AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A man of mass \( 40 \mathrm{kg} \) is standing on a uniform plank of mass 60 kg lying on horizontal frictionless ice. The man
walks from one end to the other end of
the plank. the distance walked by the man relative to ice is (given length of plank=5m)
A \( .2 \mathrm{m} \)
B. 3 \( m \)
\( c \cdot 5 m \)
D. \( 4 \mathrm{m} \)
Subject: Physics
The change in momentum of a vehicle weighing 2000 kg when its speed increases from \( 36 \mathrm{km} / \mathrm{h} \) to \( 72 \mathrm{km} / \mathrm{h} \)
uniformly is :
A. \( 15000 \mathrm{kg}, \mathrm{m} / \mathrm{s} \)
B. 4000 kg.m/s
c. \( 20000 \mathrm{kg}, \mathrm{m} / \mathrm{s} \)
D. 7200 kg.m/s
Subject: Chemistry
Assertion
In transition elements, radii of \( 5 d \) series are virtually the same as those of the
corresponding members of \( 4 d \) series.
Reason
The filling of \( 4 f \) orbitals before \( 5 d \) orbitals results in a regular decrease in atomic radii.
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
has a radius \( \boldsymbol{R} \) and height \( \boldsymbol{L}_{\mathbf{0}} \). The
cylinder is open at its bottom and has a
small hole at its top. A piston of mass
\( M \) is held at a distance \( L \) from the top
surface as shown in Fig. The
atmospheric pressure is \( \boldsymbol{p}_{0} \)
The piston is now pulled out slowly and
held at a distance \( 2 L \) from the top. The
pressure in the cylinder between its top
and the piston will then be:
\( \mathbf{A} \cdot P_{0} \)
в. \( \frac{P_{0}}{2} \)
c. \( \frac{P_{0}}{2}-\frac{M g}{\pi R^{2}} \)
D. \( P_{0}-\frac{M g}{\pi R^{2}} \)
Subject: Maths
Assertion
\( f \) is a function defined on the interval
[-1,1] such that \( f(\sin 2 x)=\sin x+ \)
\( \cos x \)
Statement I: If \( \boldsymbol{x} \in\left[-\frac{\boldsymbol{\pi}}{\boldsymbol{4}}, \frac{\boldsymbol{\pi}}{\boldsymbol{4}}\right], \) then
\( f\left(\tan ^{2} x\right)=\sec x \)
Reason
Statement II: \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\mathbf{1}+\boldsymbol{x}}, \forall \boldsymbol{x} \in \)
[-1,1]
A. Statement I is true, Statement II is also true:
Statement II is the correct explanation of Statement
B. Statement I is true, Statement II is also true Statement II is not the correct explanation of Statement
c. statement lis true, statement II is false
D. statement lis false, statement II is true
Subject: Chemistry
Match the following
\begin{tabular}{lll|l} 
& List I & & List II \\
A. & \( \mathrm{PCl}_{3} \) & I. & Square planar \\
B. & \( B F_{3} \) & II. & T-shape \\
C. & \( C I F_{3} \) & II. & Trigonal-pyramidal \\
D. & \( X e F_{4} \) & IV. & See-saw \\
& & V. & Trigonal planar
\end{tabular}
D-II
A \( . \) A-IV, B-II, C-I.
B. A-III, B-V, C-II. D-IV
\( c \)
A-III B-V, C-II, D-1
D. A-II, B-IV, C-III \( D-v \)
Subject: Physics
A parallelogram has diagonals expressed as \( \vec{A}=5 \hat{i}-4 \hat{j}+3 \hat{k} \) and \( \vec{B}=3 \hat{i}+2 \hat{j}-\hat{k} \)
Area of parallelogram is:
A. \( \sqrt{117} \) units
B. \( \sqrt{171} \) units
c. \( \sqrt{711} \) units
D. \( \sqrt{107} \) units
Subject: Maths
If two events \( A \) and \( B \) are such that
\( \boldsymbol{P}(\boldsymbol{A})=\cdot \boldsymbol{2}, \boldsymbol{P}(\boldsymbol{B})=\cdot \boldsymbol{3} \) and \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})= \)
\( \cdot 4 \) then \( P(A \cap B) \) equals?
