AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A police jeep is chasing a culprit going on a motorbike. The motorbike crosses
a turning at a speed of \( 72 \mathrm{km} / \mathrm{h} \). The jeep follows it at a speed of \( 90 \mathrm{km} / \mathrm{h} \)
crossing the turning ten seconds later than the bike.

Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike?
A. \( 3 k m \)
в. 5 kт
\( \mathrm{c} \cdot 1 \mathrm{km} \)
D. \( 7 \mathrm{km} \)
Subject: Maths
Which of the following are correct in
respect of the system of equations \( \boldsymbol{x}+ \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{8}, \boldsymbol{x}-\boldsymbol{y}+\mathbf{2} \boldsymbol{z}=\boldsymbol{6} \) and \( \boldsymbol{3} \boldsymbol{x}- \)
\( \boldsymbol{y}+\mathbf{5} \boldsymbol{z}=\boldsymbol{k} ? \)
1. They have no solution, if \( k=15 \)
2. They have infinitely many solutions, if
\( k=20 \)
3. They have unique solution, if \( k=25 \)
Select the correct answer using the code given below
\( A \cdot 1 \) and 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1,2 and 3
Subject: Physics
The field potential inside a charged ball of radius \( \mathrm{R} \) and centre at o depends only
on distance from its center as \( V(r)= \)
\( \boldsymbol{\alpha} \boldsymbol{r}^{2}+\boldsymbol{\beta} \) when \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) are \( + \) ve constant
now choose correct options
A . electric field inside the ball \( E_{r}=-2 \alpha r \)
B. electric flux passing through an imaginary sphere of radius r centre at 0 will be \( -2 \pi \alpha r^{4} \)
C. volume charge density p(r) inside ball is \( -6 \varepsilon_{0} \alpha \)
D. electric energy of charged ball will be \( \frac{48}{5} \pi \varepsilon_{0} \alpha^{2} R^{5} \)
Subject: Physics
Three concurrent co-planer forces \( 1 \mathrm{N}, 2 \mathrm{N} \) and \( 3 \mathrm{N} \) acting along different directions on a body.
A. Can keep the body in equilibrium if \( 2 \mathrm{N} \) and \( 3 \mathrm{N} \) act at right angle
B. Can keep the body in equilibrium if \( 1 \mathrm{N} \) and \( 2 \mathrm{N} \) act at right angle
c. can keep the body in the equilibrium.
D. Can keep the body in equilibrium if \( 1 \mathrm{N} \) and \( 3 \mathrm{N} \) act at an acute angle
Subject: Maths
One ticket is selected randomly from the set of 100 tickets numbered as
\( \{00,01,02,03,04,05, \ldots, 98,99\} . E_{1} \) and
\( E_{2} \) denote the sum and product of the digits of the number of the selected ticket. The value of \( \boldsymbol{P}\left(\frac{\boldsymbol{E}_{1}=\boldsymbol{9}}{\boldsymbol{E}_{2}=\mathbf{0}}\right) \) is
A \( \cdot \frac{1}{19} \)
B. \( \frac{2}{19} \)
\( c \cdot \frac{3}{19} \)
D. \( \frac{1}{18} \)
Subject: Chemistry
The outer shell electronic configuration of \( G d(Z=64) \) is
A \( \cdot 4 f^{7} 5 d^{1} 6 s^{2} \)
B \( \cdot 4 f^{8} 6 s^{2} \)
c. \( 4 f^{9} 9 s^{\text {। }} \)
D. \( 4 f^{7} 5 d^{2} 6 s^{1} \)
Subject: Physics
A point charge \( -q \) is carried from a
point \( A \) to another point \( B \) on the axis of a charged ring of radius 'r' carrying a charge \( +q / \) If the point \( A \) is at \( a \) distance \( \frac{4}{3} r \) from the centre of the ring and the point \( \mathrm{B} \) is \( \frac{3}{4} r \) from the centre but on the opposite side, what is the net work that need to be done for this?
