AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Through an inductance coil of \( \boldsymbol{L}= \)
\( 0.2 H, \) an ac current of 2 ampere is
passed first with frequency \( n_{1} \) and then
with frequency \( n_{2} \). The ratio of the
maximum value of induced emf \( \left(e_{1} / e_{2}\right) \)
in the coil, in the two cases is
A. \( n_{1} / n_{2} \)
в. \( n_{2} / n_{1} \)
c. \( n_{1}^{2} / n_{2}^{2} \)
D \( \cdot n_{2}^{2} / n_{1}^{2} \)
Subject: Physics
How far must a particle be on the line joining earth to sun, in order that the gravitational pull on it due to sun is
counterbalanced by that due to earth.
Given orbital radius of earth is \( 10^{8} \mathrm{Km} \)
and \( M_{S}=3.24 \times 10^{5} M_{E} \)
A \( \cdot 6.4 \times 10^{5} \mathrm{Km} \)
В. \( 1.75 \times 10^{2} \mathrm{Km} \)
\( \mathbf{c} \cdot 1.75 \times 10^{9} \mathrm{Km} \)
D. \( 6400 \mathrm{Km} \)
Subject: Physics
How much heat would be required to
convert \( 14 \mathrm{kg} \) of ice at \( 0^{\circ} \mathrm{C} \) into water of
\( 0^{\circ} \mathrm{C} ? \)
A . 4704 J
в. 4704 k
c. 336 J
D. 336 kJ
Subject: Chemistry
On electrolysis of aqueous \( \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{S}_{3} \) sol, using inert electrode:
A. the coagulation of particles of dispersed phase occur near cathode
B. as will deposit at cathode
c. sulphur will deposit at cathode
D. \( H_{2} \) gas will evolve at cathode
Subject: Chemistry
Assertion
Graphite is a good conductor of heat and electricity
Reason
Graphite has all the electrons firly held together in \( C-C \sigma \) -bonds
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
(a) How would you account for the following:
(i) The chemistry of actinoids is more complicated as compared to lanthanoids
(ii) Transition metals form complex
compounds
(b) Complete the following equation:
\[
\mathbf{2} M n O_{4}^{-}+6 H^{+}+S O_{3}^{2-} \longrightarrow
\]
Subject: Chemistry
Which of the following represents the composition of Carnallite mineral?
A. \( K_{2} O \cdot A l_{2} O_{3} \cdot 6 S i O_{2} \)
в. \( K N O_{3} \)
c. \( K_{2} S O_{4} \cdot M g S O_{4} \cdot M g C l_{2} \cdot 6 H_{2} O \)
D. \( K C l \cdot M g C l_{2} \cdot 6 H_{2} O \)
Subject: Physics
A road runs parallel to a vertical cliff at a distance of \( 680 \mathrm{m} \) as shown in the
figure. A truck, standing at \( P \) sounded the horn at an instance and the truck
driver hears the echo after \( 4 s \). But the
sound of the horn was heard twice by a
person standing at \( Q \) within an interval
of \( 2 s . \) Give reasons why the person at \( Q \) heard the sound twice. Neglecting the wind velocity. Calculate how far the person was from the truck?
Subject: Chemistry
Which of the following statements is/are correct?
a) In the decomposition of an oxide into
oxygen and metal vapour, entropy
increases.
b) Decomposition of an oxide is an endothermic change.
c) To make \( \Delta G^{0} \) negative, temperature
should be high enough so that \( T \Delta S^{0}> \)
\( \Delta \boldsymbol{H}^{0} \)
A. (a), (b) only are correct
B. (b), (c) only are correct
C. (a), (c) only are correct
D. \( (a),(b),(c) \) are correct
Subject: Physics
The focal length of convex mirror is 20 \( \mathrm{cm}, \) its radius of curvature will be:
A . \( 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( c .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)
Subject: Physics
A tightrope walker in a circus holds a
long flexible pole to help stay balanced
on the rope. Holding the pole
horizontally and perpendicular to the
rope helps the performer.