A . 0.2
B. 0.1
\( c \cdot 0.3 \)
D. None of these
Subject: Chemistry
The correct IUPAC name of the
coordination compound
\( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\mathbf{5}} \boldsymbol{N} \boldsymbol{O}\right] \) is \( \boldsymbol{?} \)
A. potassium pentacyanonitrosylferrate (II)
B. potassium pentacyanonitro-N-ferrate(III)
C . potassium nitritopentacyanoferrate(IV)
D. potassium nitritepentacyanoiron(II)
Subject: Chemistry
Which among the following statements is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot p H=-\log _{10} H_{3} O^{+} \)
B. pH decreases with increase of temperature
C. \( \mathrm{pH} \) cannot be zero, negative or more than 14
D. If a solution is diluted ten times, its pH increases by 1
Subject: Physics
A conductor \( A B C D E F, \) shaped as
shown, carries a current i. It is placed in
the \( x y \) plane with the ends \( A \) and \( E \) on
the \( x \) -axis. A uniform magnetic field of
magnitude \( B \) exists in the region. The
force acting on it will be :
This question has multiple correct options
A. zero, if \( B \) is in the \( x \) -direction
B. \( \lambda B i \) in the \( z \) -direction, if \( B \) is in the \( y \) -direction
C. \( \lambda B i \) in the negative \( y \) -direction, if \( B \) is in the \( z- \) direction
D. \( 2 a B i \), if \( B \) is in the \( x \) -direction
Subject: Physics
Assertion
At high temperature, a ferromagnet
becomes a paramagnet.
Reason
The ferromagnetic property depends on
temperature.
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
When simplified the value of \( \left[\boldsymbol{i}^{57}-\right. \)
\( \left.\left(1 / i^{25}\right)\right] \) is?
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 2 i \)
c. \( -2 i \)
D. 2
Subject: Chemistry
In the reaction of \( H I \) with \( H_{2} S O_{4} \) the
oxidation state of sulphur is changed to
-2. Identify the correct balanced
equation
A \( \cdot H_{2} S O_{4}+2 H I \rightarrow S O_{2}+2 H_{2} O+I_{2} \)
в. \( H_{2} S O_{4}+6 H I \rightarrow S+4 H_{2} O+3 I_{2} \)
c. \( H_{2} S O_{4}+8 H I \rightarrow H_{2} S+4 H_{2} O+4 I_{2} \)
D. All of the above
Subject: Maths
If \( \vec{a} \cdot \hat{i}=\vec{a} \cdot(\hat{i}+\hat{j})=\vec{a}(\hat{i}+\hat{j}+\hat{k}), \) thus
\( \vec{a}= \)
\( A \)
B . \( \hat{i}+j \)
c. \( \hat{k}-\hat{j} \)
D. \( \hat{i}+\hat{j}+\hat{k} \)
Subject: Chemistry
In the electrochemical cell:
\( Z n\left|Z n S O_{4}(0.01 M)\right|\left|C u S O_{4}(1.0 M)\right| C \)
the emf of this Daniel cell is \( E_{1} . \) When
the concentration of \( Z n S O_{4} \) is changed
to \( 1.0 M \) and that of \( C u S O_{4} \) changed to
\( \mathbf{0 . 0 1} \boldsymbol{M}, \) the emf changes to \( \boldsymbol{E}_{2} . \) From the followings, which one is the
relationship between \( \boldsymbol{E}_{1} \) and \( \boldsymbol{E}_{2} ? \) (Given, \( \left.\frac{\boldsymbol{R T}}{\boldsymbol{F}}=\mathbf{0 . 0 5 9}\right) \)
A \( . E_{2}=0 \neq E_{1} \)
B \( . E_{1}=E_{2} \)
c. \( E_{1}<E_{2} \)
D. \( E_{1}>E_{2} \)
Subject: Chemistry
\( ^64 C u \) (half-life-12.8 hr) decays by \( \beta^{-} \)
emission \( (38 \%), \beta^{+} \) -emission \( (19 \%) \) and
electron capture \( (43 \%) . \) Calculate partial half lives for electron capture?
