AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
If a body is taken up to a height of \( 1600 \mathrm{km} \) from the earth's surface, then the percentage loss of gravitational force acting on that body will be -
(Radius of earth \( R_{e}=6400 \mathrm{km} \) ).
A . 50\%
B. 36\%
c. 25\%
D. 10\%
Subject: Chemistry
The common impurity present in
bauxite is:
\( \mathbf{A} \cdot F e_{2} O_{3} \)
в. \( A l_{2} O_{3} . H_{2} O \)
c. \( A l C l_{3} . A I_{2} O_{3} \)
D. \( M g C l_{2} . C a C l_{2} \)
Subject: Physics
A uniform rod of mass \( 15 k g \) is held
stationary with the help of a light string as shown in fig. \( \boldsymbol{L}=\mathbf{5} \boldsymbol{m}, \) angle between
rod and ground is \( 37^{0} . \) The tension in the
string is :
A . \( 150 N \)
B. \( 225 N \)
c. \( 100 N \)
D. None of these
Subject: Maths
Solve: \( 4 x+\frac{6}{y}=15 \) and \( 6 x-\frac{8}{y}=14 \)
Hence, find \( \boldsymbol{a} \) if \( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}-\boldsymbol{2} \)
A \( \cdot x=2 ; y=26 \) and \( a=2 \frac{5}{3} \frac{5}{3} \)
B・ \( x=3 ; y=2 \) and \( a=1 \frac{1}{3} \)
c. \( _{x}=1 ; y=5 \) and \( a=2 \frac{7}{3} \)
D. \( x=5 ; y=1 \) and \( a=5 \frac{1}{8} \)
Subject: Chemistry
The angular momentum (L)(L) of an electron in a Bohr orbit is given as:
\( ^{A} \cdot L=\frac{n h}{2 \pi} \)
B. \( L=\sqrt{l(l+1) \frac{h}{2 \pi}} \)
\( \mathbf{c} \cdot L=\frac{m g}{2 \pi} \)
D. \( L=\frac{h}{4 \pi} \)
Subject: Chemistry
The main product obtained when a solution of sodium carbonate reacts
with mercuric chloride is :
\( \mathbf{A} \cdot H g(O H)_{2} \)
в. \( H g C O_{3} . H g O \)
\( \mathrm{c} . \mathrm{Hg} \mathrm{CO}_{3} \)
D. \( H g C O_{3} . H g(O H)_{2} \)
Subject: Physics
Equal masses of methane and hydrogen are mixed in an empty container at
\( 25^{\circ} \mathrm{C} . \) The fraction of the total pressure
exerted by hydrogen is:
A \( \cdot \frac{1}{2} \)
в.
\( c \cdot \frac{1}{9} \)
D. \( \frac{16}{17} \)
Subject: Physics
An AC circuit contains a variable
inductor \( L, \) connected in series with a
light bulb of resistance \( R \) as shown
Assume that the resistance of the light bulb is independent of its temperature. Now it is desired to reduce the power of the light bulb to one fourth then
(frequency of ac source is \( \frac{R}{2 \pi L_{0}} \) wher
This question has multiple correct options
A. Power factor of the circuit should be reduced to half
B. Inductance of the circuit should be increased by a factor of \( \sqrt{3} \)
c. Impedance of the circuit should be increased by a factor of 4
D. R.M.S. current in the circuit should be reduced to half
Subject: Chemistry
Column-I
(A) Tyrosine
(P)Essential amino acids
(B) Serin
(Q) Ceric Ammonium Nitrate
\( (\mathrm{C}) \)
Tryptophane
(R) Neutral \( F e C l_{3} \)
(S) Carbaylamine Test -
(D) Proline \( \quad \) Negative.
Select the correct set of answer.
\( A \cdot A-R, B-Q, C-P, D-S \)
B. A-Q, B-R, C-S, D-P
C. \( A-R, B-P, C-Q, D-S \)
D. A-S, B-Q, C-P, D-R
Subject: Physics
An \( \alpha \) -particle and proton are
accelerated from rest through same potential difference and both enter into a uniform perpendicular magnetic field. Find the ratio of their radii of curvature.