This question has multiple correct options
A. by lowering the overall centre-of-gravity.
B. by increasing the rotation inertia.
C. in the ability to adjust the centre-of-gravity to be over the rope
D. in achieving the centre of gravity to be under the rope
Subject: Physics
A body of mass \( 36 g m \), moves with
S.H. \( M \) of amplitude \( A=13 \mathrm{cm} \) and
period \( \boldsymbol{T}=\mathbf{1 2} \) sec. At a time \( \boldsymbol{t}=\mathbf{0}, \) the
displacement is \( \boldsymbol{x}=+\mathbf{1 3} \) cm. The
shortest time of passage from \( \boldsymbol{x}= \)
\( +6.5 \mathrm{cm} \) to \( x=-6.5 \) is ?
\( \mathbf{A} \cdot 4 \sec \)
B. 2 sec
\( \mathrm{c} \cdot 6 \mathrm{sec} \)
D. 3 sec
Subject: Maths
If \( \boldsymbol{y}=\tan ^{-1}\left(\cot \left(\frac{\pi}{2}-x\right)\right), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( A \)
B. -1
c. 0
D.
Subject: Chemistry
Which of the following is not a redox reaction?
A \( \cdot C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( O_{2}+2 H_{2} \longrightarrow 2 H_{2} O \)
c. \( N a+H_{2} O \longrightarrow N a O H+\frac{1}{2} H_{2} \)
D. \( M n C l_{3} \longrightarrow M n C l_{2}+\frac{1}{2} C l_{2} \)
Subject: Chemistry
At \( 80^{\circ} C, \) distilled water \( \left(H_{3} O^{+}\right) \) has
concentration equal to \( 1 \times \)
\( 10^{-6} \) mol/litre. The value of \( K_{w} \) at this
temperature will be:
A \( \cdot 1 \times 10^{-6} \)
B. \( 1 \times 10^{-12} \)
c. \( 1 \times 10^{-9} \)
D. \( 1 \times 10^{-15} \)
Subject: Physics
Find the acceleration of the point \( \boldsymbol{K} \)
A \( \cdot w=\frac{F\left(3 m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} \)
B. \( w=\frac{F\left(3 m_{1}+m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} \)
c. \( w=\frac{F\left(m_{1}+m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} \)
D. \( w=\frac{F\left(m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} \)
Subject: Physics
If \( ^{\prime} R^{\prime} \) is the radius of the earth, then the
height at which the weight of a body becomes \( \frac{1}{4} \) of its weight on the surface of the earth is:
A \( .2 . R \)
в. \( R \)
c. \( \frac{3 R}{8} \)
D. \( \frac{R}{4} \)
Subject: Maths
Two symmetrical dice are thrown 200 times. Getting a sum of 9 points is considered to be a success. The
probability distribution of successes is
\( ^{\mathbf{A}} \cdot\left(200, \frac{1}{9}, \frac{8}{9}\right) \)
в. \( \left(200, \frac{2}{9}, \frac{7}{9}\right) \)
\( ^{\mathrm{c}} \cdot\left(200, \frac{4}{9}, \frac{5}{9}\right) \)
D \( \cdot\left(200, \frac{1}{4}, \frac{3}{4}\right) \)
Subject: Physics
\( 4 \sqrt{2} m \) and breadth \( 4 m \) carrying a
current of \( 5 A \) in the anti-clockwise
direction is placed in the xy-plane. The
magnitude of the magnetic induction
field vector \( B \) at the intersection of the
diagonal is \( \left(U s e u_{0}=4 \pi x\right. \)
\( \left.10^{-7} N A^{-2}\right) \)
A \( .1 .2 \times 10^{-6} T \)
B . \( 1.2 \times 10^{-5} T \)
c. \( 2.4 \times 10^{-6} T \)
D. \( 2.4 \times 10^{-5} T \)
E \( .1 .2 \times 10^{-7} T \)
Subject: Chemistry
\( \begin{array}{ll}\text { Indicator } & \text { pH range } \\ \text { Methyl violet } & 0.3-1.8 \\ \text { Methyl orange } & 2.8-3.8 \\ \text { Congo red } & 2.8-4.8 \\ \text { Methyl red } & 3.8-6.1 \\ \text { Bromothylmol blue } & 6.0-7.9 \\ \text { Phenol Red } & 6.8-8.6\end{array} \) The table above shows the pH ranges of some common indicators. Given that
\( K_{a} \) is \( 7.3 \times 10^{-10} \) for boric acid
\( \left(H_{3} B O_{3}\right), \) Choose an indicator that can
be used for the titration of
\( \mathbf{0 . 1 0} \boldsymbol{M} \boldsymbol{K} \boldsymbol{H}_{2} \boldsymbol{B} \boldsymbol{O}_{3} \) with \( \mathbf{0 . 1 0} \mathbf{M} \mathbf{~ H C l} \)
A. Methyl orange
B. Congo Red
C. Methyl Red
D. Phenol Red
Subject: Chemistry
\( \begin{array}{cc}\boldsymbol{O H} & \boldsymbol{C H}_{3} \\ \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C H}-\boldsymbol{C H O} & \mid \\ & \boldsymbol{O H}\end{array} \)
The IUPAC name is:
A. 4 -hydroxy-1-methylpentanal
B. 3, 4-dihydroxy-2-methylpentanal
c. 2 -hydroxy- 4 -methylpentanal
D. 2, 3-dihydroxy-4-methylpentanal
Subject: Biology
Choose the correct answers from the
alternatives given. Which of the following is the correct order of classification?
