AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A resistance of \( R \Omega \) draws a current from
a potentiometer. The potentiometer has a
total resistance \( R_{0} \Omega . \) A voltage V is
supplied to the potentiometer. The
voltage across \( \mathrm{R} \) when the sliding contact
is in the middle of the potentiometer is:
A \( \cdot \frac{2 V R}{4 R_{0}+R} \)
В. \( \frac{4 V R}{R_{0}+R} \)
\( \mathbf{c} \cdot \frac{V R}{R_{0}+4 R} \)
D. \( \frac{2 V R}{R_{0}+4 R} \)
Subject: Maths
Let \( a, b \) and \( c \) be non-zero vectors such
that no two are collinear and \( (a \times b) \times \) \( c=\frac{1}{3}|b||c| a . \) If \( \theta \) is the acute angle
between the vectors b and \( c, \) then \( \sin \theta \)
equals
A \( \cdot \frac{2 \sqrt{2}}{3} \)
B. \( \frac{\sqrt{2}}{3} \)
\( c \cdot \frac{2}{3} \)
D.
Subject: Physics
A current I flows in a rectangularly shaped wire whose center lies at
\( \left(x_{0}, 0,0\right) \) and whose vertices are located
at the point \( \boldsymbol{A}\left(\boldsymbol{x}_{0}+\boldsymbol{d},-\boldsymbol{a},-\boldsymbol{b}\right), \boldsymbol{B}\left(\boldsymbol{x}_{0}-\right. \)
\( \boldsymbol{d}, \boldsymbol{a},-\boldsymbol{b}), \boldsymbol{C}\left(\boldsymbol{x}_{0}-\boldsymbol{d}, \boldsymbol{a}, \boldsymbol{+} \boldsymbol{b}\right), \) and \( \boldsymbol{D}\left(\boldsymbol{x}_{0}+\right. \)
\( \boldsymbol{d},-\boldsymbol{a},+\boldsymbol{b}) \) respectively. Assume that \( \mathbf{a} \)
b, \( d<<x_{0} \). Find the magnitude of
magnetic dipole moment vector of the rectangular wire frame in J/T. (Given:
\( \boldsymbol{b}=\mathbf{1 0 m}, \boldsymbol{I}=\mathbf{0 . 0 1 A}, \boldsymbol{d}=\mathbf{4 m}, \boldsymbol{a}=\mathbf{3 m .} \)
Subject: Physics
A body of mass 5 kg rests on a rough horizontal surface of friction coefficient
0.2. The is pulled through a distance 10
\( \mathrm{m} \) by a horizontal force of \( 25 N . \) The kinetic energy acquired by it is
A . \( 200 J \)
в. \( 150 J \)
\( c \cdot 100 J \)
D. \( 50 J \)
Subject: Maths
If vertices of a triangle are represented
by complex numbers \( z, i z, z+i z, \) then
area of triangle is
\( A \cdot|z|^{2} \)
B. \( \frac{1}{2}|z|^{2} \)
c \( \cdot 2|z|^{3} \)
D・ \( 3|z|^{2} \)
Subject: Maths
If \( \boldsymbol{a}=\boldsymbol{x} \boldsymbol{i}+(\boldsymbol{x}-\mathbf{1}) \boldsymbol{j}+\boldsymbol{k} \) and \( \boldsymbol{b}=(\boldsymbol{x}+ \)
1) \( i+j+a k \) always make an acute
angle with each other for every value of
\( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}, \) then
A \( . a \epsilon(-\infty, 2) \)
В. \( a \epsilon(2,-\infty) \)
c. \( a \epsilon(-\infty, 1) \)
D. \( a \epsilon(1,-\infty) \)
Subject: Physics
The quantity of heat flowing for \( 10 s \) through a rod of length \( 40 \mathrm{cm}, \) area
\( 50 \mathrm{cm}^{2} \) is \( 200 \mathrm{J} \). If the temperature
difference at the ends of the rod is \( 80^{\circ} \mathrm{C} \)
the coefficient of thermal conductivity of the rod in \( \mathrm{Wm}^{-1} \mathrm{K}^{-1} \) is:
A . 20
B. 60
c. 80
D. 120
Subject: Physics
Assertion (A) : Two systems which are in thermal equilibrium with a third system, are in thermal equilibrium with each other.