\( \mathbf{A} \cdot 29.78 h r \)
B. \( 28.78 h r \)
\( \mathrm{c} .59 .56 \mathrm{hr} \)
D. \( 57.56 h r \)
Subject: Maths
If the non-zero numbers \( x, y, z \) are \( A P \)
and \( \tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z \) are also in
\( A P, \) then
A. \( x y=y z \)
B \( \cdot z^{2}=x y \)
c. \( x=y=z \)
D . \( x^{2}=y z \)
Subject: Maths
Let \( a, b, c \) be such that \( b(a+c) \neq 0 \) \( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{a}+\mathbf{1} & \boldsymbol{a}-\mathbf{1} \\ -\boldsymbol{b} & \boldsymbol{b}+\mathbf{1} & \boldsymbol{b}-\mathbf{1} \\ \boldsymbol{c} & \boldsymbol{c}-\mathbf{1} & \boldsymbol{c}+\mathbf{1}\end{array}\right|+ \)
\( \left|\begin{array}{ccc}\boldsymbol{a}+\mathbf{1} & \boldsymbol{b}+\mathbf{1} & \boldsymbol{c}-\mathbf{1} \\ \boldsymbol{a}-\mathbf{1} & \boldsymbol{b}-\mathbf{1} & \boldsymbol{c}+\mathbf{1} \\ (-\mathbf{1})^{n+\mathbf{2}} \boldsymbol{a} & (-\mathbf{1})^{n+\mathbf{1}} \boldsymbol{b} & (-\mathbf{1})^{n} \boldsymbol{c}\end{array}\right|=\mathbf{0} \)
then the value of \( n \) is
A. Any integer
B. zero
c. Any even integer
D. Any odd integer
Subject: Physics
Two sound speakers are driven in phase by an audio amplifier at frequency \( 600 H z . \) The speed of sound is \( 340 m / s \)
The speakers are on the \( y \) -axis, one at \( \boldsymbol{y}=+1.0 \boldsymbol{m} \) and the other at \( \boldsymbol{y}= \)
\( -1.0 m . \) A listener begins at \( y=0 \) and
walks along a line parallel to the \( y \) -axis at a very large distance \( x \) away. At what
angle \( \theta^{o} \) (between the line from the origin to the listener at the \( x \) -axis will
she first hear a minimum sound
intensity?
Subject: Chemistry
Assertion
During covalent bonding the electronegativity difference between
two atoms is greater than 1.7
Reason
Covalent bond is formed by sharing of electrons between atoms that have
same size
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
The electronic configuration of \( \boldsymbol{R} \boldsymbol{b}^{+} \) in absence of Aufbau Principle, is:
A \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{6} \)
B \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{3} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{4} \)
c. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{3} \)
D. None of these
Subject: Physics
The magnetic field at \( O \) due to current
in the wire segment BC of the infinite wire forming a loop as shown in figure
is
\( ^{A} \cdot \frac{\mu_{0} I}{4 \pi d}\left(\cos \phi_{1}+\cos \phi_{2}\right) \)
в. \( \frac{\mu_{0}}{4 \pi} \)
c. \( \frac{\mu_{0} I}{4 \pi d}\left(\sin \phi_{1}+\sin \phi_{2}\right) \)
D. \( \frac{\mu_{0}}{4 \pi} \)
Subject: Physics
Two coherent points sources \( S_{1} \) and \( S_{2} \)
vibrating in phase emit light of wavelength \( \lambda \). The separation between
them is \( 2 \lambda \). The light is collected on a
screen \( \sum \) placed at a distance \( D>>\lambda \)
from the slit \( S_{1} \) as shown, in the fig.
Find the minimum distance so that
intensity at \( P \) is equal to intensity at \( O \)
A . \( D \)
B . \( D_{/ 3} \)
c. \( \sqrt{3} D \)
D. \( D_{/ 2} \)
Subject: Physics
When a solid sphere moves through a liquid the liquid opposes is the motion
with a force the magnitude of the force depends upon the coefficient of viscosity of the liquid the radius of the
sphere find the expression of force using dimension formula:
A \( \cdot v t=\frac{2(d-\rho) g r^{2}}{8 \eta} \)
B. \( v t=\frac{(d-\rho) g r^{2}}{6 \eta} \)
c. \( v t=\frac{2(d-\rho) g r^{2}}{9 \eta} \)
\( V t=\frac{(d-\rho) g r^{2}}{9 \eta} \)
Subject: Physics
An \( \alpha \) -particle is moving along a circle of
radius \( R \) with a constant angular
velocity \( \omega . \) Point \( A \) lies in the same
plane at a distance \( 2 R \) from the center.