A. \( \sqrt{7}: 1 \)
B. \( \sqrt{5}: 1 \)
c. \( \sqrt{2}: 1 \)
D. \( \sqrt{3}: 1 \)
Subject: Physics
In a potentiometer wire experiment, the
emf of a battery in the primary circuit is \( 20 V \) and its internal resistance is \( 5 \Omega \)
There is a resistance box in series with
the battery and the potentiometer wire, whose resistance can be varied from
\( 120 \Omega \) to \( 170 \Omega \). Resistance of the
potentiometer wire is \( 75 \Omega \). The following potential differences can be measured using this potentiometer This question has multiple correct options
\( \mathbf{A} \cdot 5 V \)
B. \( 6 V \)
c. \( 7 V \)
D. \( 8 V \)
Subject: Physics
The current \( I \) and voltage \( V \) graphs for a
given metallic wire at two different
temperatures \( T_{1} \) and \( T_{2} \) are shown in
the figure. It is concluded that :
A \( \cdot T_{1}>T_{2} \)
В. \( T_{1}<T_{2} \)
\( \mathbf{c} \cdot T_{1}=T_{2} \)
D. \( T_{1}=2 T_{2} \)
Subject: Chemistry
Among the following ions which has the highest paramagnetism?
\( \mathbf{A} \cdot\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} \)
B・ \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \)
\( \mathbf{c} \cdot\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \)
\( D \cdot\left[z n\left(H_{2} O\right)_{6}\right]^{2+} \)
Subject: Physics
A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 - divisions per milliampere and
voltage sensitivity is 2 divisions per millivolt. In order that
each division reads 1 volt, the resistence in ohms needed to be
connected in series with the coil will be
A . 103
B . 10
\( c .9995 \)
D. 99995
Subject: Maths
The contrapositive of the statement "If you believe in yourself and are honest
then you will get sucess" is
A. If you do not believe yourself and are dishonest then you will not get success.
B. If you do not believe yourself and are dishonest then you will get success
c. If you get success then you are honest and you also believe in yourself.
D. If you will not get success then you don't not believe in yourself or are not honest
Subject: Maths
If \( 2 \vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \) then the angle between \( \vec{a} \) and \( \vec{b} \) is
A \( .30^{\circ} \)
в. \( 0^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 60^{\circ} \)
Subject: Physics
A source of sound gives five beats per second, when sounded with another
source of frequency \( 100 s^{-1} \). The second
harmonic of the source together with a source of frequency \( 205 s^{-1} \) gives
5 beats/sec. The frequency of the first source is
A \( \cdot 105 s^{-1} \)
B. \( 205 s^{-1} \)
c. \( 95 s^{-1} \)
D. \( 100 s^{-1} \)
Subject: Physics
A resistance of \( 4 \Omega \) and a wire of length
\( 5 m \) and resistance \( 5 \Omega \) are joined in
series and connected to a cell of e.m,f,
\( \mathbf{1 0} V \) and internal resistance \( 1 \Omega . A \)
Parallel combination of two identical
cells is balanced across \( 300 \mathrm{cm} \) of the
wire. the e.m.f. \( \boldsymbol{E} \) each cell is then:
A \( .1 .5 ~ V \)
в. \( 3.0 V \)
\( c .0 .67 V \)
0.1 .33
Subject: Maths
\( \int \frac{2 d x}{x^{2}-1} \) equals:
\( \mathbf{A} \cdot \frac{1}{2} \log \left(\frac{x+1}{x-1}\right)+C \)
B \( \cdot \frac{1}{2} \log \left(\frac{x-1}{x+1}\right)+C \)
\( \mathbf{c} \cdot \log \left(\frac{x+1}{x-1}\right)+C \)
D \( \log \left(\frac{x-1}{x+1}\right)+C \)
Subject: Maths
Let \( a \) denote the element of the \( i^{t h} \) row
and \( j^{t h} \) column in a \( 3 \times 3 \) matrix and let