\( ^{\mathrm{A}} \cdot-\frac{7}{5} \frac{q^{2}}{4 \pi \varepsilon_{0} r} \)
В. \( -\frac{1}{5} \frac{q^{2}}{4 \pi \varepsilon_{0} r} \)
c. \( \frac{q^{2}}{54 \pi \varepsilon_{0} r} \)
D. \( \frac{q^{2}}{54 \pi \varepsilon_{e} r} \)
Subject: Physics
A particle performing SHM has time period \( \frac{2 \pi}{\sqrt{3}} \) and path length \( 4 \mathrm{cm} . \) The
displacement from mean position at which acceleration is equal to velocity is
\( A \cdot 0 c m \)
B. \( 0.5 \mathrm{cm} \)
\( c \cdot 1 c m \)
D. \( 1.5 \mathrm{cm} \)
Subject: Physics
A particle of mass is executing oscillations about the origin on the \( x \) axis. Its potential energy is \( V(x)= \)
\( k|x|^{3}, \) where \( k \) is a positive constant. If
the amplitude of oscillation is \( a \), then
its time period \( T \) is proportional
A . proportional to \( \frac{1}{\sqrt{a}} \)
B. proportional to \( \sqrt{a} \)
C . Independent \( a^{\frac{3}{2}} \)
D. None of these
Subject: Physics
A stone is dropped into a pond from the top of the tower of height, \( h \). If \( \nu \) is the speed of sound in air, then the sound of splash will be heard at the top of the tower after a time
A \( \cdot \sqrt{\frac{2 h}{g}}+\frac{h}{\nu} \)
B. \( \sqrt{\frac{2 h}{g}}-\frac{h}{\nu} \)
c. \( \sqrt{\frac{2 h}{q}} \)
D. \( \sqrt{\frac{2 h}{g}}+\frac{2 h}{\nu} \)
Subject: Maths
f \( x, y \) are rational numbers such that
\( (x+y)+(x-2 y) \sqrt{2}=2 x-y+ \)
\( (x-y-1) \sqrt{5} \) then
A. \( x=1, y=1 \)
B. \( x=2, y=1 \)
c. \( x=5, y=1 \)
D. \( x \) and \( y \) can take infinitely many values
Subject: Maths
Let \( A=\{1,2,3, \ldots, 14\} . \) Define a relation \( \boldsymbol{R} \) from \( \boldsymbol{A} \) to \( \boldsymbol{A} \) by \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}) \)
\( \mathbf{3} \boldsymbol{x}-\boldsymbol{y}=\mathbf{0} \text { where } \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{A}\} . \) Write down
its domain, co-domain and range.
Subject: Physics
Steam at \( 100^{\circ} \mathrm{C} \) is added slowly to
\( 1400 g m \) of water at \( 16^{\circ} C \) until the
temperature of water is raised to \( 80^{\circ} \mathrm{C} \)
The mass of steam required to do this is
\( \left(\boldsymbol{L}_{\boldsymbol{v}}=\mathbf{5 4 0} \boldsymbol{c a l} / \boldsymbol{g m}\right) \)
A \( .160 g m \)
В. \( 125 \mathrm{gm} \)
\( \mathrm{c} .250 \mathrm{gm} \)
D. \( 320 g m \)
Subject: Chemistry
Which of the following is always true regarding the spontaneity of reaction occuring in a galvanic cell?
A \( \cdot E^{0}_{c e l l}>0, \Delta G^{0}<0 \) and \( Q>K_{c} \)
B . \( E^{0}_{c e l l}>0, \Delta G^{0}<0 \) and \( Q<K_{c} \)
C \( \cdot E_{\text {cell }}^{0}>0, \Delta G^{0}>0 \) and \( Q>K_{c} \)
D . \( E^{0}_{c e l l}>0, \Delta G^{0}>0 \) and \( Q<K_{c} \)
Subject: Chemistry
The molecular weight of \( O_{2} \) and \( N_{2} \) are
32 and 28 respectively. At \( 15^{0} C \), the
pressure of \( 1 \mathrm{gm} \mathrm{O}_{2} \) will be the same as
that of \( 1 \mathrm{gm} N_{2} \) in the same bottle at the temperature?
