymbol{C O}_{2} \rightarrow \boldsymbol{X} \stackrel{\boldsymbol{H}_{3} \boldsymbol{O} \oplus}{\longrightarrow} \)
\( Y \) In this reaction Y is :
\( \mathbf{A} \cdot H C O O H \)
в. \( C H_{3} \) СООН
с. \( C_{2} H_{5} \)СООН
D. \( H C H O \)
Subject: Physics
The series combination of two batteries,
both of the same emf \( 10 V \), but different
internal resistance of \( 20 \Omega \) and \( 5 \Omega \), is
connected to the parallel combination of two resistors \( 30 \Omega \) and \( R \Omega \). The
voltage difference across the battery of internal resistance \( 20 \Omega \) is zero, the
value of \( R\left(\text { in } \Omega \text { is }_{-}-\dots\right. \)
Subject: Maths
\( f\left(m^{2} \cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15} \cos \frac{14 \pi}{15}=n^{2}\right. \)
then find the value of \( \frac{m^{2}-n^{2}}{n^{2}} \)
Subject: Chemistry
For gaseous reaction, the rate is often expressed in terms of dP/dt instead of dc/dt or dn/dt (where c is the
concentration and \( n \) the number of mol)
What is the relation among these three expressions?
A \( \cdot \frac{d c}{d t}=\frac{1}{V}\left(\frac{d n}{d t}\right)=\frac{1}{R T}\left(\frac{d P}{d t}\right) \)
в. \( \frac{d c}{d t}=\left(\frac{d n}{d t}\right)=\left(\frac{d P}{d t}\right) \)
\( ^{\mathbf{c}} \cdot \frac{d c}{d t}=\left(\frac{d n}{d t}\right)=\frac{V}{R T}\left(\frac{d P}{d t}\right) \)
D. None of these
Subject: Physics
If the ratio of lengths, radii and Young's modulus of steel and brass wires shown
in the figure are \( a, b \) and \( c \) respectively, the ratio between the increase in
lengths of brass and steel wires would
be :
A \( \cdot \frac{b^{2}}{2 c} \)
в. \( \frac{b c}{2 a^{2}} \)
\( c \cdot \frac{b a^{2}}{2 c} \)
D. \( \frac{2 b^{2} c}{a} \)
Subject: Chemistry
Wilkinson catalyst is:
\( \mathbf{A} \cdot\left[\left(P h_{3} P\right)_{3} R h C l\right]\left(E t=C_{2} H_{5}\right) \)
\( \mathbf{B} \cdot\left[E t_{3} P\right)_{3} I r C l \)
\( \mathbf{c} \cdot\left[E t_{3} P\right)_{3} R h C l \)
\( \mathbf{D} \cdot\left[P h_{3} P\right)_{3} I e C l \)
Subject: Physics
\( A \) block \( X \) kept on an inclined surface
just begins to slide, if the inclination is
\( \boldsymbol{\theta}_{1} . \) The block is replaced by another block \( Y \) and it is found that it just
begins to slide, if the inclination \( \theta_{2} \) if
\( \boldsymbol{\theta}_{2}>\boldsymbol{\theta}_{1} \) ). Then
A. Mass of \( x= \) mass of \( Y \)
B. Mass of \( x< \) mass of \( Y \)
c. Mass of \( x> \) mass of \( Y \)
D. All the above three options are possible
Subject: Chemistry
Question below refers to the
overall reaction and half-reactions with
standard reduction potentials below. \( 2 F e^{2+}+C l_{2} \rightarrow 2 F e^{3+}+2 C l ? \)
\( \boldsymbol{F e}^{3+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{F} e^{2+} ; \boldsymbol{E}_{r e d}^{o}=0.77 \) volts
\( C l_{2}+2 e^{-} \rightarrow 2 C l^{-} ; E_{r e d}^{o}=1.36 \) volts
Find the overall potential for the reaction?
A. 0.18 volt
B. 0.59 volts
c. \( 1.05 v o l t s \)
D. 2.13voolt
E. 2.90volts
Subject: Maths
Draw a frequency polygon of the following data using histogram.