\( \boldsymbol{a}_{i j}=-\boldsymbol{a}_{j i} \) for every i and j then this
matrix is an -
A. Orthogonal matrix
B. singular matrix
c. matrix whose principal diagonal elements are all zero
D. skew-symmetric matrix
Subject: Physics
A block of mass 2 kg falls from the wall at height of \( 2.3 \mathrm{m} \). Calculate the velocity just before it hits the ground. \( (g= \)
\( -9.8 \frac{m}{s^{2}} \)
A \( \cdot-6.76 \frac{n}{s} \)
В. \( -26.86 \frac{m}{s^{2}} \)
\( \mathbf{c} \cdot 45.08 \frac{m}{s} \)
D. \( 13.43 \frac{m}{s} \)
E \( \cdot 3.36 \frac{m}{s} \)
Subject: Physics
An automobile is started from rest with
one of its doors initially at right angles. If the hinges of the door are toward the front of the car, the door will shut as the
automobile picks up speed. The acceleration a is constant and the
centre of mass is at a distance d from
the hinges. The time \( T \) needed for the doors to close is given by:
\( \left[\text {Given}: \int_{0}^{\frac{\pi}{2}} \frac{\boldsymbol{d} \boldsymbol{\theta}}{\sqrt{\sin \theta}}=\boldsymbol{N}\right] \) (Consider
the door as a square plate)
A \( \cdot \mathrm{T}=(\sqrt{\frac{3 \mathrm{d}}{2 \mathrm{a}}}) \mathrm{N} \)
B. \( \mathrm{T}=(\sqrt{\frac{\mathrm{d}}{3 \mathrm{a}}}) \mathrm{N} \)
c. \( \mathrm{T}=(\sqrt{\frac{2 \mathrm{d}}{\mathrm{a}}}) \mathrm{N} \)
D. \( \mathrm{T}=(\sqrt{\frac{2 \mathrm{d}}{3 \mathrm{a}}}) \mathrm{N} \)
Subject: Physics
A projectile is fired 30.0 degrees above the horizontal with speed \( \left|\boldsymbol{v}_{1}\right|=\mathbf{4 0 m} / \boldsymbol{s} \)
and a second one 60.0 degrees above
the horizontal with speed \( \left|\boldsymbol{v}_{2}\right|=\mathbf{3 0 m} / \boldsymbol{S} \)
simultaneously. After 2 seconds, how far apart will the two projectiles be? Assume no air resistance and that they are fired from
the same spot, and that each moves independent of the outer projectile. Take \( \boldsymbol{g}=\mathbf{9 . 8 1 m} / \boldsymbol{s}^{2} \)
A . \( 11.96 m \)
в. \( 28.11 m \)
\( \mathrm{c} .39 .28 \mathrm{m} \)
D. 41.06 m
E . \( 41.99 \mathrm{m} \)
Subject: Chemistry
Calculate the equilibrium constants for the reactions with water of
\( H_{2} P O_{4}^{\ominus}, H P O_{4}^{2-} \) and \( P O_{4}^{3-} \) as base
Comparing the relative values of two equilibrium constants of \( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{\ominus} \) with
water, deduce whether solutions of this
ion in water are acidic or bases. Deduce
whether solutions of \( \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} \) are acidic
or bases. Given \( K_{1}, K_{2} \) and \( K_{3} \) for
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) are \( \mathbf{7 . 1} \times \mathbf{1 0}^{-\mathbf{3}}, \mathbf{6 . 3} \times \mathbf{1 0}^{-\mathbf{8}} \) and
\( 4.5 \times 10^{-13} \) respectively
A \( .1 .4 \times 10^{-12}, 1.6 \times 10^{-7}, 2.2 \times 10^{-2}, H_{2} P O_{4}^{\circ} \) is acidic
and \( H P O_{4}^{2-} \) is basic
B . \( 2.2 \times 10^{-12}, 1.6 \times 10^{-7}, 1.4 \times 10^{-2}, H_{2} P O_{4}^{\ominus} \) is basic and
\( H P O_{4}^{2-} \) is basic
C \( .2 .2 \times 10^{-12}, 1.6 \times 10^{-7}, 1.4 \times 10^{-2}, H_{2} P O_{4}^{\circ} \) is acidic
and \( H P O_{4}^{2-} \) is basic
D. \( 1.4 \times 10^{-12}, 1.6 \times 10^{-7}, 2.2 \times 10^{-2}, H_{2} P O_{4}^{\circ} \) is basic
and \( H P O_{4}^{2-} \) is acidic
Subject: Physics
Three bricks each of length \( L \) and mass
\( M \) are arranged as shown from the wall.