A . \( -21^{0} C \)
B. \( -13^{0} C \)
\( \mathbf{c} \cdot 15^{0} C \)
D. \( 56.4^{0} V \)
Subject: Chemistry
FeCl \( _{3} .4 H_{2} O \) is actually:
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{4}\right] C l_{3} \)
\( \mathbf{B} \cdot\left[F e\left(H_{2} O\right)_{3} C l\right] C l_{2} \cdot H_{2} O \)
\( \mathbf{c} \cdot\left[F e\left(H_{2} O\right)_{4} C l_{2}\right] C l \)
D. \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3} \mathrm{Cl}_{2}\right] \mathrm{Cl} . \mathrm{H}_{2} \mathrm{O} \)
Subject: Chemistry
A hydrocarbon \( ^{\prime} \boldsymbol{A}^{\prime}\left(\boldsymbol{C}_{3} \boldsymbol{H}_{8}\right) \) on treatment
with chlorine in presence of sunlight
yielded compounds ' \( B^{\prime} \) as major
product. Reaction of \( ^{\prime} B^{\prime} \) with aqueous
KOH gave \( ^{\prime} C^{\prime} \) which on treatment with
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) yielded \( ^{\prime} \boldsymbol{D}^{\prime} \)
Hydrogenation of \( ^{\prime} D^{\prime} \) gave back \( ^{\prime} A^{\prime} \). The sequence of reactions involved in above conversion is:
A. Substitution, Substitution, Addition, Dehydration
B. Substitution, Substitution, Dehydration, Addition
c. substitution, Dehydration, Addition, Addition
D. Addition, Substitution, Dehydration, Substitution
Subject: Physics
If \( V_{e} \) is the escape velocity of a body from a planet of mass \( M \) and radius \( R \) Then, the velocity of satellite revolving at height \( h \) from the surface of planet
will be
A \( \cdot V=V_{e} \sqrt{\frac{R}{(R+h)}} \)
B \( \cdot V=V_{e} \sqrt{\frac{2 R}{(R+h)}} \)
\( ^{\mathbf{c}} \cdot_{V}=V_{e} \sqrt{\frac{(R+h)}{R}} \)
D. \( V=V_{e} \sqrt{\frac{R}{2(R+h)}} \)
Subject: Maths
One mapping is selected at randon from
all mappings of the set \( S= \)
\( \{1,2,3, \dots,, n\} \) into itself. If the
probability that mapping is one-one is \( 3 / 32 \) then the value of \( n \) is
A .2
B. 3
\( c \cdot 4 \)
D. None of these
Subject: Biology
The stages in proper sequence of
prophase I are
A. Diplotene \( \rightarrow \) diakinesis \( \rightarrow \) pachytene \( \rightarrow \) zygotene \( \rightarrow \) leptotene
B. Leptotene \( \rightarrow \) zygotene \( \rightarrow \) pachytene \( \rightarrow \) diplotene \( \rightarrow \) diakinesis
C. Leptotene \( \rightarrow \) pachytene \( \rightarrow \) zygotene \( \rightarrow \) diakinesis \( \rightarrow \) diplotene
D. Zygotene \( \rightarrow \) leptotene \( \rightarrow \) pachytene \( \rightarrow \) diakinesis \( \rightarrow \) diplotene
Subject: Physics
A siren placed at a railway platform is emitting sound of frequency 5 KHz. \( A \)
passenger sitting in a moving train \( \mathbf{A} \) records a frequency of \( 5.5 \mathrm{KHz} \) while the train approaches the siren. During
