AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
Fe is protected from corrosion by
connecting Mg metal with it.
Reason
Fe acts as cathode and Mg as anode
which gradually disappears.
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
If equal volumes of \( \mathrm{BaCl}_{2}(\mathrm{aq}) \) and
NaF(aq) solutions are mixed together, which will give a precipitate? \( \left[K_{s p} \text { of } \operatorname{Ba} F_{2}=1.7 \times 10^{-7}\right] ? \)
B. 0.010M BaCl_and 0.015M NaF
D. 0.020 M BaCl_and 0.002 M Naf
Subject: Maths
If \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi} \) and \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) are
angles of \( \triangle ; \) then \( \sin A+\sin B+\sin C \)
is
\( ^{A}=\frac{3 \sqrt{3}}{2} \)
B. \( <\frac{3 \sqrt{3}}{2} \)
\( ^{c}>\frac{3 \sqrt{3}}{2} \)
D. none of these
Subject: Chemistry
Arrange the following in increasing value of magnetic moments.
(i) \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\mathbf{6}}\right]^{4-} \)
(ii) \( \left.\boldsymbol{F e}(\boldsymbol{C N})_{6}\right]^{3-} \)
(iii) \( \boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}^{3+} \)
\( \left.(\text { iv }) N i\left(H_{2} O\right)^{4}\right]^{2+} \)
A \( \cdot(I)<(I I)<(I I I)<(I V) \)
в. \( (I)<(I I)<(I V)<(I I I) \)
c. \( (I I)<(I I I)<(I)<(I V) \)
D. \( (I V)<(I I I)<(I I)<(I) \)
Subject: Maths
Which of the following statements are
correct?
This question has multiple correct options
\( \mathbf{A} \cdot \sin 1>\sin 1^{\circ} \)
B. \( \tan 2<0 \)
\( \mathbf{c} \cdot \tan 1>\tan 2 \)
D. \( \tan 2<\tan 1<0 \)
Subject: Chemistry
Reactions s with dil \( \boldsymbol{H C l} \) Appearance
Unknown
metal #1 bubbl \( \begin{array}{ll}\text { Dull gray } & \text { Dissolved with } 6 \\ \text { solid } & \text { of clear gas } \\ \text { with white } & \\ \text { oxide coating } & \end{array} \)
Unknown metal #2 Solid;
lustrous,
smooth
silver-gray
surface
Unknown metal #1 could be:
A. mercury
B. copper
\( c \cdot \) zinc
D. iron
Subject: Chemistry
An element 'X' is yellow coloured solid, insoluble in water but soluble in carbon disulphide. It has a low melting point
\( 114.5^{\circ} \mathrm{C} . \) It boils at \( 445^{\circ} \mathrm{C} \) and it burns
with pale blue flame forming pungent smelling gas 'Y' which turns moist blue litmus red and finally colourless.'X' and
'Y' are:
A \( \cdot C, C O_{2} \)
в. \( N, N O_{2} \)
\( c \cdot S, S O_{2} \)
D. \( I_{2}, I_{2} O_{5} \)
Subject: Physics
The graph \( A B \) shown in the figure is
plot of the temperature of a body in degree Celsius and degree Fahrenheit Then
A. Slope of line \( A B \) is \( 9 / 5 \)
3. Slope of line \( A B \) is \( 5 / 9 \)
C. Slope of line \( A B \) is \( 1 / 9 \)
Slope of line \( A B \) is \( 3 / 9 \)
Subject: Physics
A rigid body rotates about a stationary
axis according to the law \( \boldsymbol{\theta}=\boldsymbol{a t}-\boldsymbol{b} \boldsymbol{t}^{3} \)
awhere \( a=6 \frac{r a d}{s} \) and \( b=2 \frac{r a d}{s^{3}} . \) Then
mean value of angular velocity ( \( \omega \) ) over
the interval \( t=0 \) and the moment when
it comes to rest is:
A \( .4 \mathrm{rad} / \mathrm{s} \)
B. 3 rad /
c. 8 rad \( / s \)
D. 6 rad \( / \) s
Subject: Maths
\( \tan ^{-1}\left(\tan \frac{2 \pi}{3}\right)= \)
A \( \cdot \frac{\pi}{3} \)
B \( \cdot \frac{2 \pi}{3} \)
c. \( -\frac{\pi}{3} \)
D. \( -\frac{2 \pi}{3} \)
Subject: Maths
In the figure, 'O' is the centre of the
circle and \( 0 \mathrm{M}, \) On are the
perpendiculars from the centre to the
chords \( P Q \) and \( R S . \) If \( O M=O N \) and \( P Q=6 \)
\( \mathrm{cm} . \) Find RS
Subject: Maths
There are five boys \( A, B, C, D, E . \) The order
of their height is \( A<B<C<D<E \)

Number of ways in which they have to be arranged in 4 seats in increasing order of their height such that \( C \& E \) are never adjacent, is
A . 10
B. 6
\( c \cdot 4 \)
\( D \)
Subject: Physics
A plano-concave lens is placed on a
paper on which a flower is drawn. How
far above its actual position does the
flower appear to be?