\( \begin{array}{llll}\text { class } & \mathbf{0}- & \mathbf{1 0}- & \mathbf{2 0}- \\ \text { interval } & \mathbf{1 0} & \mathbf{2 0} & \mathbf{3 0}\end{array} \) 一年
Frequency 5
10
25
Subject: Physics
Current is flowing with a current density \( J=480 \) amp \( / \mathrm{cm}^{2} \) in a copper
wire. Assuming that each copper atom contribution one free electron and gives that Avogadro number \( =\mathbf{6 . 0} \times \)
\( 10^{23} \) atoms/mole Density of copper \( = \)
\( 9.0 g / c m^{3} . \) Atomic weight of copper \( = \)
\( 64 g / \) mole Electronic charge \( =1.6 \times \)
\( 10^{-19} \) coulomb. The drift velocity of
electrons is:
\( \mathbf{A} \cdot 1 \mathrm{mm} / \mathrm{s} \)
B. \( 2 \mathrm{mm} / \mathrm{s} \)
c. \( 0.5 \mathrm{mm} / \mathrm{s} \)
D. \( 0.36 \mathrm{mm} / \mathrm{s} \)
Subject: Physics
\( ^{200} \boldsymbol{X} \rightarrow^{110} \boldsymbol{A}+^{90} \boldsymbol{B}+\boldsymbol{E} \boldsymbol{n} e \boldsymbol{r} \boldsymbol{g} \boldsymbol{y} \)
If the binding energy per nucleon for \( X, A \) and \( B \) are \( 7.4 \mathrm{MeV}, 8.2 \mathrm{MeV} \) and
8.2 MeV respectively, the minimum
energy required to bring in this reaction will be :
A. 90 Mev
B. 100 MeV
c. 120 Mev
D. 160 Mev
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\tan ^{-1}\left(\frac{\boldsymbol{a}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{a} \boldsymbol{x}}\right)\right) \) equals if \( \mathbf{a x}>-1 \)
\( \mathbf{A} \cdot \frac{a}{1+x^{2}} \)
B. \( \frac{1}{1+x^{2}} \)
C \( \cdot-\frac{a}{1+x^{2}} \)
D. \( -\frac{1}{1+x^{2}} \)
Subject: Maths
If \( a_{r}>0, r \epsilon N \) and \( a_{1}, a_{2}, a_{3}, \dots, a_{2 n} \) are in
AP then
\( \frac{\boldsymbol{a}_{1}+\boldsymbol{a}_{2 n}}{\sqrt{\boldsymbol{a}_{1}}+\sqrt{\boldsymbol{a}_{2}}}+\frac{\boldsymbol{a}_{2}+\boldsymbol{a}_{2 n-1}}{\sqrt{\boldsymbol{a}_{2}}+\sqrt{\boldsymbol{a}_{3}}}+ \)
\( \frac{\boldsymbol{a}_{\boldsymbol{3}}+\boldsymbol{a}_{\boldsymbol{2} \boldsymbol{n}-\boldsymbol{2}}}{\sqrt{\boldsymbol{a}_{\boldsymbol{3}}}+\sqrt{\boldsymbol{a}_{\boldsymbol{4}}}}+\ldots+\frac{\boldsymbol{a}_{\boldsymbol{n}}+\boldsymbol{a}_{\boldsymbol{n}+1}}{\sqrt{\boldsymbol{a}_{\boldsymbol{n}}}+\sqrt{\boldsymbol{a}_{\boldsymbol{n}+\mathbf{1}}}} \)
is equal to
A . n-
B. \( \frac{n\left(a_{1}+a_{2 n}\right)}{\sqrt{a_{1}}+\sqrt{a_{n+1}}} \)
c. \( \frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n+1}}} \)
D. none of these
Subject: Physics
Figure shows a meter bridge (which is nothing but a practical Wheatstone bridge), consisting of two resistors \( X \)
and Y together in parallel with a meter long constantan wire of uniform cross
section. Which the help of a movable
contact \( \mathrm{D} \), one can change the ratio of resistance of the two segments of the
wire until a sensitive galvanometer \( G \)
connected across B and D shows no
deflection. The null point is found to be a distance of \( 33.7 \mathrm{cm} . \) The resistor Y is
shunted by a resistance of \( 12 \omega, \) and the null point is found to shift by a distance of \( 18.2 \mathrm{cm} . \) Determine the approximate resistance of \( X \) and \( Y \) in ohm.