his return journey in a different tran B he records a frequency of 6.0 KHz while approaching the same siren. The ratio of velocity of train \( \mathrm{B} \) to that of train \( \mathrm{A} \) is
A \( \cdot \frac{242}{252} \)
B. 2
c. \( \frac{5}{6} \)
D. \( \frac{11}{6} \)
Subject: Maths
Assertion (A):The derivative of \( (\log x)^{x} \)
w.r.t \( \boldsymbol{x} \) is \( (\log \boldsymbol{x})^{x-1}[\mathbf{1}+\log \boldsymbol{x} \log (\log \boldsymbol{x})] \)
Reason
\( (\mathrm{R}): \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left\{\boldsymbol{f}(\boldsymbol{x})^{g(\boldsymbol{x})}\right\}=\boldsymbol{f}(\boldsymbol{x})^{g(\boldsymbol{x})} \)
\( \left(g(x) \frac{f^{\prime}(x)}{f(x)}+g^{\prime}(x) \log (f(x))\right) \)
A. Both A and R are true R is correct reason of A
B. Both A and R are true R is not correct reason of
c. A is true but R is false
D. A is false but R is true
Subject: Physics
The sum of the magnitude of two forces at a point is \( 16 \mathrm{N} \). If their resultant is
normal to the smaller force and has a
magnitude of 8 N. Then two forces are
A. 6 N, 10 N
B. 8 N, 8 N
c. 4 N, 12 \( N \)
D. 2 N, 14 N
Subject: Maths
Find the distance between the point (7,2,4) and the plane determined by
the points \( \boldsymbol{A}(\mathbf{2}, \mathbf{5},-\mathbf{3}), \boldsymbol{B}(-\mathbf{2},-\mathbf{3}, \mathbf{5}) \)
and (5,3,-3)
Subject: Chemistry
Assertion
Atomic sizes of \( C s \) and \( F r \) are almost
similar.
Reason
Cs and Fr belong to same group.
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
\( \boldsymbol{H}_{2} \boldsymbol{S}<\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{e}<\boldsymbol{H}_{2} \boldsymbol{T} \boldsymbol{e}<\boldsymbol{H}_{2} \boldsymbol{O} \) This is
the correct boiling point order. If true enter 1 else 0
A
Subject: Physics
On a large tray of mass \( \mathrm{M} \), an ice cube of mass \( \mathrm{m} \), edge \( \mathrm{L} \) is kept. If the ice melts completely, the center of mass of the
system comes down by:
\( ^{\mathbf{A}} \cdot \frac{m L}{2(M+m)} \)
в. \( \frac{(M-m) L}{2(M+m)} \)
c. \( \frac{(M+2 m) L}{2(M+m)} \)
D \( \cdot \frac{2 M L}{2(M+m)} \)
Subject: Physics
A 50 kg girl wearing heel shoes balances on a single heel. The heel is circular with a diameter \( 1 \mathrm{cm} \) The pressure exerted by the heel on the horizontal floor is then (Take \( g=10 \mathrm{m} \) s -2)
A \( \cdot 6.4 \times 10^{4} \) Pa. . \( . \). 6.4 .
B. \( 6.4 \times 10^{5} \) pa
c. \( 6.4 \times 10^{6} \) Ра
D. 6.4 \( \times 10^{7} \) Ра
Subject: Chemistry
At \( 373 K, \) gaseous reaction \( A \rightarrow \)
\( 2 B+C \) is found to be first order.
Starting with pure \( A \), the total pressure at the end of 10 min. was 176 mm and
after a long time when \( A \) was
completely dissociated, it was 270 mm.