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
\( c .50 \mathrm{cm} \)
D. None of these
Subject: Chemistry
The two isomers \( X \) and \( Y \) with the
formula \( \boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5} \boldsymbol{C l B r}_{2} \) were taken
for experiment on depression in
freezing point. It was found that one
mole of \( X \) gave depression
corresponding to 2 moles of particles
and one mole of Y gave depression due
to 3 moles of particles. The structural
formulae of \( X \) and \( Y \) respectively are:
\( \mathbf{A} \cdot\left[C r\left(H_{2} O\right)_{5} C l\right] B r_{2} ;\left[C r\left(H_{2} O\right)_{4} B r_{2}\right] C l \cdot H_{2} O \)
B \( \left.\cdot\left[\operatorname{Cr}\left(H_{2} O\right)_{5} C l\right)\right] B r_{2} ;\left[\operatorname{Cr}\left(H_{2} O\right)_{3} C l B r\right] \cdot 2 H_{2} O \)
\( \mathbf{c} \cdot\left[C r\left(H_{2} O\right)_{5} B r\right] B r C l ;\left[C r\left(H_{2} O\right)_{4} C l B r\right] B r \cdot H_{2} O \)
\( \mathbf{D} \cdot\left[\operatorname{Cr}\left(H_{2} O\right)_{4} B r_{2}\right] C l \cdot H_{2} O ;\left[C r\left(H_{2} O\right)_{5} C l\right] B r_{2} \)
Subject: Maths
The value of \( \lim _{x \rightarrow 2} \frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2} \) is
\( A \cdot \frac{1}{8 \sqrt{3}} \)
в. \( \frac{1}{4 \sqrt{3}} \)
c. 0
D. None of these
Subject: Maths
The value of the determinant
\( \left|\begin{array}{ccc}\left(a^{x}+a^{-x}\right)^{2} & \left(a^{x}-a^{-x}\right)^{2} & 1 \\ \left(b^{x}+b^{-x}\right)^{2} & \left(b^{x}-b^{-x}\right)^{2} & 1 \\ \left(c^{x}+c^{-x}\right)^{2} & \left(c^{x}-c^{-x}\right)^{2} & 1\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2abc
\( \mathbf{c} \cdot a^{2} b^{2} c^{2} \)
D. None of these
Subject: Chemistry
For the reaction show:
\[
\mathbf{3} C_{2} H_{2} \leftrightharpoons C_{6} H_{6}
\]
This equilibrium is established when 0.5 mole of benzene is present at a certain temperature. If equilibrium
constant of the reaction is 4 litre \( ^{-2} \)
mole \( ^{2} \). The total number of moles of all
the substances present at equilibrium
is :
(Note : The reaction is performed in a \( 1- \) litre vessel.)