A. Domain - Kingdom - Phylum - Class - Order - FamilyGenus - Species
B. Kingdom - Domain - Class - Phylum - Order - Family Genus - Species
c. Kingdom - Domain - class - Phylum - Order - Genus Species - Family
D. Kingdom - class - Phylum - Domain - Genus - Order Family - species
Subject: Chemistry
\( 50 L t r \) of a certain liquid is confined in a piston system at the external pressure 100atm. This pressure is suddenly released and liquid is expanded against the constant atmospheric pressure, volume of the liquid increases by 1 Lt \( r \) and the final pressure of the liquid is
100 atm. Find the work done.
A. 1 L. \( a+m \)
B. 5 Latm
c. 500 Latm
D. 50 L.atm
Subject: Physics
In the figure given above, the position
time graph of a particle of mass \( 0.1 k g \)
is shown. The impulse at \( t=2 \sec \) is:
A \( .0 .2 k g m s e c^{-} \)
B. - \( 0.2 k g m \) sec \( ^{-1} \)
c. \( 0.1 k \) gmsec \( ^{-1} \)
D. - \( 0.4 k g \) msec\( ^{-} \)
Subject: Chemistry
In the reaction of p-chlorotoluene with
\( \boldsymbol{K} \boldsymbol{N} \boldsymbol{H}_{2} \) in liquid \( \boldsymbol{N} \boldsymbol{H}_{3}, \) the major
product is:
A . o-toluidine
B. m-toluidine
c. p-toluidine
D. p-chloroaniline
Subject: Maths
If the ratio of the angles of a triangle is
2: 3: 5 then angles are
A \( \cdot 36^{\circ}, 54^{\circ}, 90^{\circ} \)
В . \( 18^{\circ}, 36^{\circ}, 126^{\circ} \)
c. \( 20^{\circ}, 60^{\circ}, 180^{\circ} \)
D. \( 18^{\circ}, 60^{\circ}, 102^{\circ} \)
Subject: Chemistry
The plot of \( \log _{e} R(R \) is radius of
nucleus) \( \boldsymbol{v} \boldsymbol{s} \log _{e} \boldsymbol{A}(\boldsymbol{A} \text { is mass no. }) \)
gives a straight line with slope equal to
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D. 3
Subject: Physics
kg of iron at \( 100^{\circ} \mathrm{C} \) can melt more ice
than \( 1 \mathrm{Kg} \) of copper at same temperature. Explain \( .(\text {Iron}= \)
\( 0.117 \mathrm{cal} g^{-1 o} C^{-1} ; s_{c o p p e r}= \)
\( \left.0.093 \operatorname{cal} g^{-1}^{o} C^{-1}\right) \)
Subject: Physics
The piston is taken completely out of the cylinder. The hole at the top is
sealed. A water tank is brought below the cylinder and put in a position, so that the water surface in the tank is at
the same level as the top of the cylinder as shown in the figure. The density of
the water is \( \rho \)
n equilibrium, then height \( H \) of the
water column in the cylinder satisfies
A \( \cdot \rho g\left(L_{0}-H\right)^{2}+P_{0}\left(L_{0}-H\right)+L_{0} P_{0}=0 \)
B . \( \rho g\left(L_{0}-H\right)^{2}-P_{0}\left(L_{0}-H\right)-L_{0} P_{0}=0 \)
C \( \cdot \rho g\left(L_{0}+H\right)^{2}+P_{0}\left(L_{0}-H\right)-L_{0} P_{0}=0 \)
D \( \cdot \rho g\left(L_{0}-H\right)^{2}-P_{0}\left(L_{0}-H\right)+L_{0} P_{0}=0 \)
Subject: Physics
A man hangs from a rope attached to a hot-air balloon. The mass of the man is
greater than the mass of the balloon
and its contents. The system is stationary in air. If the man now climbs up to the balloon using the rope, the