The distance of the centre of mass of
the system from the wall is?
A \( \frac{11}{12} L \)
в. \( \frac{7}{8} L \)
c. \( \frac{1}{12} L \)
D. \( \frac{15}{1} L \)
Subject: Physics
A particle falling with constant acceleration covers \( 3 m \) distance in
third second of its motion. The distance
covered in first 5 second shall be: (Take
\( \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2} \mathbf{)} \)
A . \( 5 m \)
B. \( 15 m \)
\( c .30 m \)
D. \( 45 \mathrm{m} \)
Subject: Maths
The points \( \boldsymbol{A}(\mathbf{2}, \mathbf{9}), \boldsymbol{B}(\boldsymbol{a}, \mathbf{5}), \boldsymbol{C}(\mathbf{5}, \mathbf{5}) \) are
the vertices of a triangle \( A B C \) right
angled at B. find the value of \( ^{\prime} a^{\prime} \) and
hence the area of \( \Delta A B C \)
Subject: Physics
The escape velocity for a planet is \( \boldsymbol{v}_{e} \cdot \mathbf{A} \) tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be
A \( \cdot v_{c} \)
в. \( \frac{v_{e}}{\sqrt{2}} \)
c. \( \frac{v_{e}}{2} \)
D. zero
Subject: Chemistry
The electronic configuration of \( _{59} P r \) (Praseodymium) is?
A \( \cdot\left[_{54} X e\right] 4 f^{2} 5 d^{1} 6 s^{2} \)
B . \( \left[_{54} X e\right] 4 f^{1} 5 d^{2} 6 s^{2} \)
c. \( \left[_{54} X e\right] 4 f^{3} 6 s^{2} \)
D・ \( \left[_{54} X e\right] 4 f^{3} 5 d^{2} \)
Subject: Maths
Let \( \boldsymbol{\alpha}, \boldsymbol{\beta} \in \boldsymbol{R} \) be such that
\( \lim _{x \rightarrow 0} \frac{x^{2} \sin (\beta x)}{a x-\sin x}=1 . \) Then \( 6(\alpha+\beta) \)
equals
A . 5
B. 7
\( c \cdot 8 \)
\( D \)
Subject: Physics
A violin string emits sound of frequency \( 510 H z . \) How far will the sound waves
reach when string complete 250 vibrations? The velocity of sound is \( 340 m / s \)
A. \( 166.7 \mathrm{m} \)
B . 366.7 m.
c. \( 266.7 \mathrm{m} \)
D. \( 566.7 m \)
Subject: Chemistry
Thiosulphate reacts differently with iodine and bromine in the reaction
given below. \( \mathbf{2} \boldsymbol{S}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{3}}^{\mathbf{2}-}+\boldsymbol{I}_{\mathbf{2}} \rightarrow \boldsymbol{S}_{\mathbf{4}} \boldsymbol{O}_{\mathbf{6}}^{\mathbf{2}-}+\mathbf{2} \boldsymbol{I}^{-} \)
\( \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}+\boldsymbol{2} \boldsymbol{B} \boldsymbol{r}_{2}+\mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{4}^{2-}+ \)
\( 2 B r^{-}+10 H^{+} \)
Which of the following statement justifies the above dual behaviour of thiosulphate?
A. Bromine is stronger oxidant than iodine
B. Bromine is weaker oxidant than iodine
c. Thiosulphate undergoes oxidation by bromine and reduction by iodine in above reactions
D. Bromine undergoes oxidation and iodine undergoes reduction in above reactions
Subject: Physics
The value of \( ^{\prime} g^{\prime} \) will be \( 1 \% \) of its value at the surface of the earth at a height of
\( \left(R_{e}=6400 k m\right) \)
\( A \cdot 6400 \mathrm{km} \)
B. 57600 km
c. \( 12560 \mathrm{km} \)
D. 64000 km
Subject: Maths
A student appears for tests, I, II and III The student is successful if he passes in
tests I, Il or I, Ill. The probabilities of the student passing in tests I, II and III are espectively \( \mathrm{p}, \mathrm{q} \) and \( \frac{1}{2} . \) If the probability of the student to be successful is \( \frac{1}{2} \) then
A \( \cdot p(1+q)=1 \)
B. \( q(1+p)=1 \)
c. \( p q=1 \)
D. \( \frac{1}{p}+\frac{1}{q}=1 \)
Subject: Physics
Classify the following as motion along a straight line, circular or oscillatory
motion.