A. 0.5
B.
c. 1.5
D. 2
Subject: Physics
A small metal sphere of radius a is falling with a velocity \( v \) through a
vertical column of a viscous liquid. If the coefficient of viscosity of the liquid
is \( \eta \), then the sphere encounters an opposing force of
A \( .6 \pi \eta a^{2} v \)
в. \( \frac{6 \eta v}{\pi a} \)
c. \( 6 \pi \eta a v \)
D. \( \frac{\pi \eta v}{6 a^{3} v} \)
Subject: Physics
The isotopic masses of \( _{1}^{2} \mathbf{H} \) and \( _{2}^{4} \mathbf{H e} \) are
\( \mathbf{2 . 0 1 4 1} \) and \( \mathbf{4 . 0 0 2 6} \) amu
respectively. The velocity of light in
vacuum is \( 2.998 \times 10^{8} m / \) sec. The
quantity of energy liberated when two mole of \( _{1}^{2} \mathbf{H} \) undergo fusion to form 1
mole of \( _{2}^{4} \) He is :
A \( \cdot 2.3 \times 10^{12} J \)
В. \( 4.3 \times 10^{12} J \)
c. \( 6.6 \times 10^{12} J \)
D. none of these
Subject: Maths
If \( \tan \alpha \) and \( \tan \beta \) are the roots of the
equation \( \boldsymbol{x}^{2}+\boldsymbol{p} \boldsymbol{x}+\boldsymbol{q}=\boldsymbol{0}(\boldsymbol{p} \neq \boldsymbol{0}), \) then
This question has multiple correct options
A \( \cdot \sin ^{2}(\alpha+\beta)+p \sin (\alpha+\beta) \cos (\alpha+\beta)+q \cos ^{2}(\alpha+\beta)= \)
\( q \)
B. \( \tan (\alpha+\beta)=\frac{p}{q-1} \)
\( \mathbf{c} \cdot \cos (\alpha+\beta)=1-q \)
\( \mathbf{D} \cdot \sin (\alpha+\beta)=-p \)
Subject: Physics
A particle performs SHM with a period \( \boldsymbol{T} \)
and amplitude \( a \). The mean velocity of
particle over the time interval during which it travels a distance \( a / 2 \) from the extreme position is:
\( ^{A} \cdot \frac{6 a}{T} \)
в. \( \frac{2 a}{T} \)
\( c \cdot \frac{3 a}{T} \)
D. None
Subject: Maths
Evaluate \( \int x^{2} e^{x} d x= \)
A \( \cdot e^{x}\left(x^{2}-2 x+2\right)+c \)
B . \( e^{x}\left(x^{2}+2 x+2\right)+c \)
c. \( x^{2}+e x+c \)
D. \( e^{x}\left(x^{2}+x+2\right)+c \)
Subject: Maths
Minimum value of the polynomial \( \boldsymbol{p}(\boldsymbol{x})=\mathbf{4} \boldsymbol{x}^{2}-\boldsymbol{6} \boldsymbol{x}+\mathbf{1} \)
A. \( -\frac{3}{4} \)
B. \( -\frac{5}{4} \)
\( c \cdot-\frac{5}{16} \)
D. - œ
Subject: Maths
If \( \boldsymbol{y}=\sin ^{-1}\left(3^{-x}\right), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot \frac{-\log 3}{\sqrt{3^{2 x}-1}} \)
в. \( \frac{3^{x} \log 3}{\sqrt{3^{2 x}-1}} \)
c. \( \frac{-3^{-x} \log 3}{\sqrt{3^{2 x}-1}} \)
D. \( \frac{\log 3}{3^{x} \sqrt{3^{2 x}-1}} \)
Subject: Physics
The values of \( X_{L}, X_{C} \) and \( R \) in series
with an A.C. circuit are \( 8 \Omega, 6 \Omega \) and \( 10 \Omega \)
respectively. The total impedance of the circuit will be
\( \Omega \)
A . 10.2
B. 12.2
c. 10
D. 24.4
Subject: Biology
Assertion : The crown fires are most
destructive as they burn the tree top.
Reason: Due to crown fire the
temperature of that area may rise upto
\( 7000 C \)
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true
Subject: Maths
One card is drawn at random from a
pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
A \( \cdot \frac{1}{13} \)
в. \( \frac{2}{13} \)
c. \( \frac{3}{13} \)
D. \( \frac{4}{13} \)
Subject: Physics
A single battery is connected to three
resistances as shown in Figure.