The pressure of \( A \) at the end of 10 minutes was:
A . \( 94 \mathrm{mm} \)
B. \( 47 \mathrm{mm} \)
c. 43 mm
D. \( 90 \mathrm{mm} \)
Subject: Maths
If \( x \) and \( y \) are complex numbers, then system of equations \( (1+i) x+(1- \)
\( \boldsymbol{i}) \boldsymbol{y}=1,2 i \boldsymbol{x}+2 \boldsymbol{y}=1+\boldsymbol{i} \) has
A. unique solution
B. no solution
c. infinite numbers of solution
D. none of these
Subject: Physics
Match the following:
Column I
A. \( \mu=\tan i_{p} \)
P. Snell's law
B. \( \mu=\frac{1}{\sin i_{c}} \)
Q. Brewster's law
C. \( \mu=\frac{\sin i}{\sin r} \)
R. Prism
D. \( \mu= \)
\( \frac{\sin \left(\frac{A+D_{m}}{2}\right)}{\sin \frac{A}{2}} \begin{array}{l}\text { S. Total internal } \\ \text { reflection }\end{array} \)
Subject: Maths
Find the derivative of \( \sqrt{\tan x} \) with respect to \( x \) using the first principle.
A \( \cdot \frac{\sec ^{2} x}{2 \sqrt{\tan x}} \)
в. \( \frac{s e c x}{2 \sqrt{\tan x}} \)
\( ^{\mathrm{c}} \cdot \frac{\sec ^{2} x}{\sqrt{\tan x}} \)
D. \( \frac{\sec ^{2} x}{2 \sqrt{\tan } x} \)
Subject: Physics
In the figure shown \( \mathrm{S} \) is the source of
white light kept at a distance \( x_{0} \) from
the plane of the slits. The source moves with a constant speed u towards the slits on the line perpendicular to the plane of the slits and passing through the slit \( S_{1} \). Find the instantaneous velocity (magnitude and direction) of the central maxima at time t having range \( 0 \leq t<<\frac{x_{0}-d}{u} . \) Assume that
\( D>>d \)
Subject: Chemistry
Predict hybridization and shape of \( \boldsymbol{S} \boldsymbol{F}_{4} \)
molecule.
A \( \cdot s p^{3} d \) and see saw
B . sp \( ^{3} \) and tetrahedral
c. sp and T-shape
D. \( s p^{3} d^{2} \) and octahedral
Subject: Physics
A long wire carrying current \( i \) is placed
close to a U-shaped conductor (of negligible resistance). A wire of length \( l \)
as shown in figure slides with a velocity
v. Find the current induced in the loop
as a function of distance \( x \) from the
current carrying wire to slider.
A \( \cdot \frac{\mu_{0} i l u}{R x} \)
в. \( \frac{\mu_{0} i l u}{2 \pi R x} \)
c. \( \frac{\mu_{0} i l u}{2 R x} \)
D. \( \frac{\mu_{0} i l u}{4 \pi R x} \)
Subject: Maths
If you subtract \( \frac{1}{2} \) from a number and multiply the result by \( \frac{1}{2}, \) you get \( \frac{1}{8} \) What is the number?