Point \( A \) records magnetic field
produced by the \( \alpha \) -particle. If the
minimum time interval between
successive times at which \( A \) records
zero magnetic field is \( t \), the angular
speed \( \omega, \) in terms of \( t, \) is :
A. \( \frac{2 \pi}{t} \)
в. \( \frac{2 \pi}{3 t} \)
c. \( \frac{\pi}{3 t} \)
D.
Subject: Physics
Weight' of a body may have the following attributes. It is the gravitational force acting on a body at the earth's surface
II. It is independent of the mass of the
body
III. The body is weightless during free fall
IV. It is different at different places on
earth's surface.
A . I, Il and III only
B . I, III and IV only
c. I and III only
D. I, II, III and IV
Subject: Chemistry
With partial pressure of \( \boldsymbol{S O}_{3} \) and \( \boldsymbol{S O}_{2} \)
taken to be equal to \( 10^{-5} \) atm and 10 atm respectively then what must be the
partial pressure of \( \boldsymbol{O}_{2} \) so that the reaction may remain in equilibrium?
A . 10 atm
B. 0.01 atm
c. 100 atm
D. 0.1 atm
Subject: Chemistry
A sample of \( A g C l \) was treated with
\( 5 m L \) of \( 1.5 M N a_{2} C O_{3} \) solution to
\( \operatorname{give} A g_{2} C O_{3} . \) The remaining solution
contained \( 0.0026 g C l^{-} \) per litre
Calculate the solubility product of \( A g C l \)
\( \left(\boldsymbol{K}_{s p}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C O}_{3}\right)=\boldsymbol{8} \cdot \boldsymbol{2} \times \mathbf{1 0}^{-12}\right) \)
Subject: Chemistry
\( \boldsymbol{H} \boldsymbol{F}+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \rightarrow \boldsymbol{H}_{2} \boldsymbol{F}^{+}+\boldsymbol{H}_{2} \boldsymbol{O} \)
In the above reaction, Bronsted bases
are:
A. \( H_{3} O^{+}, H_{2} O \)
в. \( H F, H_{3} O^{+} \)
c. \( H_{2} F^{+}, H_{2} O \)
D. \( H F, H_{2} O \)
Subject: Maths
If \( \int x \frac{\ln (x+\sqrt{1+x^{2}})}{\sqrt{1+x^{2}}} d x= \)
\( \boldsymbol{a} \sqrt{\mathbf{1}+\boldsymbol{x}^{2}} \ln (\boldsymbol{x}+\sqrt{\mathbf{1}+\boldsymbol{x}^{2}})+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} \)
then
A \( . a=1, b=-1 \)
В. \( a=1, b=1 \)
c. \( a=-1, b=1 \)
Subject: Physics
A block is gently placed on a conveyor belt moving horizontally with constant
speed. After \( t=4 s, \) the velocity of the
block becomes equal to the velocity of the belt. If the coefficient of friction
between the block and the belt is \( \mu= \)
\( 0.2, \) then the velocity of the conveyor
belt is
\( \mathbf{A} \cdot 8 m s^{-1} \)
B. \( 4 m s^{-1} \)
\( \mathbf{c} \cdot 6 m s^{-1} \)
D. \( 18 \mathrm{ms}^{-1} \)
Subject: Physics
If the resistivity of copper is \( 1.7 \times \)
\( 10^{-6} \Omega c m, \) then the mobility of electrons
in copper, if each atom of copper contributes one free electron
for conduction, is
[The atomic weight of copper is 63.54 and its density is \( 8.96 g / c c] \)
A. \( 23.36 \mathrm{cm}^{2} / \mathrm{Vs} \)
B. \( 503.03 \mathrm{cm}^{2} / \mathrm{Vs} \)
c. \( 43.25 \mathrm{cm}^{2} / \mathrm{V} s \)
D. \( 88.0 \mathrm{cm}^{2} / \mathrm{Vs} \)
Subject: Maths
If \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 7}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5 5}, \boldsymbol{P}(\boldsymbol{C})= \)
\( \mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\boldsymbol{x}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{C})= \)
\( \mathbf{0 . 4 5}, \boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{C})=\mathbf{0 . 3} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \)
\( C)=0.2, \) then
A. \( 0.2 \leq x \leq 0.45 \)
в. \( 0.2 \leq x \leq 0.5 \)
c. \( 0.2 \leq x \leq 0.65 \)
D. \( 0.2 \leq x \leq 1 \)
Subject: Physics
The particle executing simple harmonic motion has a kinetic energy \( K_{0} \cos ^{2} \omega t \) The maximum values of the potential energy and the total energy are respectively
A. \( K_{0} \) and \( K_{0} \)
B. 0 and \( 2 K_{0} \)
c. \( \frac{K_{0}}{2} \) and \( K_{0} \)
D. \( K_{0} \) and \( 2 K_{0} \)
Subject: Physics
A biconvex lens of focal length f forms a circular image of radius r of sun in focal plane. Then which option is correct?
