AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Fastest rate of reaction will be when \( \boldsymbol{R} \)
is:
\( \mathbf{A} \cdot C H_{3}- \)
в. \( C H_{3}-C H_{2} \)
c. \( C H_{3}-\begin{array}{r}C H- \\ \\ C H_{3}\end{array} \)
\( \begin{array}{l}\text { D. } \\ \qquad C H_{3}-\begin{aligned} & C H_{3} \\ & C H \end{aligned} \\ & _{C H_{3}}\end{array} \)
Subject: Physics
If \( \alpha \) represent linear expansion, \( \beta \)
represent superficial expansion and \( \gamma \) represent cubical expansion, then choose the correct statement:
B. \( \alpha: \beta: \gamma::: 2: 3: 1 \)
c. \( \alpha: \beta: \gamma:: 3: 1: 1 \)
D. \( \alpha: \beta: \gamma:: 1: 2: 3 \)
Subject: Physics
Assertion
The weight of an object changes from
place to place but not mass.
Reason
The weight of the object is independent
of the value of \( \mathfrak{g} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
A coil of inductance \( 1 H \) and resistance
\( 10 \Omega \) is connected to a resistanceless
battery of emf \( 50 V \) at time \( t=0 . \) The
ratio of the rate at which magnetic energy is stored in the coil to the rate at
which energy is supplied by the battery
at \( t=0.1 s \) is \( \frac{37}{n} . \) Find \( x \)
Subject: Maths
The coefficient of the term independent of \( x \) in the expansion of
\( \left(\frac{x+1}{x^{\frac{2}{3}}-x^{\frac{1}{3}}+1}-\frac{x-1}{x-x^{\frac{1}{2}}}\right)^{10} \)
\( A \cdot 70 \)
в. 112
c. 105
D. 210
Subject: Physics
Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and
magnetic fields \( \mathrm{E}=\mathrm{EO} \mathrm{j} \) and \( \mathrm{B}=\mathrm{BO} \mathrm{j}, \mathrm{At} \)
time \( t=0, \) this charge has velocity \( v \) in the \( x \) -y plane, making an angle 0 with the \( x \) -axis. Which of the following option(s) is(are) correct for time \( t>0 ? \)
Subject: Physics
In a certain charge distribution, all points having zero potential can be joined by a circle S. Points inside S have positive potential, and points outside have negative potential. A positive charge, which is free to move, is placed
inside S.
A. It will remain in equilibrium
B. It can move inside s, but is cannot cross
c. It must cross \( S \) at some time.
D. It may move, but will ultimately return to its starting point
Subject: Chemistry
Assertion: Artificial sweeteners are
added to the food to control the intake of
calories.
Reason: Most of the artificial
sweeteners are inert and do not
metabolise in the body.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct.
Subject: Physics
Q Type your question
When in equilibrium, there is a gap of
\( \Delta l \) between the sphere and the floor. The
sphere is gently pushed aside so that it
makes an angle \( \theta \) with the vertical. Find
\( \theta_{\max } \) so that sphere fails to rub the
Floor, Young's modulus of the wire is \( Y \)
A \( \cdot \sin ^{-1}\left(1-\frac{Y \pi d^{2} \Delta l}{8 M g L}\right) \)
B. \( \tan ^{-1}\left(1-\frac{Y \pi d^{2} \Delta l}{8 M g L}\right) \)
c. \( \cos ^{-1}\left(1-\frac{Y \pi d^{2} \Delta l}{8 M g L}\right) \)
\( D \)
Subject: Physics
Distance between sun and earth is \( 2 \times \)
\( 10^{8} \mathrm{km}, \) temperature of sun \( 6000 \mathrm{K} \)
radius of \( \operatorname{sun} 7 \times 10^{5} \mathrm{km}, \) if emissivity
of earth is \( 0.6, \) then find out
temperature of earth in thermal
equilibrium.
A . 400 к
в. 300 к
\( c .500 k \)
D. 600 к
Subject: Physics
\( 2 n d \) equation of motion \( (s=u t+ \)
\( \left.\frac{1}{2} a t^{2}\right) \) can be derived graphically form
\( \boldsymbol{v}-\boldsymbol{t} \) graph by finding
A. Slope
в. Area
c. Either(A) or (B)
D. Insufficient data
Subject: Chemistry
Which of the following are the observations of the experiment
conducted to determine whether a given compound is acid, base or salt?