(i) Motion of your hands while running.
(ii) Motion of a horse pulling a cart on a straight road.
(iii) Motion of a child in a merry-goround.
(iv) Motion of a child on a see-saw.
(v) Motion of a hammer of an electric
bell.
(vi) Motion of a train on a straight bridge.
Subject: Physics
An object of height \( 2.5 \mathrm{cm} \) is placed at a
distance of \( 15 \mathrm{cm} \) from the optical centre 'O' of a convex lens of focal length
10cm. Draw a ray diagram to find the position and the size of the image formed. Mark optical center'o', principal focus \( F \) and height of the image in the diagram.
Subject: Chemistry
\( F e_{2} O_{3}(s) \) may be converted be Fe by the
reaction, \( \boldsymbol{F e}_{2} \boldsymbol{O}_{3}+\boldsymbol{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{F} \boldsymbol{e}(\boldsymbol{s})+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) ; \) for which \( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{8} \) at
temperature \( 720^{0} C . \) What \( \% \) of \( H_{2} \)
remains unreacted after the reaction
has come to equilibrium:
\( \mathbf{A} \cdot \approx 22 \% \)
в. \( \approx 34 \% \) о
\( \mathbf{c} \cdot \approx 66 \% \)
\( \mathrm{D} \cdot \approx 78 \% \)
Subject: Chemistry
The half life of \( C-14 \) is 5600 years. \( A \)
sample of freshly cut wood from a tree contains \( 10 \mathrm{mg} \) of \( \mathrm{C}-14 . \) The amount left in the sample after 50000 years is \( (a- \)
\( x) \times 100 . \) The value of \( (a-x) \times 100 \) is :
A . \( 1 \mathrm{mg} \)
B. 2 mg
c. \( 3 \mathrm{mg} \)
D. \( 4 \mathrm{mg} \)
Subject: Maths
Evaluate: \( \int_{\alpha}^{\beta} \sqrt{\frac{\boldsymbol{x}-\boldsymbol{\alpha}}{\boldsymbol{\beta}-\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot \frac{\pi}{2}(\beta-\alpha) \)
В \( \cdot \frac{\pi}{2}(\alpha-\beta) \)
c. \( \pi(\beta-\alpha) \)
D. \( \pi(\alpha-\beta) \)
Subject: Biology
Which of the following statements will not hold true if a plant is grown in only
sand \( (\mathrm{S}), \) only clay (C) and only humus
\( (H) ? \)
A. Water availability to the roots will be more in (C) and
(H) as compared to (S)
B. Ability of roots to penetrate (S) and (H) will be low as compared to (C).
C. Nutrient availability to roots will be less in (S) as compared to (C) and (H).
D. Oxygen availability to roots will be low in (C) as compared to (S) and (H).
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c} \) are mutually perpendicular vectors of equal magnitudes, then the angle between the vectors \( \vec{a} \) and \( \vec{a}+ \) \( \vec{b}+\vec{c} \) is
A \( \cdot \frac{\pi}{3} \)
в.
\( ^{\mathrm{c}} \cdot \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
D.
Subject: Maths
Find matrix \( \boldsymbol{X} \) so that \( \boldsymbol{X}\left[\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5} & \mathbf{6}\end{array}\right]= \)
\( \left[\begin{array}{ccc}-\mathbf{7} & -\mathbf{8} & -\mathbf{9} \\ \mathbf{2} & \mathbf{4} & \mathbf{6}\end{array}\right] \)
Subject: Chemistry
Standard enthalpies of formation of \( \boldsymbol{O}_{3} \)
\( C O_{2}, N H_{3} \) and \( H I \) are 142.2,-393.2
-46.2 and +25.9 kJ \( m o l^{-1} \) respectively
The order of their increasing stabilities will be:
A. \( O_{3}, C O_{2}, N H_{3}, H I \)
в. \( C O_{2}, N H_{3}, H I, O_{3} \)
c. \( O_{3}, H I, N H_{3}, C O_{2} \)
D. \( N H_{3}, H I, C O_{2}, O_{3} \)
Subject: Physics
In a circuit \( \mathrm{L}, \mathrm{C} \) and \( \mathrm{R} \) are connected in
series with an alternating voltage source of frequency v. The current leads
the voltage by \( 45^{0} . \) The value of \( C \) is
A \( \cdot \frac{1}{\pi v(2 \pi v L-R)} \)
B . \( \frac{1}{2 \pi v(2 \pi u L-R)} \)
c. \( \frac{1}{\pi v(2 \pi v L+R)} \)
D. \( \frac{1}{2 \pi v(2 \pi v L+R)} \)
Subject: Chemistry
Assuming that the behavior of ammonia is correctly described by the van der Waal's equation near the critical point, and knowing the critical
molar volume of \( 0.72500 \mathrm{mol} L^{-1} \) and
critical temperature of \( 405.3 \mathrm{K} \) determine the critical pressure of
ammonia.