Reason (R) : The heat flows always from a system at higher temperature to a system at a lower temperature.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
c. Assertion is true but Reason is false
D. Both Assertion and Reason are false
Subject: Chemistry
\( \Delta H_{f}^{o} \) of \( N_{2} O \) is \( 82 k J / m o l \) and bond
energy for \( N_{2}, N=N, O=O \) and
\( N=O \) bonds are 946,418,498 and
\( 607 k J / \) mol respectively. Resonance
energy of \( N_{2} O \) is:
A. \( -170 k J / m o l \)
в. \( -252 k J / m o l \)
c. \( -88 k J / m o l \)
D. \( -1195 k J / \) mol
Subject: Chemistry
Hybridization and structure of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) is:
A \( \cdot s p^{3} d \), triogonal bipyramidal
B \( \cdot s p^{3} \), tetrahedral
c. \( s p^{3} d^{2} \), square planar
D. \( s p^{3} d^{2} \), hexagonal
Subject: Physics
topp
Q Type your question
are arranged in 100 rows, each row stretching horizontally along the body of
the fish containing 5000 electroplaques. The arrangement is suggestively shown below. Each
electroplaques has an emf of 0.15 V and
internal resistance of \( 0.25 \Omega . \) The water
surrounding the Eel completes a circuit between the head and its tail. If the
water surrounding it has a resistance of
\( 500 \Omega, \) the current an Eel can produce in
water is about :
\( A \cdot 1.5 \mathrm{A} \)
в. 3.0 А
\( c \cdot 15 \)
0.30
Subject: Maths
The vector equation \( \boldsymbol{r}=\boldsymbol{i}-\boldsymbol{2} \boldsymbol{j}-\boldsymbol{k}+ \)
\( t(6 j-k) \) represents a straight line
passing through the points:
A. (0,6,-1) and (1,-2,-1)
в. (0,6,-1) and (-1,-4,-2)
c. (1,-2,-1) and (1,4,-2)
D. (1,-2,-1) and (0,-6,1)
Subject: Chemistry
Mixture of conc. \( \mathbf{H} \mathbf{N} \mathbf{O}_{3} \) and conc.
\( \mathbf{H}_{2} \mathbf{S} \mathbf{O}_{4} \) is known as :
A. Sulphonating mixture
B. Nitrating mixture
c. Explosion mixture
D. Fusion mixture
Subject: Chemistry
t-butyl methyl ether on reaction with
anhydrous \( H I \) gives an alcohol \( (A) \) and
halide (B). Which of the following
statement is correct?

This question has multiple correct options
A. Alcohol (A) performs Lucas test immediately at room temperature
B. Halide
(B) undergoes \( S_{N} 1 \) reaction most readily
C. Alcohol (A) on heating with copper gives formaldehyde
D. Halide
(B) on reaction with \( K C N \) undergoes \( S_{N} 2 \) reaction
Subject: Physics
Work function of three metals \( A, B, C \) are
\( 4.5 \mathrm{eV}, 4.3 \mathrm{eV} ., 3.5 \) ev respectively. If a light of wavelength 4000 A is incident on the metals, then
A. photoelectron are emitted from \( c \)
B. photoelectrons are emitted from A
c. photoelectrons are emitted from B
D. photoelectron will not emitted from all the surfaces
Subject: Maths
The least vlue of the function \( f(x)= \) \( \boldsymbol{a x}+\frac{\boldsymbol{b}}{\boldsymbol{x}}(\boldsymbol{a}>\mathbf{0}, \boldsymbol{b}>\mathbf{0}, \boldsymbol{x}>\mathbf{0}) \) is
Subject: Maths
If \( a b c=1, \) then \( \frac{1}{1+a+b^{-1}}+ \)
\( \frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}} \) is equal to
\( A \)
B. 0
\( c \)
D. - 5
Subject: Maths
Let \( x=\sin 1^{\circ}, \) then the value of the
\( \operatorname{expression} \frac{1}{\cos 0^{\circ} \cdot \cos 1^{\circ}}+ \)
\( \frac{1}{\cos 1^{\circ} \cdot \cos 2^{\circ}}+\frac{1}{\cos 2^{\circ} \cdot \cos 3^{\circ}}+\dots+ \)
\( \frac{1}{\cos 44^{\circ} \cdot \cos 45^{\circ}} \) is equal to
A . \( x \)
в. \( \frac{1}{x} \)
\( c \cdot \frac{\sqrt{2}}{x} \)
D. \( \frac{x}{\sqrt{2}} \)
Subject: Physics
The grid voltage of any triode valve is changed from -1 volt to -3 volt and the mutual conductance is \( 3 \times 10^{-4} \) mho.