A \( \cdot \frac{3}{4} \)
B. \( \frac{1}{6} \)
\( c \cdot \frac{7}{4} \)
D. \( \frac{3}{5} \)
Subject: Maths
Simplify: \( \boldsymbol{x}+\mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{x} \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. \( 5 x \)
\( c .6 \)
D. \( 6 x \)
Subject: Physics
A spherical volume contains a
uniformly distributed charge density of
\( 2 \times 10^{-4} \mathrm{Cm}^{-3} . \) The electric field at a
distance of \( 4 \mathrm{cm} \) from the centre is :
A . \( 3 \times 10^{5} \)
B . \( 3 \times 10^{4} \)
\( c \cdot 2 \times 10^{5} \)
D. \( 3 \times 10^{6} \)
Subject: Physics
Two blocks of masses \( 10 \mathrm{kg} \) and \( 30 \mathrm{kg} \) are placed along a vertical line. If the first block is raised through a height of 7 cm by what distance should the second mass be moved to raise the
center of mass by \( 1 \mathrm{cm} \)
A. \( 1 \mathrm{cm} \) up
B. \( 1 \mathrm{cm} \) down
c. \( 2 \mathrm{cm} \) down
D. \( 2 \mathrm{cm} \) up
Subject: Maths
If \( \boldsymbol{A}=\left|\begin{array}{ll}\mathbf{0} & \mathbf{0} \\ \mathbf{1} & \mathbf{1}\end{array}\right| \) then the value of \( \boldsymbol{A}+ \)
\( \boldsymbol{A}^{2}+\boldsymbol{A}^{3}+\ldots+\boldsymbol{A}^{n}=? \)
\( A \cdot A \)
B. nA
c. \( (n+1) A \)
\( D \)
Subject: Chemistry
Benzene and naphthalene form an ideal
solution at room temperature. For this process, the true statements are:
(i) \( \Delta G \) is positive
(ii) \( \Delta S_{s y s t e m} \) is positive
(iii) \( \Delta S_{\text {surroundings}}=0 \)
(iv) \( \Delta \boldsymbol{H}=\mathbf{0} \)
A. (ii) and (iv) only
B. (i) and (iii) only
C. (ii), (iii) and (iv) only
D. all of these
Subject: Biology
Assertion
Deforestation sequesters \( C O_{2} \) from atmosphere.
Reason
Global warming is beneficial for plants and human health.
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
Amongst the following compounds, the optically active alkane having the
lowest molecular mass is:
A. \( C H_{3}-C H_{2}-C \equiv C H \)
в. \( C H_{3}-C H_{2}-C H\left(C H_{3}\right)-C H_{3} \)
\( c \)
D. \( C H_{3}-C H_{2}-C H_{2}-C H_{3} \)
Subject: Physics
Two conducting spheres of radii \( r_{1} \) and
\( r_{2} \) are charged such that they have the same electric field on their surfaces.
The ratio of the electric potential at
their centres is :
A. \( \sqrt{\frac{r_{1}}{r_{2}}} \)
в. \( \frac{r_{1}}{r_{2}} \)
c. \( \frac{r_{1}^{2}}{r_{2}^{2}} \)
D. none of the above
Subject: Chemistry
If ' \( \alpha \) ' is degree of dimerisation of
\( C H_{3} C O O H \) in benzene, then van't Hoff factor 'i' for circulation of colligative
properties is:
\( \mathbf{A} \cdot 1+\alpha \)
B \( \cdot 1-\frac{\alpha}{2} \)
\( c \cdot 1+\frac{\alpha}{2} \)
D. \( 1+2 \alpha \)
Subject: Physics
Statement 1: If the amplitude of a
simple harmonic oscillator is doubled,
its total energy becomes four times.
Statement 2: The total energy is directly proportional to the square of the amplitude of vibration of the harmonic
oscillator.
A. Statement 1 is false, Statement 2 is true
B. Statement 1 is true, Statement 2 is true; Statement 2 the correct explanation for Statement
c. statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation for Statement
D. Statement 1 is true, Statement 2 is false
Subject: Chemistry
When \( 25 \mathrm{mL} \) of \( 0.1 M A g N O_{3} \) is mixed
with \( 50.0 \mathrm{mL} \) of \( 0.08 M N a_{2} C O_{3} \)
solution, then the molar concentration
of \( N a_{2} C O_{3} \) in the solution is \( x \times \)
\( \mathbf{1 0}^{-\mathbf{2}} \boldsymbol{M} . \) Here \( \boldsymbol{x} \) is:
Subject: Maths
The value of \( \lim _{n \rightarrow \infty} \Sigma_{i=1}^{n-1} \sqrt{4+\frac{5 i}{n}} \) is equal
to?
A \( \cdot 15 / 38 \)
B. \( 38 / 15 \)
c. \( 21 / 15 \)
D . \( 22 / 15 \)
Subject: Biology
A leaf has labeled as \( A \) has 20 stomata.