A. Glowing of the bulb indicates conduction of electricity through the electrolyte
B. If a solution is a strong electrolyte the bulb glows brightly when the current is switched on
c. If a solution is a weak electrolyte the bulb glows dimly when the current is switched on
D. All of the above
Subject: Maths
Prove that
\( \operatorname{cosec}\left(\tan ^{-1}\left(\cos \left(\cot ^{-1}\left(\sec \left(\sin ^{-1} a\right)\right)\right)\right)\right) \)
\( \sqrt{\mathbf{3}-\boldsymbol{a}^{2}}, \) where \( \boldsymbol{a} \in[\mathbf{0}, \mathbf{1}] \)
Subject: Maths
Which condition can be used to prove
that the given triangles are SAS
congruent?
\( A . \angle B=\angle F, \overline{A B} \cong \overline{D F} \) and \( \overline{A C} \cong \overline{D E} \)
B. \( \angle A=\angle F, \overline{A B} \cong \overline{D C} \) and \( \overline{A C} \cong \overline{D E} \)
\( \mathrm{c} . \angle B=\angle C, \overline{A B} \cong \overline{D C} \) and \( \overline{A C} \cong \overline{D E} \)
D. \( \angle B=\angle F, \overline{A C} \cong \overline{D C} \) and \( \overline{A C} \cong \overline{D E} \)
\( E \)
Subject: Physics
Half-life of a radioactive substance A is
two times the half-life of another
radioactive substance
B. Initially, the
number of \( A \) and \( B \) are \( N_{A} \) and \( N_{B} \)
respectively. After three half-lives of \( A \) number of nuclei of both are equal
Then, the ratio \( N_{A} / N_{B} \) is
A . \( 1 / 4 \)
в. \( 1 / 8 \)
c. \( 1 / 3 \)
D. \( 1 / 6 \)
Subject: Physics
Figure
(a) shows two plano-convex lenses in contact as shown. The
combination has focal length \( 24 \mathrm{cm} \) Figure (b) shows the same with a liquid introduced between them. If refractive
index of glass of the lenses is 1.50 and that of the liquid is \( 1.60, \) the focal length of system in Fig. (b) will be
(a)
(b)
A \( .-120 \mathrm{cm} \)
В. \( 120 \mathrm{cm} \)
\( \mathbf{c} .-24 c m \)
D. \( 24 c m \)
Subject: Chemistry
From the following given statements
i) \( 0-\dots \) Hydrogen bond length is more than covalent "O-H" bond length
ii) The ionic bond strength of \( C s F \) is more than that of \( N a F \)
iii) The number of electrons present in all shells of sodium atom is 10
The correct combination is:
A. only (i) is correct
B. only (i) and (ii) are correct
c. only (ii) and (iii) are correct
D. all are incorrect
Subject: Chemistry
Give the balanced reaction for the
manufacture of the ammonia gas.
A. \( 3 N_{2}+3 H_{2} \rightarrow 6 N H_{3} \)
в. \( N_{2}+3 H_{2} \rightarrow 2 N H_{3} \)
c. \( N_{2}+3 H_{2} \rightarrow N H_{3} \)
D. \( N_{2}+6 H_{2} \rightarrow 4 N H_{3} \)
Subject: Maths
If \( A \) and \( B \) are arbitrary events, then
\( \mathbf{A} \cdot P(A \cap B) \geq P(A)+P(B) \)
B \( \cdot P(A \cap B) \leq P(A)+P(B) \)
C \( \cdot P(A \cap B)=P(A)+P(B) \)
D. none of these
Subject: Physics
A circular coil of radius \( 10 \mathrm{cm}, 500 \)
turns and resistance \( 2 \Omega \) is placed with its plane perpendicular to the horizontal component of the earth's magnetic field It is rotated about its vertical diameter
through \( 180^{\circ} \) in 0.25 s. Estimate the
magnitudes of the emf and current
induced in the coil. Horizontal
component of earth's magnetic field at the place is \( 3.0 \times 10^{-5} \mathrm{T} \)
Subject: Chemistry
During the Rutherford's \( \alpha \) -particle
scattering experiment, he concluded that:
(i) electrons have negative charge.