The change in plate circuit current will be
A. \( 0.8 \mathrm{mA} \)
B. \( 0.6 \mathrm{mA} \)
c. \( 0.4 \mathrm{mA} \)
D. \( 1 \mathrm{m} \)
Subject: Chemistry
There is a transition from \( n=1 \) to \( n=2 \)
and then \( n=2 \) to \( n=3, \) then:
A. \( \Delta E \) values as well as frequency are additive
B. wave length as well as frequency are additive
c. \( \Delta E \) values as well as wavelength are additive
D. all of the parameters, \( (\Delta E, \) frequency and wave length are additive
Subject: Chemistry
\( C l_{2} \) gas is passed into aqueous
solution of KBr and KI and \( C H C l_{3} \)
added . It is observed that there is:
A. violet colour in \( C H C l_{3} \) layer
B. yellow colour in \( C H C l_{3} \) layer
c. yellow colour in aqueous layer
D. violet colour in aqueous layer
Subject: Physics
The internal resistance of a cell of emf 2
V is \( 0.1 \pi \). If it is connected to a
resistance of \( 3.9 \pi, \) then the voltage across the cell will be (in volts)
A \( .2 v \)
B. \( 0.5 v \)
c. \( 1.95 v \)
D. 2.5v
Subject: Chemistry
A reaction system in equilibrium
according to reaction \( 2 S O_{2}(g)+ \)
\( O_{2}(g) \rightarrow 2 S O_{3}(g)(k=5) \) in one litre
vessel at a given temperature was
found to be 0.12 mole each of \( S O_{2} \) and
\( \boldsymbol{S} \boldsymbol{O}_{3} \) and 5 mole of of \( \boldsymbol{O}_{2} \) must be added
to this vessel to order that at
equilibrium \( 20 \% \) of \( S O_{2} \) is oxidized to
\( S O_{3} . \) Find out the mass of oxygen formed?
A. \( 0.41245 \mathrm{g} \)
B. \( 11.6 g \)
c. \( 1.6 g \)
D. None of these.
Subject: Physics
The total momentum of electrons in a
straight wire of length \( l=1000 m \)
carrying a current \( \mathrm{I}=\mathbf{7} \mathbf{0} \boldsymbol{A}, \) will be (in
\( N-s) \)
A . \( 0.40 \times 10^{-6} \)
B. \( 0.20 \times 10^{-6} \)
c. \( 0.80 \times 10^{-6} \)
D. \( 0.16 \times 10^{-6} \)
Subject: Chemistry
An electron in an atom undergoes transition in such a way that its kinetic energy changes from \( x \) to \( \frac{x}{4}, \) the change in potential energy will be:
A \( \cdot+\frac{3}{2} x \)
B. \( -\frac{3}{8} x \)
\( c \cdot+\frac{3}{4} x \)
D. \( -\frac{3}{4} x \)
Subject: Maths
n the given fig 0 is a point in the
nterior of a triangle of a triangle \( A B C, O D \perp B C, O E \perp A C \) and
\( O F \perp A B \) show that
\( \mathbf{O} \mathbf{A}^{2}+\mathbf{O B}^{2}+\mathbf{O C}^{2}-\mathbf{O D}^{2}-\mathbf{O E}^{2}- \)
\( \mathrm{OF}^{2}=\mathrm{AF}^{2}+\mathrm{BD}^{2}+\mathrm{CE}^{2} \)
Subject: Physics
If \( g \) is the acceleration due to gravity on
the earth's surface, the gain in the potential energy of an object of mass \( \boldsymbol{m} \)
raised from the surface of the earth to a
height equal to the radius \( R \) of the earth
is
\( ^{\mathbf{A}} \cdot \frac{1}{2}^{m g R} \)
в. \( 2 m g R \)
\( ^{\mathrm{c}} \cdot \frac{1}{4}^{m g R} \)
D. \( m g R \)
Subject: Physics
In a ripple tank when one pulse is sent every tenth of a second, the distance between consecutive pulses is \( 30 m m \)
In the same depth of water pulses are produced at half second intervals. What
is the new distance between
consecutive pulses?