Subject: Chemistry
An element along with its atomic
number and mass number is represented as \( _{Z} X^{A} \) where \( X \) is the symbol of the element, \( Z \) is the atomic
number and \( A \) is the mass number.

Represent elements \( A, B, C, D \) and \( E \) with its atomic number and mass number
from the given data.
of \( \begin{array}{lll}\text { Elements } & \begin{array}{l}\text { Number } \\ \text { of } \\ \text { protons }\end{array} & \begin{array}{l}\text { Number } \\ \text { of } \\ \text { electrons }\end{array}\end{array} \) \( e \)
\( B \)
\( \mathrm{m} \)
\( E \)
Subject: Chemistry
In black and white photography, the developed film is fixed by washing with hypo solution which dissolves the under
composed \( A g B r \) to form a complex ion formed is:
\( A \cdot\left[A g\left(S_{2} O_{3}\right)_{2}\right]^{2} \)
B . \( \left[A g\left(S_{2} O_{3}\right)_{2}\right]^{3} \)
c. \( \left[A g\left(S_{2} O_{3}\right)_{2}\right] \)
D. none of these
Subject: Maths
The function \( \boldsymbol{f}:(-\infty,-1) \rightarrow\left(\mathbf{0}, e^{5}\right] \)
defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2}} \) is
A. many-one and onto
B. many-one and into
c. one-one and onto
D. one-one and into
Subject: Chemistry
Which of the following statements
is/are correct?
This question has multiple correct options
A. Nitroprusside ion is \( \left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NO}\right]^{2-} \)
B. Nitroprusside ion is \( \left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right]^{2-} \)
C. Prussian blue and Tumbull's blue, respectively, are \( F e_{4}\left[F e(C N)_{6}\right]_{3} \) and \( F e_{3}\left[F e(C N)_{6}\right]_{2} \)
D. Prussian blue and Thmbull's blue, respectively, are \( F e_{3}\left[F e(C N)_{6}\right]_{2} \) and \( F e_{4}\left[F e(C N)_{6}\right]_{3} \)
Subject: Physics
The surface of a metal is illuminated
with the light of 400 nm. The kinetic energy of the ejected photoelectrons
was found to be \( 1.68 \mathrm{eV} \). The work
function of the metal is :
\( (h c=1240 \mathrm{eV} . n m) \)
A . \( 3.09 \mathrm{eV} \)
в. \( 1.41 \mathrm{eV} \)
c. \( 1.51 \mathrm{eV} \)
D. \( 1.68 \mathrm{eV} \)
Subject: Physics
Two elastic bodies \( P \) and \( Q \) having equal masses are moving along the same line with velocities of \( 16 \mathrm{m} / \mathrm{s} \) and \( 10 \mathrm{m} / \mathrm{s} \)
respectively. Their velocities after the elastic collision will be in \( \mathrm{m} / \mathrm{s} \)
A. 0 and 25
B. 5 and 20
c. 10 and 16
D. 20 and 5
Subject: Maths
Let \( a_{1}, a_{2}, \dots \) be positive real numbers in geometric progression. For each \( n \), let
\( A_{n}, G_{n}, H_{a} \) be respectively, the arithmetic mean, geometric mean and
harmonic mean of \( a_{1}, a_{2}, \dots, a_{n} . \) Find an
expression for the geometric mean of
\( G_{1}, G_{2}, \ldots, G_{n} \) in terms of
\( \boldsymbol{A}_{1}, \boldsymbol{A}_{2}, \ldots ., \boldsymbol{A}_{n}, \boldsymbol{H}_{1}, \boldsymbol{H}_{2}, \ldots . ., \boldsymbol{H}_{n} \)
Subject: Physics
If \( F_{g} \) and \( F_{e} \) are gravitational and electrostatic forces between two
electrons at a distance \( 0.1 m \) then
\( \boldsymbol{F}_{\boldsymbol{g}} / \boldsymbol{F}_{e} \) is in the order of
A \( \cdot 10^{43} \)
B . \( 10^{-43} \)
\( \mathbf{c} \cdot 10^{35} \)