(ii) the mass and positive charge of the
atom is concentrated in the nucleus.
(iii) neutron exists in the nucleus.
(iv) most of the space in atom is empty.
Choose the correct statements.
\( A \). (i) and (iii)
B. (ii) and (iv)
c. (i) and (iv)
D. (iii) and (iv)
Subject: Maths
Prove the following:
\( \left|\begin{array}{ccc}\boldsymbol{b} \boldsymbol{c} & \boldsymbol{b} \boldsymbol{c}^{\prime}+\boldsymbol{b}^{\prime} \boldsymbol{c} & \boldsymbol{b}^{\prime} \boldsymbol{c}^{\prime} \\ \boldsymbol{c} \boldsymbol{a} & \boldsymbol{c} \boldsymbol{a}^{\prime}+\boldsymbol{c}^{\prime} \boldsymbol{a} & \boldsymbol{c}^{\prime} \boldsymbol{a}^{\prime} \\ \boldsymbol{a b} & \boldsymbol{a b}^{\prime}+\boldsymbol{d}^{\prime} \boldsymbol{b} & \boldsymbol{d}^{\prime} \boldsymbol{b}^{\prime}\end{array}\right|= \)
\[
\left(b c^{\prime}-b^{\prime} c\right)\left(c a^{\prime}-c^{\prime} a\right)\left(a b^{\prime}-d b\right)
\]
Subject: Chemistry
The cell reaction for the given cell is spontaneous if:
\( \boldsymbol{P t}\left|\boldsymbol{C l}_{2}\left(\boldsymbol{P}_{1} \boldsymbol{a} \boldsymbol{t m}\right)\right| \boldsymbol{C l}^{-}(\boldsymbol{1} \boldsymbol{M}) \mid \boldsymbol{C l}_{2}\left(\boldsymbol{P}_{2} \boldsymbol{a}\right. \)
A \( \cdot P_{1}>P_{2} \)
в. \( P_{1}<P_{2} \)
c. \( P_{1}=P_{2} \)
D. \( P_{1}=1 \) at \( m \)
Subject: Physics
One mole of an ideal gas u ndergoes a
process:
\( P=\frac{P_{0}}{1+\left(V_{0} / V\right)^{2}} \)
Here \( P_{0} \) and \( V_{0} \) are constants.change in temperature of the gas when volume is
changed from \( V=V_{0} \) to \( V=2 V_{0} \) is:
A. \( -\frac{2 P_{0} V_{0}}{5 R} \)
в. \( \frac{11 P_{0} V_{0}}{10 R} \)
c. \( -\frac{5 P_{0} V_{0}}{4 R} \)
D. \( P_{0} V_{0} \)
Subject: Physics
A ball is dropped from a height \( h \) on a
floor of coefficient of restitution \( e \). The
total distance covered by the ball just before the second hit is
\( \mathbf{A} \cdot h\left(1-2 e^{2}\right) \)
B. \( h\left(1+2 e^{2}\right) \)
c. \( h\left(1-e^{2}\right) \)
\( D \cdot h e^{2} \)
Subject: Maths
Which of the following complex numbers is equivalent to \( \frac{3-5 i}{8+2 i} ? \) (Note: \( i=\sqrt{-1}) \)
A \( \cdot \frac{3}{8}-\frac{5 i}{2} \)
в. \( \frac{3}{8}+\frac{5 i}{2} \)
c. \( \frac{7}{34}-\frac{23 i}{34} \)
D. \( \frac{7}{34}+\frac{23 i}{34} \)
Subject: Physics
The displacement \( x \) of a particle in
motion is given in terms of time by \( x(x- \)
4) \( =1-5 \cos \omega t \)
A. The particle executes SHM
B. The particle executes oscillatory motion which is not SHM
C. motion of the particle is neither oscillator; nor simple harmonic
D. The particle is not acted upon by a force when it is at \( x \) \( =4 \)
Subject: Maths
Water flows through a cylindrical pipe of internal diameter \( 7 \mathrm{cm} \) at \( 5 \mathrm{m} / \mathrm{s} \)
Calculate:
(i) the volume, in litres, of water
discharged by the pipe in 1 minute
(ii) the time, in minutes, the pipe would take to fill an empty rectangular tank
\( 4 m \) by \( 3 m \) by \( 2.31 m \)
Subject: Maths
Solve the following linear programming problem by graphical method:
Maximize \( Z=3 x+2 y \)
subject to the in constraints \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \leq \mathbf{1 0}, \mathbf{3} \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{1 5}, \boldsymbol{x}, \boldsymbol{y} \geq \mathbf{0} \)
Subject: Physics
in fig consists of two horizontal
conducting plates of equal area A. The
bottom plate rests on a fixed support and the top plate is suspended by four springs with spring constant \( \mathrm{k} \)
positioned at each of the four corners of
the plate as shown in Fig. When uncharged, the plates are separated by
a distance \( z_{0} . \) A battery is connected to the plates and produces a potential difference V between them. This causes
the plate separation to decrease to z.