A leaf labeled as B has 10 stomata.
Which of the following statement defines the percentage of water vapour released by both the leaves?
A. Leaf A releases more water vapour than leaf \( B \)
B. Leaf A releases less water vapour than leaf B.
c. Leaf A equals leaf
D. None of the above
Subject: Physics
In Searle's experiment to find Young's modulus the diameter of wire is
measured as \( \boldsymbol{d}=\mathbf{0 . 0 5 c m}, \) length of
wire is \( l=125 c m \) and when a weight,
\( \boldsymbol{m}=\mathbf{2 0 . 0 k g} \) is put, extension in wire
was found to be \( 0.100 \mathrm{cm} \). Find the
maximum permissible error in Young's modulus \( (Y) . \) Use: \( Y=\frac{m g l}{(\pi / 4) d^{2} x} \)
A . \( 6.3 \% \)
в. \( 5.3 \% \)
\( c .2 .3 \% \)
D. 1\%
Subject: Physics
What is the torque of the force \( \overrightarrow{\boldsymbol{F}}= \) \( (2 \hat{i}-3 \hat{j}+4 \hat{k}) N, \) acting at the point \( \vec{r}=(3 \hat{i}+2 \hat{j}+3 \hat{k}) m \) about the origin
\( (\operatorname{in} N-m) \)
A . \( 6 \hat{i}-6 \hat{j}+12 \hat{k} \)
B . \( 17 \hat{i}-6 \hat{j}-13 \hat{k} \)
c. \( -6 \hat{i}+6 \hat{j}-12 \hat{k} \)
D. \( -17 \hat{i}+6 \hat{j}-13 \hat{k} \)
Subject: Physics
Three rods of equal lengths are joined to form an equilateral triangle \( A B C \). D is the of AB. The coefficient of linear
expansion is \( \alpha_{1} \) for material of \( \operatorname{rod} A B \)
and \( \alpha_{2} \) for \( n \) rods \( A C \) and \( B C \). It the
distance DC remains constant for small
changes in temperature.
Subject: Physics
A body of mass 100 g is sliding from an inclined plane of inclination \( 30^{0} \). What is the frictional force experienced if
\( \mu=0.7 ? \)
A. \( 0.35 \times \sqrt{3} \)
B.
\( c \cdot \frac{\sqrt{3}}{2} \)
D. 0.35
Subject: Maths
\( \int \frac{\ln (1+x)}{1+x} d x \) equals
A \( \cdot \frac{(\ln (1+x))^{2}}{2} \)
B . \( -\pi \ln (1+x) \)
c. \( \frac{\pi}{2} \ln (1+x) \)
D. \( -\frac{\pi}{2} \ln (1+x) \)
Subject: Maths
If \( x^{2}+\frac{1}{x^{2}}=A \) and \( x-\frac{1}{x}=B, \) then least value of \( \frac{\mathbf{A}}{B} \) is
A .2
B. \( \sqrt{2} \)
\( c \cdot-\sqrt{2} \)
D. \( 2 \sqrt{2} \)
Subject: Maths
Solve the following system of equations by the method of substitution:
\( \mathbf{3} \boldsymbol{x}-\mathbf{4} \boldsymbol{y}=\mathbf{1 0}, \mathbf{4} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{5} \)
Subject: Maths
If \( A \) and \( B \) be two events such that
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{1} / \mathbf{4}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{1} / \mathbf{3} \) and \( \boldsymbol{P}(\boldsymbol{A} \cup \)
\( B)=1 / 2 \) show that \( A \) and \( B \) are
independence events.