This question has multiple correct options
A. The current through 7 \( \Omega \) resistance is 4 A
B. The current through \( 3 \Omega \) resistance is 4 A
c. The current through \( 6 \Omega \) resistance is 2 A
D. The current through \( 7 \Omega \) resistance is 0
Subject: Physics
A ball of mass \( m \) is thrown vertically
upwards. Another ball of mass \( 2 m \) is
thrown simultaneously at an angle \( \theta \) with horizontal. Both of them hit the
ground at the same time when thrown from the same height. The heights attained by the two are in the ratio?
A .2:
B. 1:
\( c \cdot 1: \cos \theta \)
D. \( 1: \sec \theta \)
Subject: Physics
A ray of light passes from a medium \( \mathbf{A} \) having refractive index 1.6 to the medium B having refractive index 1.5 The value of critical angle of medium \( A \)
is
\( ^{\mathbf{A}} \cdot \sin ^{-1}\left(\frac{16}{15}\right) \)
B. \( \sin ^{-1} \sqrt{\frac{16}{15}} \)
\( ^{\mathbf{c}} \cdot \sin ^{-1}\left(\frac{1}{2}\right) \)
D. \( \sin ^{-1}\left(\frac{15}{16}\right) \)
Subject: Physics
A varying current in a coil change from
\( 10 A \) to 0 in 0.5 sec. If the average emf
induced in the coil is \( 220 V \), the self
inductance of the coil is :
A . \( 5 H \)
в. \( 6 H \)
\( c .11 H \)
D. \( 12 H \)
Subject: Maths
If the point \( A(2,4) \) is equidistant from \( P(3,8) \) and \( Q(7, y), \) find the values of \( y \)
\( \mathbf{A} \cdot 6 \& 4 \)
B. \( 12 \& 2 \)
c. \( 10 \& 4 \)
D. None of these
Subject: Maths
The figure is a circle with center \( O \) and
diameter \( 10 \mathrm{cm}, P Q=1 \mathrm{cm} . \) Find the
length of \( \boldsymbol{R} \boldsymbol{S} \)
\( \mathbf{A} \cdot 6 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( \mathbf{c} .5 \mathrm{cm} \)
D. \( 3 \mathrm{cm} \)
Subject: Biology
Three of the following statements about
enzymes are correct and one is wrong. Which one of the following is wrong?
A. Enzymes require optimum pH for maximal activity
B. Enzymes are denatured at high temperature but in certain exceptional organisms they are effective even at temperatures \( 80-90^{\circ} \mathrm{C} \)
c. Enzymes are highly specific.
D. Most enzymes are proteins but some are lipids
Subject: Physics
The rainbow and the rainbow-like
colours seen on a thin film of oil on a
water surface are two phenomenon.
They are:
A. Similar in nature and both are due to interference of light
B. Different in nature and rainbow is due to interference of light, while colour of this film is due to diffraction
C. Similar in nature and both are due to refraction of light
D. Different in nature and rainbow is due to refraction, while colour of thin film is dues to interference of light
Subject: Maths
Construct a triangle, \( \triangle A B C \) with \( A B=5, B C=12 \) and \( A C=13 . \) What
is the measure of \( \angle A B C \)
A \( .90^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 40^{\circ} \)
D. \( 75^{\circ} \)
Subject: Chemistry
The negative Zn pole of a Daniel cell, sending a constant current through a circuit, decreases in mass by 0.13 g in 30 minutes. If the electrochemical
equivalent of Zn and Cu are 32.5 and
31.5 respectively, the increase in the mass of the positive Cu pole in this time is:
A. 0.180 g
B. 0.141 g
c. \( 0.126 \mathrm{g} \)
D. 0.242
Subject: Chemistry
For the reaction, \( \boldsymbol{C O}_{(\boldsymbol{g})}+\boldsymbol{C l}_{2(\boldsymbol{g})} \rightleftharpoons \)
\( C O C l_{2(g)}, \) the value of \( K_{p} / K_{c} \) is equal
to?
A . 1.0
в. RT
c. \( \sqrt{R T} \)
D. \( \frac{1}{R T} \)
Subject: Chemistry
Balance the following reaction.