centre of mass of the 'man plus balloon
system wiii
A. remain stationary
B. move up
c. move down
D. first move up and then return to its initial position
Subject: Physics
When we press the bulb of dropper with
its nozzle kept in water, air in the
dropper is seen to escape in the form of bubbles. Once we release the pressure
on the bulb, water gets filled in the
dropper. The rise of water in the dropper
is due to:
A. Pressure of water
B. Gravity of the earth
c. shape of rubber bulb
D. Atmospheric pressure
Subject: Chemistry
If \( \mathrm{M} \) is the molarity, d is the density (in
\( g / m !), M_{B} \) is the molar mass of solute and \( m \) is the molality, then choose the correct relation?
A. \( \frac{1000 M}{1000 d+M \cdot M_{B}}=m \)
в. \( \frac{1000 M}{1000 d-m \cdot M_{B}}=M \)
c. \( \frac{1000 M}{1000 d-M \cdot M_{B}}=m \)
D. \( \frac{1000 M}{1000 d+m . M_{B}}=M \)
Subject: Maths
If \( \operatorname{Re}(a), \operatorname{Re}(b)>0, \) and \( x=|a-b| \)
\( |\bar{a}+b|, \) then
\( \mathbf{A} \cdot x<0 \)
B . \( x>0 \)
c. \( x \geq 1 \)
D.
Subject: Physics
An electric bulb has a rated power of \( 50 W \) at \( 100 V . \) If it is used on an \( A C \)
source \( 200 V, 50 H z, \) a choke has to be
used in series with it. This choke should
have an inductance of
\( \mathbf{A} \cdot 0.01 m H \)
в. \( 1 m H \)
\( c .0 .1 H \)
D. \( 1.1 H \)
Subject: Chemistry
Solid PCls exists as:
A \( . \) PCls molecule
в. \( \mathrm{P}_{2} \mathrm{Cl}_{10} \)
\( \mathbf{c} \cdot\left[\mathbf{P} \mathrm{Cl}_{4}\right]^{+} \) and \( \left[\mathrm{PCl}_{6}\right] \)
D. None of these
Subject: Chemistry
When an excess of a very dilute
aqueous solution of \( \mathrm{Kl} \) is added to a very dilute aqueous solution of silver nitrate, the colloidal particles of silver iodide
are associated with which of the
following Helmholtz double layer?
\( A \)
\[
\mathbf{A} \mathbf{g} \mathbf{I} / \mathbf{A} \mathbf{g}^{+} \vdots \mathbf{I}^{-}
\]
в.
\[
\mathbf{A} \mathbf{g} \mathbf{I} / \mathbf{K}^{+}: \mathbf{N} \mathbf{O}_{\mathbf{3}}^{-}
\]
c.
\[
\mathbf{A} \mathbf{g} \mathbf{I} / \mathbf{N} \mathbf{O}_{\mathbf{3}}^{-} \vdots \mathbf{A} \mathbf{g}^{+}
\]
D. \( \mathbf{A} \mathbf{g} \mathbf{I} / \mathbf{I}^{-} \vdots \mathbf{K}^{+} \)
Subject: Chemistry
The value of \( n \) in the following reaction
is :
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{n} e^{-}+\mathbf{1 4 H}^{+} \rightarrow \boldsymbol{2 C r}^{3+}+ \)
\( \mathbf{7} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O} \)
Subject: Chemistry
The brown ring test for \( N O_{2}^{-} \) and \( N O_{3}^{-} \) is due to the formation of complex ion
with formula:
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{2+} \)
B. \( \left[F e(N O)(C N)_{5}\right]^{2} \)
c. \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{NO}\right]^{2} \)
D. \( \left[F e\left(H_{2} O\right)(N O)_{5}\right]^{2+} \)
Subject: Biology
I ne gıven mgure represenis a sıngle nephron from a mammalian kidney.