D. \( 10^{-35} \)
Subject: Chemistry
What amount of heat energy (kJ) is released in the combustion of 12.0 g of
\[
\begin{array}{l}
C_{3} H_{4} ? \\
C_{3} H_{4}(g)+4 O_{2}(g) \rightarrow 3 C O_{2}(g)+
\end{array}
\]
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \quad \boldsymbol{\Delta} \boldsymbol{H}^{\circ}=-\mathbf{1} \mathbf{9} \mathbf{3} \mathbf{9} . \mathbf{1} \boldsymbol{k} \boldsymbol{J} \)
[Atomic weights: \( C=12.01, H=1.008,0= \)
16.00]
A. 725
B. 504
c. 783
D. 581
Subject: Physics
Energy gaps between the highest band and the lowest empty bands in elements \( A, B, C \) and \( D \) are 0,70,530 and \( 90 k J m o l^{-1} . \) Then
A. element A is metal
B. element C is insulator
c. element B and D can be semiconductors
D. all are correct conclusion about elements A, B, C and D
Subject: Chemistry
\( \triangle U^{\theta} \) of combustion of methane is \( -x \) k
mol \( ^{-1} \). The value of \( \triangle \boldsymbol{H}^{\boldsymbol{\theta}} \) is:
\( \mathbf{A} \cdot=\Delta U^{\theta} \)
в. \( <\Delta U^{\theta} \)
c. zero
\( \mathrm{D} \cdot>\Delta U^{\theta} \)
Subject: Maths
\( X, Y, Z, U \) are four points in a straight
line. If distance from \( X \) to \( Y \) is \( 15, Y \) to
\( Z \) is \( 5, Z \) to \( U \) is 8 and \( X \) to \( U \) is \( 2, \) what
is the correct sequence of the points?
A. \( X-Y-Z-U \)
в. \( X-Z-Y-U \)
c. \( X-U-Z-Y \)
D. \( X-Z-U-Y \)
Subject: Chemistry
How much energy is required to change
\( 2 K g \) of ice at \( 0^{0} C \) into water at \( 20^{0} C ? \)
(specific latent of heat of fusion of
water \( =3,34,000 J / K g, \) specific heat capacity of water \( =4200 J K g^{-1} K^{-1} \) ).
Subject: Physics
An object of mass 40 kg having velocity \( 4 \hat{\text { ì }} m / s \) collides with another objects of mass 40 kg having velocity \( 3 \hat{i} \). If the collision is perfectly inelastic, then the loss of mechanical energy.
\( A \). \( 250 J \)
B. 100
c. 125
D. 35 J
Subject: Maths
\( \int e^{x}\left[\log (\cosh x)-\operatorname{sech}^{2} x\right] d x= \)
A \( \cdot e^{x}(\log \cosh x-\tanh x)+c \)
B. \( e^{x} \log \cosh x+c \)
c. \( -e^{x} \tanh x+c \)
D. \( e^{x}(\log \cosh x+\tanh x)+c \)
Subject: Physics
In an SHM, restoring force is \( \boldsymbol{F}=-\boldsymbol{k} \boldsymbol{x} \)
where \( k \) is force constant, \( x \) is
displacement and \( A \) is the amplitude of motion, then the total energy depends
upon
A. \( k, A \) and \( M \)
в. \( k, x, M \)
\( c \cdot k, A \)
D. \( k, x \)
Subject: Maths
The expansion \( \left[\boldsymbol{x}+\left(\boldsymbol{x}^{\mathbf{3}}-\mathbf{1}\right)^{\mathbf{1} / \mathbf{2}}\right]^{\mathbf{5}}+[\boldsymbol{x}- \)
\( \left.\left(x^{3}-1\right)^{1 / 2}\right]^{5} \) is a polynomial of degree
A. 5
B. 6
\( c \cdot 7 \)
\( D \)
Subject: Physics
A car of mass \( 100 \mathrm{kg} \) moves on a circular track of radius \( 20 \mathrm{m} \). If the coefficient of friction is \( 0.64, \) then the maximum
velocity with which the car can move is
A. \( 22.4 \mathrm{m} / \mathrm{s} \)
B. \( 5.6 \mathrm{m} / \mathrm{s} \)
c. \( 11.3 \mathrm{m} / \mathrm{s} \)
D. 20 \( \mathrm{m} / \mathrm{s} \)
Subject: Maths
\( \cos \frac{\pi}{7}+\cos \frac{2 \pi}{7}+\cos \frac{3 \pi}{7}+\cos \frac{4 \pi}{7}+ \)
\( \cos \frac{5 \pi}{7}+\cos \frac{6 \pi}{7}+\cos \frac{7 \pi}{7}= \)
\( A \)
в.
c.