\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{P b C l}_{2}(\boldsymbol{a q}) \longrightarrow \boldsymbol{P b}(\boldsymbol{s})+ \)
\( Z n C l_{2}(a q) \)
\( \mathbf{A} \cdot Z n(s)+P b C l_{2}(a q) \longrightarrow P b(s)+Z n C l_{2}(a q) \)
B \( \cdot 2 Z n(s)+P b C l_{2}(a q) \longrightarrow P b(s)+2 Z n C l_{2}(a q) \)
\( \mathbf{c} \cdot Z n(s)+2 P b C l_{2}(a q) \longrightarrow P b(s)+Z n C l_{2}(a q) \)
D \( \cdot Z n(s)+2 P b C l_{2}(a q) \longrightarrow P b(s)+2 Z n C l_{2}(a q) \)
Subject: Physics
Two identical glass \( \left(\mu_{g}=\frac{3}{2}\right) \) equiconvex lenses of focal length fare
kept in contact. The space between the two lenses is filled with water \( \left(\mu_{w}=\frac{4}{3}\right) . \) The focal length of the combination is :
A. \( f \)
в. \( \frac{f}{2} \)
c. \( \frac{4 f}{3} \)
D. \( \frac{3 f}{4} \)
Subject: Chemistry
school organized a seminar in which he invited parents and principle to discuss the serious issue of diabetes and
depression in students They all resolved
this issue by strictly banning the junk food in school and to introduce healthy snacks and drinks like soup, lassi, milk etc in school canteens. They also
decided to make compulsory half an hour physical activities for the students in the morning assembly daily After six months, Mr, Roy conducted the health survey in most of the schools and
discovered a tremendous improvement in the health of students.
After reading the above passage, answer the following:
(i) What are the values (at least two)
displayed by Mr.Roy?
(ii) As a student, how can you spread
awareness about this issue?
(iii) What are tranquilizers? Give an example.
(iv) Why is use of aspartame limited to cold foods and drinks?
Subject: Physics
A compound microscope consists of two convex lenses of focal length \( 2 \mathrm{cm} \)
and \( 5 \mathrm{cm} . \) When an object is kept at a
distance of \( 2.1 \mathrm{cm} \) from the objective, a virtual and magnified image is formed \( 25 \mathrm{cm} \) from the eye piece. Calculate the magnifying power of the microscope.
Subject: Maths
Three players play a total of 9 games. In each game, one person wins and the other two lose; the winner gets 2 points and the losers lose 1 each. The number
of ways in which they can play all the 9 games and finish each with a zero score
is
\( \mathbf{A} \cdot 84 \)
B. 1680
c. 7056
D.
Subject: Chemistry
The energy of the first orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) is \( -871.6 \times 10^{-20} J . \) The energy of the
electron in the first orbit of hydrogen would be:
\( \begin{array}{lll}\text { A. }-871.6 \times & 10^{-20} J\end{array} \)
B . \( -435.8 \times \quad 10^{-20} J \)
\( \begin{array}{lll}\text { C. }-217.9 \times & 10^{-20} J\end{array} \)
\begin{tabular}{ll} 
D. \( -108.9 \times \) & \( 10^{-20} \mathrm{J} \) \\
\hline
\end{tabular}
Subject: Physics
The diameter of a wire as measured by
screw gauge was found to be
2.620,2.625,2.628 and \( 2.626 \mathrm{cm} \)
Calculate absolute error in each
measurement.
A \( . \Delta a_{5}=2.626-2.626=+0.000 \mathrm{cm} \)
в. \( \Delta a_{4}=2.626-2.626=0.000 \mathrm{cm} \)
C. \( \Delta a_{3}=2.626-2.630=-0.004 \mathrm{cm} \)
D. All of these
Subject: Chemistry
Assertion
Statement \( -1: C_{3} O_{2} \) has linear
structure.
Reason
Statement -2: Each \( C \) atom in \( C_{3} O_{2} \) is
sp - hybridised.