A \( \cdot \pi r^{2} \propto f \)
В \( \cdot \pi r^{2} \propto f^{2} \)
c. If lower half part is covered by black sheet, then area of the image is equal to \( \pi r^{2} / 2 \)
D. If fis doubled, intensity will increase
Subject: Maths
Solve the following equations:
\( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\frac{\mathbf{1}}{\boldsymbol{x}}+\frac{\mathbf{1}}{\boldsymbol{y}}+\frac{\mathbf{1}}{\boldsymbol{z}}=\frac{\mathbf{7}}{\mathbf{2}}, \boldsymbol{x} \boldsymbol{y} \boldsymbol{z}=\mathbf{1} \)
Subject: Maths
A business man is expecting two telephone calls. Mr Walia may call any time between 2 p.m and 4 p.m. while \( \mathrm{Mr} \) Sharma is equally likely to call any time between 2.30 p.m. and 3.15 p.m. The probability that Mr Walia calls before Mr Sharma is:
A \( \cdot \frac{1}{18} \)
в. \( \frac{1}{9} \)
\( c \cdot \frac{1}{6} \)
D. None of these
Subject: Physics
A wave of frequency \( 400 H z \) has a
velocity of \( 320 m s^{-1} . \) The distance between the particles differing in phase
by \( 90^{\circ} \) is
\( \mathbf{A} \cdot 80 \mathrm{cm} \)
B. \( 60 \mathrm{cm} \)
c. \( 40 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)
Subject: Maths
BD is a median of a triangle ABC.F is a point on \( A B \) such that \( C F \) intersects \( B D \)
at \( \mathrm{E} \) and \( B E=B D . \) If \( B F=5 \mathrm{cm} . \) BA
is equal to
A . 10
B. 12
c. 15
D. 17
Subject: Physics
Two particles \( X \) and \( Y \), of equal mass
and with unequal positive charges, are free to move and are initially far away
from each other. With \( Y \) at rest, \( X \)
begins to move towards it with initial
velocity \( u \). After a long time, finally
A. \( X \) will stop, \( Y \) will move with velocity \( u \)
B. \( X \) and \( Y \) will both move with velocities \( u / 2 \) each
c. \( X \) will stop, \( Y \) will move with velocity \( <u \)
D. both will move with velocities \( <u / 2 \)
Subject: Chemistry
The alcohol which gives the most
stable carbonium ion on dehydration is:
A \( \cdot\left(C H_{3}\right)_{2} C H C H_{2} O H \)
В . \( \left(C H_{3}\right)_{3} C-O H \)
c. \( C H_{3} C H_{2} C H_{2} C H_{2} O H \)
D. \( C H_{3}-C H-C H_{2} C H_{3} \)
Subject: Maths
The solution of \( \frac{d y}{d x}+2 x=e^{3 x} \) is:
A \( \cdot y=3 e^{3 x}-x^{2}+c \)
B. \( y=\frac{e^{3 x}}{3}-x^{2}+c \)
C . \( y=e^{3 x}-x^{2 x}+c \)
D. \( y=e^{3 x}-x^{2}+c \)
Subject: Maths
The value of \( \cos ^{-1}\left(-\frac{1}{2}\right)+ \)
\( \sin ^{-1}\left(-\frac{\sqrt{\mathbf{3}}}{\mathbf{2}}\right) \) is
\( A \cdot \frac{\pi}{3} \)
B.