Neglect any fringing effects. Find the condition of stable equilibrium:
A. z shall have positive root
B. z shall negative root
c. no dependence on value of \( z \)
D. none of these
Subject: Maths
A solid metal cone with radius of base
\( 12 \mathrm{cm} \) and height \( 24 \mathrm{cm}, \) is melted to form spherical solid balls of diameter 6 \( \mathrm{cm} \) each. Find the number of balls thus
formed.
A . 30
B. 31
\( c \cdot 32 \)
D. 34
Subject: Chemistry
Assuming that the degree of hydrolysis
is small, the \( p H \) of \( 0.1 \mathrm{M} \) solution of
sodium acetate \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 0} \times \mathbf{1 0}^{-\mathbf{5}}\right) \) will
be:
A. 6.0
B. 8.0.
\( c .9 .0 \)
D. 5.0
Subject: Maths
Order and degree of \( \left(x^{2}+2 x\right) y_{2}^{2}+\left(x^{2}-2\right) y_{1}^{3}-2(x+ \)
\( \mathbf{3}) \boldsymbol{y}=\mathbf{0} \) are:
A . 2,3
B. 2,
c. 3,1
D. 3,
Subject: Chemistry
A metal \( X \) on heating in nitrogen gas gives a compound \( Y . \) Compound \( Y \)
on treatment with \( H_{2} O \) gives a colourless gas which when passed
through \( C u S O_{4} \) solution gives a blue colour. Then, compound \( Y \) is:
A \( . M g\left(N O_{3}\right)_{2} \)
в. \( M g_{3} N_{2} \)
c. \( N H_{3} \)
D. \( M g O \)
Subject: Biology
Tidal Volume and Expiratory Reserve Volume of an athlete is \( 500 \mathrm{mL} \) and 1000
\( \mathrm{mL}, \) respectively. What will be his Expiratory Capacity if the Residual Volume is \( 1200 \mathrm{mL} \) ?
A. \( 1500 \mathrm{mL} \)
B. \( 1700 \mathrm{mL} \)
c. \( 2200 \mathrm{mL} \)
D. \( 2700 \mathrm{mL} \)
Subject: Physics
Two skaters \( A \) and \( B \) of mass 50 kg and 70 kg respectively stand facing each other 6 metres apart. They then pull on a light rope stretched between them. How far has each moved when they meet?
A. Both have moved 3 metres
B. A moves 2.5 metres and B moves 3.5 metres.
C. A moves 3.5 metres and \( B \) moves 2.5 metres
D. A moves 2 metres and B moves 4 metres
Subject: Physics
The conductor AD moves to the right in a uniform magnetic field directed into
the paper:
\( (x) \)
This question has multiple correct options
A. The free electrons in AD will move towards A
B. D will acquire a positive potential with respect to A
C. If \( D \) and \( A \) are joined by a conductor externally, a current will flow from A to D in AD
D. The current in AD flows from lower to higher potential
Subject: Physics
A uniform cylindrical wire is subjected to a longitudinal tensile stress of \( 5 \times \) \( 10^{7} N / m^{2} . \) Young's modulus of the
material of the wire is \( 2 \times 10^{11} N / m^{2} \)
The volume change in the wire is \( 0.02 \% \)
The fractional change in the radius is
A. \( 0.25 \times 10^{-4} \)
B. \( 0.5 \times 10^{-4} \)
c. \( 0.1 \times 10^{-4} \)
D. \( 1.5 \times 10^{-4} \)
Subject: Chemistry
A chemist prepares \( 1.00 g \) of pure \( _{6}^{11} C . \)
This isotope has half life of 21 minutes, decaying by the equation:
\[
_{6}^{11} C \rightarrow_{5}^{11} B+_{1}^{0} e
\]
(a) What is the rate of disintegration per second (dps) at start?