A. Statement - 1 is true, Statement - 2 is true and Statement - 2 is correct explanation for Statement -
1
B. Statement - 1 is true, Statement - 2 is true and Statement - 2 is NOT the correct explanation for Statement - 1
c. statement -1 is true, statement -2 is false
D. statement -1 is false, Statement - 2 is true
Subject: Chemistry
Assertion
The radial probability distribution curves of \( 1 s, 2 p, 3 d- \) orbitals are identical in shape.
Reason
The number of nodal planes present in
these orbitals are different.
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 and Reason are correct
Subject: Physics
A moving coil galvanometer has a coil of area \( A \) and number of turns \( N . A \)
magnetic field B is applied on it. The torque acting on it is given by \( \boldsymbol{\tau}=\boldsymbol{k} \boldsymbol{i} \)
where i is current through the coil. If moment of inertia of the coil is I about
the axis of rotation.
If the value of torsional constant if
current \( i_{0} \) produces angular deflection of \( \pi / 2 \) rad is \( C=\frac{x N B A i_{0}}{\pi} . \) Find \( x \)
Subject: Maths
The median of the following discrete series is
\( \begin{array}{lllllll}x_{i} & 3 & 6 & 5 & 8 & 12 & 7\end{array} \)
\( f_{i} \quad 5 \quad 2 \quad 4 \quad 6 \quad 7 \)
A. 7
B. 8
c. 9
D. 6
Subject: Physics
Which logic gate corresponds to the truth table given below.
\( \begin{array}{lll}\text { A } & \text { в } & \text { c } \\ & & \\ \text { 0 } & \text { o } & \text { 1 } \\ \text { 0 } & \text { 1 } & \text { o } \\ \text { 1 } & \text { 0 } & \text { o } \\ \text { 1 } & \text { 1 } & \text { o }\end{array} \)
A. AND
в. NOR
\( c . \) or
D. NAND
Subject: Chemistry
At \( p H=2, E_{Q u i n h y d r o n e} \) will be:
\( \left(E_{Q u i h y d r o n e}^{o}=1.30 V\right) \)
A . \( 1.36 V \)
B . \( 1.30 V \)
c. \( 1.42 v \)
D. \( 1.20 V \)
Subject: Chemistry
The equilibrium constant for the
following reactions are \( \boldsymbol{K}_{\mathbf{1}} \) and \( \boldsymbol{K}_{\mathbf{2}} \)
respectively.
\( \mathbf{2} \boldsymbol{P}(\boldsymbol{g})+\mathbf{3} \boldsymbol{C} \boldsymbol{l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g}) \)
\( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \)
Then the equilibrium constant for the
reaction
\( \mathbf{2} \boldsymbol{P}(\boldsymbol{g})+\mathbf{5} \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \) is:
A. \( K_{1} K_{2} \)
B. \( K_{1} K_{2}^{2} \)
\( \mathbf{c} \cdot K_{1}^{2} K_{2}^{2} \)
D. \( K_{1}^{2} K_{2} \)
Subject: Maths
If \( A \) be a \( 3 \times 3 \) matrix and \( I \) be the unit
matrix of that order such that \( \boldsymbol{A}= \)
\( A^{2}+I \) then \( A^{-1} \) is equal to
A . \( A \)
в. \( A+I \)
c. \( I-A \)
D. \( A-I \)
Subject: Physics
A bullet of mass \( m=50 \) gm strikes a bag of mass \( \mathrm{M}=5 \mathrm{kg} \) hanging from a fixed point, with a horizontal velocity \( \bar{V}_{p} . \) If bullet sticks to the sand bag then just after collision the ratio of final
\( \& \) initial kinetic energy of the bullet is approximately:
A \( \cdot 10^{-2} \)
- \( ^{-2} \)
B. \( 10^{-3} \)
\( \mathbf{c} \cdot 10^{-6} \)
D. \( 10^{-4} \)
Subject: Physics
Q Type your question
parallel smooth conducting rails. A conducting rod lies on these fixed
horizontal rails and a uniform
constant magnetic field \( B \) exists
perpendicular to the plane of the rails as shown in the figure. If the rod is given
a velocity \( v \) and released as shown in
figure, it will stop after some time. The
total work done by magnetic field is negative

STATEMENT - 2 : If force acts opposite to direction of velocity its work done is negative.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement- -
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Maths
Let \( p, q \) and \( r \) be any three logical
statements. Which one of the following is true?