D.
Subject: Maths
Which of the following is/are the value of \( \cos \left[\frac{1}{2} \cos ^{-1}\left(\cos \left(-\frac{14 \pi}{5}\right)\right)\right] ? \)
This question has multiple correct options
A \( \cdot \cos \left(-\frac{7 \pi}{5}\right) \)
B \cdot \( \sin \left(\frac{\pi}{10}\right) \)
c. \( \cos \left(\frac{2 \pi}{5}\right) \)
D. \( \cos \left(-\frac{3 \pi}{5}\right) \)
Subject: Maths
Observe the following patterns \( \mathbf{1}=\frac{\mathbf{1}}{\mathbf{2}}(\mathbf{1} \times(\mathbf{1}+\mathbf{1})) \)
\( \mathbf{1}+\mathbf{2}=\frac{\mathbf{1}}{\mathbf{2}}(\mathbf{2} \times(\mathbf{2}+\mathbf{1})) \)
\( \mathbf{1}+\mathbf{2}+\mathbf{3}=\frac{\mathbf{1}}{\mathbf{2}}(\mathbf{3} \times(\mathbf{3}+\mathbf{1})) \)
\( \mathbf{1}+\mathbf{2}+\mathbf{3}+\mathbf{4}=\frac{\mathbf{1}}{\mathbf{2}}(\mathbf{4} \times(\mathbf{4}+\mathbf{1})) \)
and find the value of each of the
following
\[
\mathbf{1}+\mathbf{2}+\mathbf{3}+\mathbf{4}+\mathbf{5}+\ldots+\mathbf{5 0}
\]
Subject: Maths
The rational number of the form \( \frac{p}{q}, q \neq \) \( 0, p \) and \( q \) are positive integers, which represents \( 0.1 \overline{34} \) i.e., \( (0.1343434 \ldots . .) \) is
A \( \cdot \frac{134}{999} \)
в. \( \frac{134}{990} \)
c. \( \frac{133}{999} \)
D. \( \frac{133}{990} \)
Subject: Chemistry
For the Paschen series the value of \( n_{1} \)
and \( n_{2} \) in the expression \( \Delta E=R_{H} \times \) \( c\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right] \) is:
A \( \cdot n_{1}=1, n_{2}=2,3,4 \)
в. \( n_{1}=2, n_{2}=3,4,5 \dots \)
c. \( n_{1}=3, n_{2}=4,5,6 \)
D. \( n_{1}=4, n_{2}=5,6,7 \)
Subject: Chemistry
State the IUPAC names of the following compounds:
(i) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
(ii) \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{O} \boldsymbol{O} \boldsymbol{H} \)
(iii) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \)
Subject: Maths
The equation of the plane passing through the intersection of the planes \( \mathbf{3} \boldsymbol{x}-\boldsymbol{y}+\mathbf{2} \boldsymbol{z}-\mathbf{4}=\mathbf{0} \) and \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}- \)
\( \mathbf{2}=\mathbf{0} \) and passing through the point
\( A(2,2,1) \) is given by?
A. \( 7 x+5 y-4 z-8=0 \)
в. \( 7 x-5 y+4 z-8=0 \)
c. \( 5 x-7 y+4 z-8=0 \)
D. \( 5 x+7 y-4 z+8=0 \)
Subject: Maths
Let \( * \) be a binary operation on the set of all non zero real numbers, given by \( a * \)
\( \boldsymbol{b}=\frac{\boldsymbol{a} \boldsymbol{b}}{\mathbf{5}} \forall \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{R}-\{\mathbf{0}\}, \) find the value of
\( x, \) given that \( 2 *(x * 5)=10 \)
Subject: Maths
If the base of a parallelogram is \( (x+4) \)
altitude to the base is \( (x-3) \) and the
area is \( \left(x^{2}-4\right), \) then what is the actual
area equal to?