c. \( \frac{2 \pi}{3} \)
D. none of these
Subject: Physics
In a charged spherical conductor id radius \( 10 \mathrm{cm} \) has potential \( V \) at point
distant \( 5 c m \) from its center, then the
potential at a point \( 15 \mathrm{cm} \) away from the
center will be then
A. \( 3 V \)
в. \( \frac{3}{2} V \)
c. \( \frac{2}{3} V \)
D. \( \frac{1}{3} v \)
Subject: Physics
A conducting rod of mass \( m \) and length
is free to move without friction on two
parallel long conducting rails, as shown below. There is a resistance \( R \) across
the rails. In the entire space around,
there is a uniform magnetic field \( \boldsymbol{B} \)
normal to the plane of the rod and rails.
The rod is given an impulsive velocity \( \boldsymbol{v}_{0} \) Finally, the initial energy \( \frac{1}{2} m v_{0}^{2} \)
A. Will be converted fully into heat energy in the resistor
B. Will enable rod to continue to move with velocity \( v_{0} \)
since the rails are frictionless
c. will be converted fully into magnetic energy due to induced current
D. Will be converted into the work done against the magnetic field
Subject: Physics
Proton which kinetic energy of \( 1 M e V \)
moves from south to north. It gets an
acceleration of \( 10^{12} m / s^{2} \) by an applied
magnetic field (west to east). The value of magnetic field:
(Rest mass of proton is \( \left.1.6 \times 10^{-27} k g\right) \)
A. \( 0.071 m T \)
B. \( 71 m T \)
\( c .0 .71 m T \)
D. \( 7.1 m T \)
Subject: Physics
A circular disc of M.I. \( 10 \mathrm{kg}-\mathrm{m}^{2} \) rotates
about its own axis at a constant speed of 60 r.p.m. under the action of an
electric motor of power 31.4 W. If the motor is switched off, how many
rotations will it cover before coming to rest?
A . 3.14
в. 31.4
c. 314
D. 6.28
Subject: Chemistry
The electronic configuration of valence
shell of \( C u \) is:
A \( \cdot 3 d^{10} 4 s^{2} \)
B. \( 3 d^{9} 9 s^{2} \)
\( \mathbf{c} \cdot 3 d^{10} 4 s \)
D. \( 3 d^{10} 4 s^{0} \)
Subject: Chemistry
A 0.2 molar solution of formic acid is
\( 3.2 \% \) ionised, its ionisation constant is:
A. \( 9.6 \times 10^{-3} \)
B. \( 2.1 \times 10^{-4} \)
c. \( 1.25 \times 10^{-6} \)
D. \( 2.1 \times 10^{-8} \)
Subject: Physics
The mass of the earth is \( 6.00 \times 10^{24} k g \)
and that of the moon is \( 7.40 \times 10^{22} k g \)
The constant of gravitation \( G= \)
\( 6.67 \times 10^{-11} N m^{2} k g^{-2} \). calculate
gravitational force of attraction.
\( \mathbf{A} \cdot 38 \times 10^{18} \)
В. \( 20.2 \times 10^{19} \)
c. \( 7.60 \times 10^{8} \)
D. \( 1.90 \times 10^{8} \)
Subject: Physics
A biconvex lens has radii of curvature of
two faces \( 0.1 \mathrm{m} \) and 0.12 respectively. If the focal length of the lens is \( 0.1 \mathrm{m} \). Find
(i) the refractive index of the material of
lens
(ii) power of lens (iii) nature and position of the image of an object placed at a distance of \( 6 \mathrm{cm} \) from the lens.
Subject: Maths
At what rate percent compound interest, \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{8 0 0} \) amounts to \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{9 2 6 . 1 0} \)
in \( 1 \frac{1}{2} \) years, interest being compounded half yearly?