\( A \cdot 109.8 \) atm
B. 141.3 atm
c. 152.6 atm
D. 17.20 atm
Subject: Maths
A farmer spends \( 30 \% \) of his earning of a month on buying seeds and deposits \( 15 \% \) of his earning in the bank. If he spent Rs 9000 on these two items, then his total earning of the month is
A. \( R s .10 .000 \)
B. \( R s .20,000 \)
c. \( R s .24,000 \)
D. Rs.25, 000
Subject: Maths
A box contains 100 tickets numbered
\( 1,2, \dots, 100 . \) Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not
more than \( 10 . \) The probability that the
minimum number on them is 5 is
A \( \cdot \frac{1}{9} \)
B. \( \frac{2}{9} \)
\( c \cdot \frac{3}{9} \)
D. \( \frac{4}{9} \)
Subject: Physics
A \( 0.5 m \) long straight wire in which a
current of \( 3.2 A \) is flowing is kept at right angle to a uniform magnetic field
of \( 2.0 T . \) The force acting on the wire will
be:
A \( .2 N \)
в. 2.4 и
\( c .3 .2 N \)
D. 3N
Subject: Physics
The deflection in galvanometer falls to \( \left[\frac{1}{4}\right]^{t h} \) when it is shunted by \( 3 \Omega \). If additional shunt of \( 2 \Omega \) is connected to earlier shunt, the deflection in galvanometer falls to
A \( \cdot \frac{1}{2} \)
B. \( \frac{1^{r d}}{3} \)
c. \( \frac{1}{4}^{t h} \)
D. \( \frac{1}{8.5} \)
Subject: Physics
In the elastic collision of heavy vehicle
moving with a velocity \( 10 \mathrm{ms}^{-1} \) and a small stone at rest, the stone will fly away with a velocity equal to:
A. \( 40 \mathrm{ms}^{-1} \)
B. 20 \( \mathrm{ms}^{-1} \)
\( c \cdot 10 \mathrm{ms}^{-1} \)
\( D \cdot 5 \mathrm{ms}^{-1} \)
Subject: Physics
The instantaneous values of alternating current and voltages in a circuit are given as
\( \mathrm{i}=\frac{1}{\sqrt{2}} \sin (100 \pi t) \) ampere
\( \mathrm{e}=\frac{1}{\sqrt{2}} \sin (100 \pi t+\pi / 3) \mathrm{volt} \)
The average power in Watts consumed in the circuit is:
A \( \frac{\sqrt{3}}{4} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{8} \)
D. 4
Subject: Physics
An element \( d l=d x i=(w h e r e d x= \)
1 \( c m \) ) is placed at origin and carries a
current \( 10 A . \) What is the magnetic field
on \( y \) - axis at a dist. of \( 0.5 m ? \)
A \( \cdot 2 \times 10^{-8} k T \)
В. \( 4 \times 10^{-8} k T \)
c. \( -2 \times 10^{-8} k T \)
D. \( -4 \times 10^{-8} k T \)
Subject: Chemistry
Consider a sample of helium and a
sample of neon, both \( a t 30^{0} C \) and
1.5 atm. Both samples have a volume of
5.0 \( L \). Which statement concerning these samples is not true?