A. \( 0.67 m m \)
B. \( 6.0 m m \)
\( \mathrm{c} .150 \mathrm{mm} \)
D. \( 600 \mathrm{mm} \)
Subject: Physics
A body is released from the top of a smooth inclined plane at height h above the ground. Simultaneously another body is pushed up with a velocity u from the bottom. If they meet after time \( t, \) an inclination of that inclined plane to the horizontal is
A \( \cdot \sin ^{-1}\left(\frac{t}{h u}\right) \)
B. \( \cos ^{-1}\left(\frac{t}{h u}\right) \)
c. \( \sin ^{-1}\left(\frac{h}{u t}\right) \)
D. \( \cos ^{-1}\left(\frac{h u}{t}\right) \)
Subject: Maths
Assertion
The point \( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{1}, \boldsymbol{6}) \) is the mirror image
of the point \( B(1,3,4) \) in the plane \( x- \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
Reason
The plane \( x-y+z=5 \) bisects the line
segment joining \( \boldsymbol{A}(\mathbf{3}, \mathbf{1}, \boldsymbol{6}) \) and
\( \boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \boldsymbol{4}) \)
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: Physics
The interference pattern with two
coherent light sources of density ratio \( n \) In the interference pattern, the ratio \( \frac{\boldsymbol{I}_{m a x}-\boldsymbol{I}_{m i n}}{\boldsymbol{I}_{m a x}+\boldsymbol{I}_{m i n}} \) will be:
A. \( \frac{\sqrt{n}}{n+1} \)
B. \( \frac{2 \sqrt{n}}{n+1} \)
c. \( \frac{\sqrt{n}}{(n+1)^{2}} \)
D. \( \frac{2 \sqrt{n}}{(n+1)^{2}} \)
Subject: Chemistry
Which gas is evolved when \( P b O_{2} \) is
treated with conc \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} ? \)
A \( . N O_{2} \)
в. \( O_{2} \)
c. \( N_{2} \)
D. \( N_{2} \) O
Subject: Physics
toppr
Q Type your question
coefficient of viscosity \( \eta \) and density
\( \boldsymbol{\rho}\left(<\frac{\sigma}{2}\right) . \) If the length of the liquid
column is sufficiently long, the terminal
velocity attained by the ball is given by
(assume all pulleys to be mass-less and
string as mass-less and inextensible):
A \( \cdot \frac{2}{9} \frac{r^{2}(2 \sigma-\rho) g}{\eta} \)
B \( \cdot \frac{1}{9} \frac{r^{2}(\sigma-2 \rho) g}{\eta} \)
c. \( \frac{2}{9} \frac{r^{2}(\sigma-4 \rho) g}{\eta} \)
D.
Subject: Maths
Consider the matrix \( \boldsymbol{A}=\left(\begin{array}{ll}\mathbf{3} & -\mathbf{2} \\ \mathbf{4} & -\mathbf{1}\end{array}\right) \)
Then all possible values of \( \lambda \) such that
the determinant of \( B=A-\lambda I \) is 0
where \( \boldsymbol{I}=\left(\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right) \) and \( i=\sqrt{-\mathbf{1}} \)
\( \mathbf{A} \cdot 1 \pm 2 i \)
B . \( 2 \pm 3 i \)
c. \( 3 \pm 4 i \)
\( \mathbf{D} \cdot 5 \pm 6 i \)
Subject: Maths
If \( \theta \) is the angle between the lines
\( A B, A C \) where \( A, B, C \) are the three points with coordinates (1,2,-1)\( ;(2,0,3) ;(3,-1,2) \)
respectively, then \( \sqrt{462} \cos \theta \) is equal to
A . 20
B . 40
c. 60
D. 120
Subject: Maths
The probability that the value of certain stock will remain the same is \( 0.46 . \) The probability that its value will increase
by Rs. 0.50 or Re. 1 per share are respectively 0.17 and 0.23 and the probability that its value will decrease by Rs. 0.25 per share is 0.14 . The expected gain per share is