A. 60 sq units
B. 45 sq units
c. 77 sq units
D. 96 sq units
Subject: Physics
A student connects four cells, each of internal resistance \( \frac{1}{4} \Omega, \) in series. One of the cells is incorrectly connected because its terminals are reversed. The
value of external resistance is \( 1 \Omega . \) If the
emf of each cell is 1.5 volt then current
in the circuit will be
A \( \cdot \frac{4}{3} A \)
B. 0
c. \( \frac{3}{4} \)
D. \( 1.5 A \)
Subject: Physics
A particle of mass \( \mathrm{M} \) is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the
centre will be :
\( A \cdot \frac{G M}{a} \)
B. \( \frac{2 G M}{a} \)
\( \mathrm{c} \cdot \frac{3 G M}{a} \)
D. \( \frac{4 G M}{a} \)
Subject: Chemistry
Arrange the following species in order of increasing stability: \( \boldsymbol{L} \boldsymbol{i}_{2}, \boldsymbol{L} \boldsymbol{i}_{2}^{+}, \boldsymbol{L} \boldsymbol{i}_{2} \)
A \( \cdot L i_{2}^{+}<L i_{2}^{-}<L i_{2} \)
c. \( L i_{2}<L i_{2}^{+}=L i_{2} \)
D. \( L i_{2}^{+}=L i_{2}^{-}<L i_{2} \)
Subject: Physics
If the particle moves from \( A \) to \( B \) as
shown in figure, then the ratio of displacement to distance covered by particle is (if \( \mathrm{R} \) is the radius of track)
\( A \cdot \frac{2 \sqrt{2}}{3 \pi} \)
в. \( \frac{3 \pi}{2 \sqrt{2}} \)
c. \( \frac{\pi}{\sqrt{2}} \)
D. \( \frac{\pi}{2 \sqrt{2}} \)
Subject: Physics
A parallel plate capacitor of capacitance \( C \) is connected to a battery and is charge to a potential difference
\( V . \) Another capacitor of capacitor \( 2 C \) is similarly charged to a potential
difference \( 2 V . \) The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is:
A . zero
B \( \cdot(3 / 2) C V^{2} \)
\( \mathbf{c} \cdot 25 / 6 C V^{2} \)
\( \mathbf{D} \cdot(9 / 2) C V^{2} \)
Subject: Physics
A gun is mounted on a railroad car. The
mass of the car, the gun, the shells and
the operator is \( 50 \mathrm{m} \) where \( \mathrm{m} \) is the mass of the one shell. If the muzzle
velocity of shell is \( 200 \mathrm{m} / \mathrm{s} \), what is recoil speed of car after second shot?
A \( \cdot \frac{200}{49} \mathrm{m} / \mathrm{s} \)
в. \( 200\left(\frac{1}{48}+\frac{1}{48}\right) \mathrm{m} / \mathrm{s} \)
\( ^{\mathrm{c}} \cdot_{200}\left(\frac{1}{48}+\frac{1}{49}\right) \mathrm{m} / \mathrm{s} \)
D. \( 200\left(\frac{1}{48}+\frac{1}{48 \times 49}\right) \mathrm{m} / \mathrm{s} \)
Subject: Biology
Fermentation products of yeast are
\( \mathbf{A} \cdot \mathrm{H}_{2} \mathrm{O}+\mathrm{C} \mathrm{O}_{2} \)
B. Methyl alcohol \( +\mathrm{CO}_{2} \)
C. Methyl alcohol + Water
D. Ethyl alcohol \( +\mathrm{CO}_{2} \)
Subject: Physics
The minimum and maximum speeds
are
\( ^{\mathbf{A}} \cdot \sqrt{\frac{G M}{9 R}}, \sqrt{\frac{2 G M}{R}} \)
в. \( \sqrt{\frac{G M}{5 R}}, \sqrt{\frac{3 G M}{2 R}} \)
c. \( \sqrt{\frac{G M}{6 R}}, \sqrt{\frac{2 G M}{3 R}} \)
D. \( \sqrt{\frac{G M}{3 R}}, \sqrt{\frac{5 G M}{2 R}} \)
Subject: Chemistry
At constant temperature, the
equilibrium constant \( \left(\boldsymbol{K}_{\boldsymbol{p}}\right) \) for the
decomposition reaction. \( N_{2} O_{4} \rightleftharpoons \)
\( 2 N O_{2} \) is expressed by
\[
\begin{array}{c}
\boldsymbol{K}_{\boldsymbol{p}}=\frac{\left(\boldsymbol{4} \boldsymbol{x}^{2} \boldsymbol{P}\right)}{\left(\mathbf{1}-\boldsymbol{x}^{2}\right)} \\
\text { where, } \boldsymbol{P}=\text { pressure, } \boldsymbol{x} \text { =extent of }
\end{array}
\]
decomposition. Which of the following
statements is true?