Subject: Physics
A body throws a ball to his friend \( 20 m \)
away. The ball reaches to the friend in
4s. The friend then throws the ball back
to boy and it reaches the boy in \( 5 s \)
A . The average velocity is \( \frac{40}{9} \mathrm{ms}^{-1} \)
B. The average acceleration is zero
c. The average velocity is zero but average acceleration
is non zero
D. Average acceleration of the motion cannot be defined
Subject: Physics
Three elastic wires, \( P Q, P R \) and \( P S \)
support a body \( P \) of mass \( M, \) as shown
in the figure. The wires. are of the same
material and cross-sectional area, the
middle one being vertical. The load carried by the middle wire is:
A \( \cdot \frac{M g}{1+2 \cos ^{2} \theta} \)
в. \( \frac{M g}{1+2 \cos ^{3} \theta} \)
\( c \)
D. \( \frac{M g}{\cos \theta+2 \cos ^{3} \theta} \)
Subject: Maths
If \( d \) is the \( H C F \) of 56 and \( 72, \) find \( x, y \)
satisfying \( \boldsymbol{d}=\mathbf{5 6 x}+\mathbf{7 2 y} . \) Also, show
that \( x \) and \( y \) are not unique.
Subject: Chemistry
Equilibrium constant for the following
reaction is \( 1 \times 10^{-9} \)
\[
\begin{array}{c}
C_{5} H_{5} N(a q .)+H_{2} O(l) \rightleftharpoons \\
C_{5} H_{5} N H^{+}(a q .)+O H^{-}(a q .)
\end{array}
\]
Determine the mole of pyridirium
cholride \( \left(C_{5} H_{5} N . H C l\right) \) that should be
added to \( 500 m L \) solution of \( 0.4 M \)
pyridine \( \left(C_{5} H_{5} N\right) \) to obtain a buffer
solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{5} \)
A. 0.1 mole
B. 0.2 mole
c. 0.3 mole
D. 0.4 mole
Subject: Maths
n figure \( D \) and \( E \) are the mid points of
sides \( A B \) and \( A C \) respectively of \( \triangle A B C \)
Find \( \angle E D B \)
\( A \cdot 110 \)
\( 3 \cdot 120 \)
\( c \cdot 70^{\circ} \)
\( D \cdot 80 \)
Subject: Chemistry
If \( N a^{+} \) ion is larger than \( M g^{2+} \) ion, and
\( S^{2-} \) ion is larger than \( C l^{-} \) ion, which of the following will be less soluble in water?
A. \( N a C l \)
B. \( N a_{2} S \)
c. \( M g C l_{2} \)
D. \( M g S \)
Subject: Chemistry
Which of the following statement is
correct?
This question has multiple correct options
A . oxidizing power order: \( \operatorname{SiCl}_{4}<\operatorname{SnCl}_{4}<P b C l_{4} \)
B. Ionic character order: \( C s B r>R b B r>K B r>N a B r>L i B r \)
c. The ionic character of lead(II) halides decrease with the increase in atomic no. of halogen
D. The oxidation state of \( T l \) in \( T l I_{3} \) is +3
Subject: Physics
The \( Q \) factor of a series LCR circuit with
\( \mathrm{L}=2 \mathrm{H}, \mathrm{C}=32 \mu \mathrm{F} \) and \( \mathrm{R}=10 \Omega \mathrm{is} \)
A . 15
B. 20
\( c \cdot 25 \)
D. 30
Subject: Chemistry
70 calories of heat are required to raise the temperature of 2 moles of an ideal
gas at constant pressure from \( 30^{\circ} \mathrm{C} \) to
\( 35^{\circ} \mathrm{C} . \) The amount of heat required to
raise the temperature of same gas
through the same range \( \left(30^{\circ} C t o 35^{\circ} C\right) \)
at constant volume \( (\boldsymbol{R}= \) \( 2 c a l / m o l / K) \) is:
A . 30
B. 50
c. 70
D. 90
Subject: Physics
Charge 1 attracts Charge \( 2, \) Charge 2 repels Charge \( 3, \) and Charge 3 attracts Charge 4. Which of the following option must hold good for the given condition of four point charges?
A. Charge 1 attracts Charge 4
B. Charge 2 attracts Charge 3
c. charge 1 repels Charge 3
D. charge 2 repels Charge 4
E. charge 1 repels charge 4