A . Rs. 0.75
B. Rs. 0.25
c. Rs. 0.28
D. Rs. 0.50
Subject: Chemistry
According to the Arrhenius equation,
This question has multiple correct options
A. A high activation energy usually implies a fast reaction.
B. Rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy.
C. Higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant
D. The pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy.
Subject: Chemistry
Formula of ferrocene is:
\( A \)
\( \left[F e(C N)_{6}\right]^{4-} \)
в. \( \left[F e(C N)_{6}\right]^{3+} \)
\( \left.\mathrm{c} \cdot_{[\mathrm{Fe}}(\mathrm{CO})_{5}\right] \)
D. \( \left[\mathrm{Fe}\left(C_{5} \mathrm{H}_{5}\right)_{2}\right. \)
Subject: Maths
The population \( p(t) \) at time \( t \) of a certain mouse species satisfies the differential equation \( \frac{\boldsymbol{d} \boldsymbol{p}(\boldsymbol{t})}{\boldsymbol{d} \boldsymbol{t}}= \)
\( 0.5 p(t)-450 . \) If \( p(0)=850, \) then the time at which the population becomes
zero is
A \( \cdot \frac{1}{2} \ln 18 \)
B. \( \ln 18 \)
c. \( 2 \ln 18 \)
D. \( \ln 9 \)
Subject: Physics
A solid sphere of radius \( R \) has a charge
\( +2 Q . \) A hollow spherical shell of radius
\( 3 R \) placed concentric with the first
sphere has net charge - \( Q \). Calculate
the potential difference between the
spheres:
\( ^{A} \cdot \frac{Q}{3 \pi \varepsilon_{0} R} \)
в. \( \frac{2 Q}{3 \pi \varepsilon_{\Omega} R} \)
c. \( \frac{3 Q}{\pi \varepsilon_{0} R} \)
\( D \)
Subject: Maths
Eliminate the arbitrary constant and obtain the differential equation satisfied by it
\( \boldsymbol{y}=\boldsymbol{2} \boldsymbol{x}+\boldsymbol{c} \boldsymbol{e}^{\boldsymbol{x}} \)
A \( \cdot y^{\prime}-y=2(1-x) \)
В. \( y^{\prime}-y=2(3-x) \)
c. \( y^{\prime}-y=2(1-3 x) \)
D . \( y^{\prime}-y=3(1-x) \)
Subject: Maths
An Egg Seller distributes eggs to the shop in a city. The number of eggs he distributes for each shop has been recorded and the data obtained was
grouped into a class shown in the table
below. Find the mean using shortcut
method.
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline Number of eggs & \( 0-30 \) & \( 30-60 \) & \( 60-90 \) & \( 90-120 \) & \( 150- \) 150 & \( 150- \) 180 \\
\hline Frequency & 40 & 26 & 38 & 12 & 25 & 30 \\
\hline
\end{tabular}
A. 91.5
B. 83.07
c. 87.34
D. 89.76
Subject: Maths
Given that the vectors \( \bar{a} \) and \( \bar{b} \) are non-
collinear, the value of \( x \) and \( y \) for which
the vector quantity \( 2 \bar{u}-\bar{v}=\bar{w} \) holds true if \( \bar{u}=x \bar{a}+2 y \bar{b}, \bar{v}=-2 y \bar{a}+ \)
\( \mathbf{3} \boldsymbol{x} \overline{\boldsymbol{b}}, \overline{\boldsymbol{w}}=\mathbf{4} \overline{\boldsymbol{a}}-\mathbf{2} \overline{\boldsymbol{b}} \) are
A \( \cdot x=\frac{4}{7}, y=\frac{6}{7} \)
в. \( x=\frac{10}{7}, y=\frac{4}{7} \)
c. \( x=\frac{8}{7}, y=\frac{2}{7} \)