A. Each sample contains the same number of atoms of gas
B. Each sample weighs the same amount
c. Each sample contains the same number of moles of gas
D. The density of the neon is greater than the density of the helium
Subject: Maths
If \( \boldsymbol{y}=\cos ^{-1} \boldsymbol{x} \) then \( \left(1-\boldsymbol{x}^{2}\right) \boldsymbol{y}^{\prime \prime}-\boldsymbol{x} \boldsymbol{y}^{\prime}=? \)
where \( \boldsymbol{y}^{\prime}=\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
A . 1
B.
\( c \cdot 2 x \)
D. \( 2 y \)
Subject: Physics
A thin metal rod of length \( 0.6 m \) is in
vertical straight position on horizontal floor. This rod is falling freely to a side without slipping. The angular velocity of rod when its top end touches floor, is :
A .7 rads\( ^{-1} \)
B. 4.2 rads\( ^{-1} \)
c. 3.5 rads\( ^{-1} \)
D. \( 2.1 \mathrm{rads}^{-1} \)
Subject: Physics
A \( 10 m \) long uniform metallic write
having a resistance of \( 20 \Omega \) is used as a potentiometer wire. This wire is
connected in series with another
resistance of \( 480 \Omega \) and a battery of emf \( 5 V \) having negligible internal resistance. If an unknown emf e is
balanced across \( 6 m \) of the
potentiometer wire, calculate:
(i) The potential gradient across the potentiometer wire.
(ii) The value of the unknown emf e.
Subject: Physics
A car of mass \( M \) is moving on a
horizontal circular path of radius \( r . A t \)
an instant, its speed is \( \boldsymbol{v} \) and is
increasing at the rate \( a \). Then
This question has multiple correct options
A. The acceleration of the car is towards the centre of the path
B. The magnitude of the frictional force on the car is greater than \( \frac{m v^{2}}{r} \)
C. The friction coefficient between the ground and the car is not less than a/g
D. The friction coefficient between the ground and the car is \( \mu=\tan ^{-1} \frac{v^{2}}{r g} \)
Subject: Physics
When two unknown resistances are
placed in the gaps of meterbridge, the null point is found to be \( 40 \mathrm{cm} \) from one
end of the bridge wire. When one of the
resistances is shunted with a 10
ohm coil, the null point is \( 25 \mathrm{cm} \) from the same end. The value of each of the
unknown resistances is
\( \mathbf{A} \cdot 15 \Omega, 10 \Omega \)
в. \( 10 \Omega, 15 \Omega \)
\( \mathbf{c} \cdot 20 \Omega, 30 \Omega \)
D. \( 30 \Omega, 20 \Omega \)
Subject: Maths
If \( \overline{\boldsymbol{a}}=(2 \overline{\boldsymbol{i}}-\mathbf{1 0} \overline{\boldsymbol{j}}+\mathbf{6} \overline{\boldsymbol{k}}) ; \overline{\boldsymbol{b}}= \)
\( (5 \bar{i}-3 \bar{j}+\bar{k}) . \) The ratio of projection of
\( \bar{a} \) on \( \bar{b} \) to projection of \( \bar{b} \) on \( \bar{a} \) is
A . 2: 1
B. 1: 2
\( c \cdot 2: 3 \)
D. 3: 2
Subject: Maths
(a) What is the slope of the line joining the points \( A(2,-3) \) and \( B(6,3) ? \) Find the equation of this line.
(b) Find the co-ordinates of the point \( C \) at which the line cuts the \( x \) -axis.
(c) Show that \( C \) is the mid-point of the
line \( \boldsymbol{A B} \)
Subject: Chemistry
(a) Draw the structures of the following
molecules:
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{\boldsymbol{4}} \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
(b) Write the structural difference
between white phosphorus and red
phosphorus.
Subject: Maths
If \( S_{1} \) and \( S_{2} \) are respectively the sets of local minimum and local maximum
points of the functions, \( f(x)=9 x^{4}+ \)
\( 12 x^{3}-36 x^{2}+25, x \in R, \) then
A \( . S_{1}=\{-2,1\} ; S_{2}=\{0\} \)
B. \( S_{1}=\{-2,0\} ; S_{2}=\{1\} \)
c. \( S_{1}=\{-2,\} ; S_{2}=\{0,1\} \)
D. \( S_{1}=\{-1\} ; S_{2}=\{0,2\} \)