Identify the labelled parts, match them
with the functions (i-iv) and select the
correct option.
(i) The site of ultrafiltration.
(ii) Particularly sensitive to ADH.
(iii) The main site for the re-absorption
of glucose and amino acids.
(iv) Largely responsible for the
maintenance of blood pH.
A \( \cdot(\text { i) }-A, \) (ii)-E, (iii)-C, (iv)-D
B. (i)-A, (ii)-B, (iii)-C, (iv)-D
C \( \cdot(i)-A,(\text { ii })-B,(i i i)-C,(i v)-E \)
D. (i)-A, (ii)-B, (iii)-D, (iv)-E
Subject: Physics
A tuning fork of frequency \( 340 H z \) is vibrated just above the tube of \( 120 \mathrm{cm} \) height. Water is poured slowly in the tube. What is the minimum height of water necessary for the resonance?
speed of sound in air \( =340 m / s \)
\( \mathbf{A} \cdot 45 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 40 \mathrm{cm} \)
D. \( 25 \mathrm{cm} \)
Subject: Physics
A particle A having a charge of \( 5.0 \times \)
\( 10^{-} 7 C \) is fixed in a vertical wall. \( A \)
second particle \( B \) of mass 100 g and having equal charge is suspended by a
silk thread of length \( 30 \mathrm{cm} \) above the
particle A. Find the angle of thread with
the vertical when it stays in
equilibrium.
Subject: Chemistry
A zinc electrode is placed in a \( 0.1 \mathrm{M} \)
solution at \( 25^{0} C . \) assuming that the salt is \( 20 \% \) dissociated at this dilutions
calculate the electrode reduction
potential. \( \boldsymbol{E}^{0}\left(\boldsymbol{Z} \boldsymbol{n}^{2+} \mid \boldsymbol{Z} \boldsymbol{n}\right)=-\mathbf{0 . 7 6} \boldsymbol{V} \)
Subject: Chemistry
A reaction mixture containing \( \boldsymbol{H}_{2}, \boldsymbol{N}_{2} \)
and \( N H_{3} \) has partial pressure 2 atm, latm and 3 atm respectively at 725 K. If
the value of \( K \) for the reaction. \( N_{2}+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3} \) is \( \mathbf{4 . 2 8} \times \mathbf{1 0}^{-\mathbf{5}} \)
\( \operatorname{atm}^{-2} \) at \( 725 \mathrm{K}, \) in which direction the net reaction will go:
A. forwarddard
B. backward
c. no net reaction
D. direction of reaction cannot be predicted
Subject: Biology
\( \ln \mathrm{F}_{2} \) generation, quantitative
inheritance ratio \( 1: 4: 6: 4: 1, \) is
obtained instead of
\( A \cdot 9: 3: 3: 1 \)
B. 8: 6: 4: 1
c. 7: 4: 1: 4
D. 6: 6: 4: 7
Subject: Physics
\( 5 k g \) block rests on horizontal surface.
Which of the following option is
incorrect? \( \left(\boldsymbol{g}=\mathbf{1} \mathbf{0} \mathbf{m} / \mathbf{s}^{\mathbf{2}}\right) \)