D. \( x=2, y=3 \)
Subject: Physics
In the nuclear reaction
\( \boldsymbol{n}+_{\mathbf{9 2}}^{235} \boldsymbol{U} \rightarrow_{\mathbf{5 4}}^{\boldsymbol{a}} \boldsymbol{X} \boldsymbol{e}+_{\boldsymbol{b}}^{\mathbf{9 4}} \boldsymbol{S r}+\mathbf{2 n} \)
determine the values of a and \( b \)
Subject: Chemistry
One pink solid (X) has the formula
\( \mathrm{CoCl}_{3} \cdot 5 N \mathrm{H}_{3} \cdot \mathrm{H}_{2} \mathrm{O} \cdot \mathrm{A} \) solution of this
salt (X) in water is also pink and
precipitates 3 mole \( A g C l \) on treatment with silver nitrate solution. When the
pink solid (X) is heated, it loses
1 \( \operatorname{mole} H_{2} O \) to yield a purple solid \( (Y) \)
with the same molar ratio of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
\( C l: C o . \) The purple solid releases two of
its chlorides rapidly on dissolution and
after treatment with \( A g N O_{3} \) solution. The coordination number of cobalt in
complexes \( (X) \) and \( (Y) \) is six. The IUPAC
name of pink (X) and purple (Y) complexes respectively are:
A. Tetraamminechloridoaquacobalt(III) chloride and pentaamminechloridocobalt(III) chloride
B. Pentaamminechloridocobalt(III) chloride and pentaammineaquacobalt(III) chloride,
c. Pentaammineaquacobalt(III) chloride and pentaamminechloridocobalt(III) chloride
D. Pentaammineaquacobaltate(III) chloride and pentaamminechloridocobaltate(III) chloride
Subject: Physics
A satellite is moving in a circular orbit at a certain height above the
earth's surface. It takes \( 5.26 \times 10^{3} s \) to
complete one revolution with a centripetal acceleration equal to 9.32
\( \mathrm{m} / \mathrm{s}^{2} . \) The height of satellite orbiting
above the earth is
(Earth's radius \( \left.=\mathbf{6 . 3 7} \times \mathbf{1 0}^{\mathbf{6}} \mathbf{m}\right) \)
A. \( 220 \mathrm{km} \)
B. 160 km
c. 70 \( \mathrm{km} \)
D. 120 km
Subject: Maths
A biased coin (with probability of
obtaining a Head equal to \( p>0 \) ) is tossed repeatedly and independently until the first head is observed.

Compute the probability that the first head appears at an even numbered
toss.
A \( \cdot \frac{2-p}{3-p} \)
в. \( \frac{1-p}{3-p} \)
c. \( \frac{1-p}{2-p} \)
D. none of these
Subject: Maths
If the determinant \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a} \boldsymbol{t}-\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{t}-\boldsymbol{c} \\ \boldsymbol{2} & \boldsymbol{1} & \boldsymbol{0}\end{array}\right|=0 \)
if \( a, b, c \) are in
A. \( A . P \)
в. G.Р.
c. \( H . P \)
D. \( k=1 / 2 \)
Subject: Physics
A particle of mass \( 1 \mathrm{kg} \) is placed at a distance of \( 4 \mathrm{m} \) from the centre and on
the axis of a uniform ring of mass \( 5 \mathrm{kg} \)
and radius 3m. The work done to
increase the distance of the particle from \( 4 \mathrm{m} \) to \( \sqrt{3} m \) is.