\( \mathbf{A} \cdot \sim[p \wedge(\sim q)] \simeq(\sim p) \wedge q \)
В . \( (p \vee q) \wedge(\sim r) \equiv(\sim p) \vee(\sim q) \vee(\sim r) \)
c. \( \sim[p \vee(\sim q)] \equiv(\sim p) \wedge q \)
D . \( [p \wedge(\sim q)] \equiv(\sim p) \wedge \sim q \)
E . \( [p \wedge(\sim q)] \equiv p \wedge q \)
Subject: Chemistry
What is \( \Delta_{r} G(k J / \text { mole }) \) for synthesis of ammonia at \( 298 \mathrm{K} \) at following sets of
partial pressure :
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons \)
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) ; \boldsymbol{\Delta}_{r} \boldsymbol{G}^{\circ}=-\mathbf{3 3} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l} \)
\( [\text { Take } \boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} / \boldsymbol{K} \text { mole, } \log \mathbf{2}= \)
\( \mathbf{0 . 3} ; \log \mathbf{3}=\mathbf{0 . 4 8} \)
Gas \( \quad: N_{2} \quad H_{2} \quad N H_{3} \)
Pressure (atm) : 1
3
A \( .+6.5 \)
B . -6.5
c. +60.5
D. - 60.5
Subject: Chemistry
The main reason for the extremely low solubility of carbon dioxide in benzene
\( \left(C_{6} H_{6}\right) \) at room temperature is due to which of the following?
A. The increased disorder due to mixing of the solute and solvent
B. The relatively low strength of the intermolecular forces between carbon dioxide and benzene
c. The strong hydrogen bonding in benzene
D. The weak solvation of carbon and oxygen ions by benzene
Subject: Physics
When disc \( B \) is brought in contact with
disc \( A, \) they acquire a common angular velocity in time \( t . \) The average frictional torque on one disc by the other during this period is
A \( \cdot \frac{2 I \omega}{3 t} \)
в. \( \frac{9 \text { Гс }}{2 t} \)
c. \( \frac{9 \text { ा }}{4 t} \)
D. \( \frac{3 I \omega}{2 t} \)
Subject: Physics
The value of \( G \) for two bodies in vacuum
is \( 6.67 \times 10^{-11} N / m^{2} / K g^{2} . \) Its value in
a dense medium of density
\( 10^{10} g m / c m^{3} \) will be:
A \( .6 .67 \times 10^{-11} N / m^{2} / K g \)
B. \( 6.67 \times 10^{-31} N / m^{2} / K g \)
c. \( 6.67 \times 10^{-21} N / m^{2} / K g \)
D. \( 6.67 \times 10^{-10} N / m^{2} / K g \)
Subject: Physics
The velocity vector of a particle moving in the xy plane is given by \( v=t i+x j \). If initially, the particle was at origin then the equation of trajectory of the projectile is:
A \( \cdot 4 x^{2}-9 y=0 \)
B. \( 9 x^{2}-2 y^{3}=0 \)
c. \( 16 x^{3}-9 y^{2}=0 \)
D. \( 9 x^{3}-2 y^{2}=0 \)
Subject: Chemistry
How many geometric isomers are possible in the following coordination
entities?
\( (a)\left[C r(O X)_{3}\right]^{3-} \)
\( (b)\left[C o C l_{3}\left(N H_{3}\right)_{3}\right] \)
\( A \cdot 0,2 \)
B. 2, 0
c. 2,2
D. 4,0
Subject: Physics
The area of a triangle formed with sides \( \mathbf{5} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}-\hat{\boldsymbol{k}} \) and \( \mathbf{3} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}-\hat{\boldsymbol{k}} \) is:
A \( \cdot \sqrt{6} \)
B. \( \sqrt{3} \)
\( c \cdot \sqrt{\frac{3}{2}} \)
D. \( \sqrt{\frac{5}{2}} \)