This question has multiple correct options
A. The normal force on the block equals its weight because of Newton's second law
B. The normal force on the block is equal to the weight not because of Newton's third law
C. The normal force on the block equals its weight because of Newton's third law
D. The normal force on the block is 50 N.
Subject: Physics
When a sound wave of wavelength \( \lambda \) is propagating in a medium the maximum velocity of the particle is equal to wave velocity. The amplitude of the wave is
\( A \cdot \lambda \)
B. \( \frac{\lambda}{2} \)
\( c \cdot \frac{\lambda}{2 \pi} \)
D. \( \frac{\lambda}{4 \pi} \)
Subject: Physics
The figure given below shows a container \( C \) partially filled with water There is a plane mirror \( \mathrm{M} \) at the bottom of the container. A light ray AB incidents on the surface of water at angle of
incidence \( 30^{\circ} . \) Copy and complete the ray diagram. Mark the ray emerging from the water surface. Refractive index
of water \( =\frac{4}{3} \)
Subject: Physics
A small spherical drop fall from rest in viscous liquid. Due to friction, heat is produced. The correct relation between the rate of production of heat and the radius of the spherical drop at terminal velocity will be
A \( \cdot \frac{d H}{d t} \propto \frac{1}{r^{5}} \)
в. \( \frac{d H}{d t} \propto r^{4} \)
c. \( \frac{d H}{d t} \propto \frac{1}{r^{4}} \)
D. \( \frac{d H}{d t} \propto r^{5} \)
Subject: Chemistry
A fuel cell is:
I.A voltaic cell in which continuous supply of fuels are sent at anode to perform oxidation.
II. A voltaic cell in which fuels such as:
\( C H_{4}, H_{2} \) and \( \mathrm{CO} \) are used up at anode.
III. One which involves the reaction of
\( H_{2} O_{2} \) fuel cell such as:
Anode \( : 2 H_{2}+4 \stackrel{\ominus}{O} H \rightarrow 4 H_{2} O(l)+4 e^{-} \)
Cathode \( : O_{2}+2 H_{2} O(l)+4 e^{-} \rightarrow 4 \stackrel{\ominus}{O} H \)
IV. The efficiency of \( H_{2}-O_{2} \) fuel cell is 70
to \( 75 \% \)
A. \( I, I I I \)
в. \( I, I I I, I V \)
c. \( I, I I, I I I, I V \)
D. \( I, I I, I I I \)
Subject: Physics
A ray of light travelling in impure water is incident on a glass plate immersed in
it. When the angle of incidence is \( 51^{\circ} \) the reflected ray is totally plane polarized. Given that refractive index of impure water if \( 1.4 . \) The refractive index
of glass should be
\( \left(\tan 51^{\circ}=1.235\right) \)
A . 1.64
в. 1.34
c. 1.53
D. 1.73
Subject: Chemistry
The pair of compounds that can exist
together is:
\( \mathbf{A} \cdot F e C l_{3}, S n C l_{2} \)
\( \mathbf{B} \cdot H g C l_{2}, S n C l_{2} \)
\( \mathbf{c} \cdot F e C l_{2}, S n C l_{2} \)
\( \mathbf{D} \cdot F e C l_{3}, K I \)
Subject: Physics
A student is rotating on a stool at an
angular velocity \( ^{\prime} \omega^{\prime} \) with their arms outstretched while holding a pair of
masses. The frictional effects of the
stool are negligible. Which of the following actions would
result in a change in angular momentum for the student?
A. A clockwise torque of \( 50 \mathrm{Nm} \) and a counterclockwise torque of \( 25 \mathrm{Nm} \) are both applied to the students arms by fellow students
B. The student brings the masses closer to their body
c. The student stretches the masses further away from their body
D. A second student steps onto the stool with the first student
E. A clockwise torque of \( 50 \mathrm{Nm} \) and a counterclockwis torque of \( 50 \mathrm{Nm} \) are both applied to the students arms
by fellow students
Subject: Chemistry
Assertion
In trigonal bipyramidal structure two axial bonds are longer than the
equitorial bonds.
Reason
Axial bonds suffer more repulsion as
compared to equitorial bonds.