Subject: Physics
A ball falling in a lake of depth \( 200 \mathrm{m} \) shows \( 0.1 \% \) decrease in its volume at
the bottom. What is the Bulk modulus
of the ball material? (Take density of water \( =1000 \mathrm{kg} / \mathrm{m}^{3} \) ):
A \( \cdot 19.6 \times 10^{8} N / m^{2} \)
В. \( 19.6 \times 10^{-10} \mathrm{N} / \mathrm{m}^{2} \)
c. \( 19.6 \times 10^{10} N / m^{2} \)
D. \( 19.6 \times 10^{-8} N / m^{2} \)
Subject: Maths
\( n \) arithmetic means are inserted
between 3 and \( 17 . \) If the ratio of last and
the first arithmetic mean is \( 3: 1, \) then
the value of \( n \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 6
\( c \cdot 7 \)
D.
Subject: Chemistry
\( 0.284 \mathrm{g} \) of an organic substance gave \( 0.287 \mathrm{g} \) of silver chloride in a Carius estimation of halogen. Find out the percentage of chlorine in the compound. \( (A g=108, C l=35.5) \)
A . \( 35 \% \)
B . 25\%
c. \( 30 \% \)
D . 20\%
Subject: Physics
Two clocks are being tested against a
standard clock located in a nationa
laboratory. At 12: 00: 00 noon bv the standard clock, the readings of the two
clocks are:
\( \begin{array}{lll} & \text { Clock 1 } & \text { Clock 2 } \\ \text { Monday } & 12: 00: 05 & 10: 15: 06 \\ \text { Tuesday } & 12: 01: 15 & 10: 14: 59 \\ \text { Wednesday } & 11: 59: 08 & 10: 15: 18 \\ \text { Thursday } & 12: 01: 50 & 10: 15: 07 \\ \text { Friday } & 11: 59: 15 & 10: 14: 53 \\ \text { Saturday } & 12: 01: 30 & 10: 15: 24 \\ \text { Sunday } & 12: 01: 19 & 10: 15: 11\end{array} \) If you are doing an experiment that requires precision time interval
measurements, which of the two clocks
will you prefer?
Subject: Physics
toppr
Q Type your question
from point \( P \) to \( Q \) as shown in figure. The velocities at \( P \) and \( Q \) are respectively, \( \boldsymbol{v} \overrightarrow{\boldsymbol{i}} \) and \( -2 v \vec{j} . \) Then which of the following
statements \( (A, B, C, D) \) are the correct?
(Trajectory shown in schematic and not
to scale)
\( (\mathbf{A}) \boldsymbol{E}=\frac{\mathbf{3}}{\mathbf{4}}\left(\frac{\boldsymbol{m} \boldsymbol{v}^{2}}{\boldsymbol{q} \boldsymbol{a}}\right) \)
(B) Rate of work done by the electric field at \( P \) is \( \frac{3}{4}\left(\frac{m v^{3}}{a}\right) \)
(C) Rate of work done by both the fields
at Qis zero
(D) The difference between the
magnitude of angular momentum of
the particle at \( P \) and \( Q \) is 2 mav.
\( A \cdot(A),(B),(C),(D) \)
B. \( (A),(C),(D) \)
\( c \cdot(B),(C),(D) \)
D. \( (A),(B),(C) \)
Subject: Maths
If \( \boldsymbol{y}=\tan \boldsymbol{x} . \tan 2 \boldsymbol{x} . \tan 3 \boldsymbol{x}, \) then \( \frac{d \boldsymbol{y}}{d \boldsymbol{x}} \) has
the value equal to
A \( \cdot 6 \sec ^{2} 3 x \cdot \tan x \cdot \tan 2 x+2 \sec ^{2} x \cdot \tan 2 x \cdot \tan 3 x+ \)
\( 4 \sec ^{2} 2 x \). \( \tan 3 x \cdot \tan x \)
B . \( 2 y(\operatorname{cosec} 2 x+2 \operatorname{cosec} 4 x+3 \operatorname{cosec} 6 x) \)
c. \( 3 s e c^{2} 3 x-2 \sec ^{2} 2 x-\sec ^{2} x \)
D. \( \sec ^{2} x+2 \sec ^{2} 2 x+3 \sec ^{2} 3 x \)