A \( \cdot \frac{G}{3} J \)
в. \( \frac{G}{4} J \)
c. \( \frac{G}{5} J \)
D. \( \frac{G}{6} J \)
Subject: Chemistry
When \( C a C O_{3} \) is heated to a high
temperature, it undergoes
decomposition into \( C a C O \) and \( C O_{2} \)
whereas it is quite stable at room temperature. The most likely explanation of it is:
A. The enthalpy of reaction \( (\Delta H) \) overweight the term \( T \Delta S \) at high temperature
B. The term \( T \Delta S \) overweight the enthalpy of reaction at high temperature
c. At high temperature, both enthalpy of reaction and entropy change become negative
D. None of these
Subject: Physics
Consider the optical system shown in the figure that follows. The point source
of light \( S \) is having wavelength equal to
\lambda. The light is reaching screen only after
reflection. For point \( \boldsymbol{P} \) to be \( 2^{n d} \) maxima
the value of \( \lambda \) would be \( (D>>d \) and
\( \boldsymbol{d}>>\boldsymbol{\lambda}) \)
A \( \cdot \frac{12 d^{2}}{D} \)
B. \( \frac{6 d^{2}}{D} \)
c. \( \frac{3 d^{2}}{D} \)
D. \( \frac{24 d^{2}}{n} \)
Subject: Maths
Assertion
The differential equation of all straight
lines which are at a constant distance \( \boldsymbol{p} \)
from the origin is \( \left(\boldsymbol{y}-\boldsymbol{x} \boldsymbol{y}_{1}\right)^{2}= \)
\( \boldsymbol{p}^{2}\left(\mathbf{1}+\boldsymbol{y}_{1}^{2}\right) \)
Reason
The general equation of any straight line which is at a constant distance \( \boldsymbol{p} \)
from the origin is \( \boldsymbol{x} \cos \boldsymbol{\alpha}+\boldsymbol{y} \sin \boldsymbol{\alpha}=\boldsymbol{p} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
Two stars of masses \( m_{1} \) and \( m_{2} \) are
parts of a binary star system. The radii
of their orbits are \( r_{1} \) and \( r_{2} \) respectively,
measured from the centre of mass of
the system. The magnitude of
gravitational force \( \boldsymbol{m}_{1} \) exerts on \( \boldsymbol{m}_{2} \) is
then
A. \( \frac{m_{1} m_{2} G}{\left(r_{1}+r_{2}\right)^{2}} \)
в. \( \frac{m_{1} G}{\left(r_{1}+r_{2}\right)^{2}} \)
c. \( \frac{m_{2} G}{\left(r_{1}+r_{2}\right)^{2}} \)
D. \( \frac{G\left(m_{1}+m_{2}\right)}{\left(r_{1}+r_{2}\right)^{2}} \)
Subject: Maths
The converse of "if \( \boldsymbol{x} \in \boldsymbol{A} \cap \boldsymbol{B} \) then \( \boldsymbol{x} \in \)
\( A \) and \( x \in B " \), is
A. If \( x \in A \) and \( x \in B \), then \( x \in A \cap B \)
B. If \( x \notin A \cap B \), then \( x \notin A \) or \( x \notin B \).
c. If \( x \notin A \) or \( x \notin B, \) then \( x \notin A \cap B \)
D. If \( x \notin A \) or \( x \notin B \), then \( x \in A \cap B \).
Subject: Maths
If \( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{x}^{\boldsymbol{y}} \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{e q u a l s -} \)
A \( \frac{y x^{y-1}-1}{1-x^{y} \log x} \)
В. \( \frac{y x^{y-1}-1}{x^{y} \log x-1} \)
c. \( \frac{y x^{y-1}+1}{x^{y} \log x+1} \)
D. None of these
Subject: Chemistry
Assertion
Oxidation number of sulphur in \( \boldsymbol{H}_{2} \boldsymbol{S O}_{5} \)
is +6
Reason
It has one peroxy linkage.
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
Determine the standard reduction
potential for the half reaction:
\( \boldsymbol{C l}_{2}+\boldsymbol{2} \boldsymbol{e}^{-} \longrightarrow \boldsymbol{2} \boldsymbol{C l}^{-} \)
Given: \( \boldsymbol{P} \boldsymbol{t}^{2}+\boldsymbol{2} \boldsymbol{C l} \longrightarrow \boldsymbol{P} \boldsymbol{t}+ \)
\( \boldsymbol{C l}_{2}, \boldsymbol{E}_{c e l l}^{0}=-\mathbf{0 . 1 5} \boldsymbol{V} \)
\( \boldsymbol{P t}^{2}+\boldsymbol{2} \boldsymbol{e}^{-} \longrightarrow \boldsymbol{P t}, \boldsymbol{E}^{0}=\mathbf{1 . 2 0} \boldsymbol{V} \)
Subject: Chemistry
For the general reaction,
If \( K_{f} \) and \( K_{b} \) are the equilibrium constant for the forward and backward
reactions, then, which of the following relationships hold good?
\[
A+B \frac{K_{f}}{F_{B_{b}}} C+D
\]
This question has multiple correct options
\( \mathbf{A} \cdot K_{f}=\frac{1}{K_{b}} \)
\( \mathbf{B} \cdot K_{f} \times K_{b}=1 \)
\( \mathbf{c} \cdot K_{f}-1=K_{b} \)
\( \mathbf{D} \cdot K_{b}+1=K_{f} \)