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
If \( \boldsymbol{P}\left(\boldsymbol{E}_{k}\right)=\boldsymbol{C} \) for \( \mathbf{0} \leq \boldsymbol{k} \leq \boldsymbol{n}, \) then the
probability that \( X \) is the only student to pass the examination is
A \( .3 / 4 n \)
B. \( 2 /(n+1) \)
c. \( 2 / n(n+1) \)
D. \( 3 / n(n+1) \)
Subject: Physics
A rod \( 70 \mathrm{cm} \) long is clamped from middle. The velocity of sound in the
material of the rod is 3500 ms\( ^{-1} \). The
frequency of fundamental note
produced by it is :
A. \( 3500 \mathrm{Hz} \)
B . \( 2500 H z \)
c. \( 1250 H z \)
D. \( 700 \mathrm{Hz} \)
Subject: Maths
A vector of magnitude \( |\Psi| \) is turned
through angle \( \frac{\phi}{2} . \) The magnitude of
change in the vector is given by
A \( \cdot 2 \mid \Psi \| \cos \phi / 4 \)
B . \( |\Psi| \mid \sin \phi / 4 \)
\( \mathbf{C} \cdot|\Psi|^{2}|\sin \phi / 4|^{2} \)
D. \( 2|\Psi \| \sin \phi / 4| \)
Subject: Chemistry
1.0 molal aqueous solution of an
electrolyte \( A_{2} B_{3} \) is \( 60 \% \) ionized. The
boiling point of the solution at 1 atm is:
\( \left[\boldsymbol{K}_{\boldsymbol{b}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)}=\mathbf{0 . 5 2} \boldsymbol{K} \boldsymbol{k g} \boldsymbol{m o l}^{-1}\right] \)
A. \( 274.76 \mathrm{K} \)
B. 377 К
c. 376.4 к
D. \( 374.72 \mathrm{K} \)
Subject: Physics
The circuit shown in Figure contains
three resistors \( \boldsymbol{R}_{1}=\mathbf{1 0 0} \boldsymbol{\Omega}, \boldsymbol{R}_{2}=\mathbf{5 0} \boldsymbol{\Omega} \)
and \( R_{3}=20 \Omega \) and cells of emfs \( E_{1}= \)
\( 2 V \) and \( E_{2} . \) The ammeter indicates a
current of 50 mA. Determine the
currents in the resistors and the emf of
the second cell. The internal resistance
of the ammeter and of the cells should
be neglected
Subject: Physics
A current \( i \) ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any
point inside the tube is
\( A \cdot \infty \)
в. zero
c. \( \frac{\mu_{0}}{4 \pi} \cdot \frac{2 i}{r} \) tesla
D. \( \frac{2 i}{r} \) tesla
Subject: Maths
If \( f(x) \) is a polynomial in \( x, \) then
the second derivative of \( f\left(e^{x}\right) \) at \( x=1 \)
is
A \( \cdot e f^{\prime \prime}(e)+f^{\prime}(e) \)
B . \( \left(f^{\prime \prime}(e)+f^{\prime}(e)\right) e^{2} \)
c. \( e^{2} f^{\prime \prime}(e) \)
D. \( \left(f^{\prime \prime}(e) e+f^{\prime}(e)\right) e \)
Subject: Maths
Find \( \boldsymbol{a}^{3} \) if \( \left(\frac{2}{\mathbf{7}}\right)^{\boldsymbol{a}}=\left(\frac{\mathbf{1 6}}{\mathbf{2 1}}\right)^{-\mathbf{5}} \times\left(\frac{\mathbf{3}}{\mathbf{8}}\right)^{-5} \)
Subject: Physics
An otherwise infinite, straight wire has
two concentric loops of radii \( a \) and \( b \)
carrying equal currents in opposite directions as shown in figure. The
magnetic field at the common center is
zero for:
\( ^{\mathrm{A}} \cdot \frac{a}{b}=\frac{\pi-1}{\pi} \)
B. \( \frac{a}{b}=\frac{\pi}{\pi+1} \)
c. \( \frac{a}{b}=\frac{\pi-1}{\pi+1} \)
D. \( \frac{a}{b}=\frac{\pi+1}{\pi-1} \)
Subject: Physics
For the battery shown in the figure:
This question has multiple correct options
A. equivalent internal resistance R is given by:
\( \frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}} \)
B. if \( E_{3}=\frac{\left(E_{1} R_{2}+E_{2} R_{1}\right)}{\left(R_{1}+R_{2}\right)} \), equivalent e.m.f. of the battery
will be equal to \( E_{3} \)
C . equivalent e.m.f. of the battery is equal \( E=\left(E_{1}+\right. \)
\( E_{2}+E_{3} / 3 \)
D. equivalent e.m.f. of the battery not only depends upon values \( E_{1}, E_{2} \) and \( E_{3} \) but depends upon valiues of \( R_{1} \) and \( R_{3} \) also