\( \mathbf{A} \cdot K_{p} \) increases with increase of \( P \)
B. \( K_{p} \) increases with increase of \( x \)
C. \( K_{p} \) increases with decrease of \( x \)
D. \( K_{p} \) remains constant with change in \( P \) and \( x \) decreases with pressure
Subject: Maths
\( \boldsymbol{n} \stackrel{\boldsymbol{L} t}{\rightarrow} \infty\left[\frac{\boldsymbol{1}^{3}}{\boldsymbol{n}^{4}+\boldsymbol{1}^{4}}+\frac{\boldsymbol{2}^{\boldsymbol{3}}}{\boldsymbol{n}^{4}+\mathbf{2}^{4}}+\ldots+\right. \)
\( \left.\frac{\mathbf{1}}{\boldsymbol{2} \boldsymbol{n}}\right]= \)
A. \( \frac{1}{4} \log 4 \)
B. \( \frac{1}{2} \log 2 \)
c. \( \frac{1}{4} \log 3 \)
D. \( \frac{1}{4} \log 2 \)
Subject: Physics
A long solenoid has 200 turns per cm
and carries a current I. The magnetic field at its centre is \( 6.28 \times \)
\( 10^{-2} W b / m^{2} . \) Another long solenoid has
100 turns per \( \mathrm{cm} \) and it carries a
current i/3. The value of the magnetic
field at its centre is
A \( \cdot 1.05 \times 10^{-2} \mathrm{Wb} / \mathrm{m}^{2} \)
B . \( 1.05 \times 10^{-5} \mathrm{Wb} / \mathrm{m}^{2} \)
c. \( 1.05 \times 10^{-3} \mathrm{Wb} / \mathrm{m}^{2} \)
D. \( 1.05 \times 10^{-4} \mathrm{Wb} / \mathrm{m}^{2} \)
Subject: Chemistry
The two equilibria \( A B \rightleftharpoons A^{+}+B^{-} \) and
\( A B+B^{-} \rightleftharpoons A B_{2}^{-} \) are simultaneously
maintained in a solution with
equilibrium constants, \( \boldsymbol{K}_{1} \) and \( \boldsymbol{K}_{2} \)
respectively. The ratio of \( \boldsymbol{A}^{+} \) to \( \boldsymbol{A} \boldsymbol{B}_{\mathbf{2}}^{-} \) in the solution is:
A. directly proportional to the concentration of \( B \)
B . inversely proportional to the concentration of \( B \)
c. directly proportional to the square of the concentration of \( B^{-} \)
D. inversely proportional to the square of the concentration of \( B \)
Subject: Maths
The intercept on x-axis made by tangent to the curve, \( y=\int_{0}^{x}|t| d t, x \in R, \) which
are parallel to the line \( y=2 x, \) are equal
to
A . ±1
B. ±2
\( c .\pm 3 \)
\( \mathrm{D} \cdot \pm 4 \)
Subject: Physics
One mole of an ideal gas in initial state
A undergoes a cyclic process \( A B C A, \) as
shown in the figure. Its pressure at \( A \) is
\( P_{0} . \) Choose the correct option(s) from
the following.
This question has multiple correct options
A. Internal energies at A and B are the same
B. Work done by the gas in process AB is \( P_{o} V_{o} \) In 4
c. pressure at \( c \) is \( \frac{P_{o}}{4} \)
D temperature at \( C \) is \( \frac{T_{o}}{4} \)