(b) What are the activity and specific activity of \( _{6}^{11} \mathrm{C} \) at start?
(c) How much of this isotope \( _{6}^{11} C \) is left
after 24 hours of its preparation?
Subject: Physics
At a certain locations, the strength of the electric field is \( 30.0 \mathrm{N} / \mathrm{C} \). A charge of \( 3.00 \mathrm{C} \) is placed at this location. How much force does this charge experience due to the electric field?
A. 90.0 N
B. 10.0
c. \( 0.100 \mathrm{N} \)
D. 270 N/C
E. \( 3.33 \mathrm{N} / \mathrm{C} \)
Subject: Physics
Which of the following is true in context
of Eddy currents?
A. By Lenz's law, an eddy current creates a magnetic field that opposes the magnetic field that created it.
B. Eddy currents are loops of electrical current induced within conductors by a changing magnetic field in the conductor, due to Faraday's law of induction
C. Eddy currents are a cause of energy loss in alternating current (AC) inductors, transformers, electric motors and generators etc.
D. All of the above
Subject: Maths
If \( \frac{b+c-a}{a}, \frac{c+a-b}{b}, \frac{a+b-c}{c} \) are in
\( A . P ., \) then which of the following is in
A.P.?
This question has multiple correct options
A. \( a, b, c \)
B \( \cdot a^{2}, b^{2}, c^{2} \)
c. \( \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \)
D. \( b c, a c, a b \)
Subject: Physics
If a charged particle goes unaccelerated in a region containing electric and magnetic fields, then This question has multiple correct options
A. \( \vec{E} \) must be perpendicular to \( \vec{B} \)
B . \( \vec{v} \) must be perpendicular to \( \vec{E} \)
C. \( \vec{v} \) must be perpendicular to \( \vec{B} \)
D. E must be equal to vB
Subject: Physics
Identical charges \( (-q) \) are placed at
each corner of a cube of side b then
E.P.E. of charge \( (+\boldsymbol{q}) \) which is placed at the centre of the cube will be:
\( ^{\mathbf{A}} \cdot \frac{-4 \sqrt{2} q^{2}}{\pi \epsilon_{0} b} \)
B. \( \frac{-8 \sqrt{2} q^{2}}{\pi \epsilon_{0} b} \)
c. \( \frac{-4 q^{2}}{\sqrt{3} \pi \epsilon_{0} b} \)
D. \( \frac{8 \sqrt{2} q^{2}}{4 \pi \epsilon_{0} b} \)
Subject: Maths
A machine has three parts, \( A, B \) and \( C \)
whose chances of being defective are 0.02,0.10 and 0.05 respectively. The machine stops working if any one of the arts becomes defective. What is the
probability that the machine will not stop working?
A . 0.06
B. 0.16
c. 0.84
D. 0.94
Subject: Maths
Find the discriminant of the equation
and the nature of roots. Also find the
roots, if they are real:
\( 3 x^{2}-2 x+\frac{1}{3}=0 \)
A. Roots are imaginary
B. \( \mathrm{D}=0, \) Roots are real and equal \( \frac{1}{3}, \frac{1}{3} \)
\( \mathrm{c} \cdot_{\mathrm{D}=} \frac{2}{5}, \) Roots are real and unequal \( \frac{1}{5}, \frac{1}{2} \)
D. Cannot be determined
Subject: Physics
In Figure a spherical part of radius \( \frac{R}{2} \) is
removed from a bigger solid sphere of
radius \( R . \) Assuming uniform mass
distribution, a shift in the centre of
mass will be:
\( A \cdot \frac{-R}{6} \)
B. \( -\frac{R}{14} \)
\( \mathbf{c} \cdot \frac{R}{9} \)
D. \( \frac{R}{3} \)
Subject: Chemistry
Assertion
\( N C l_{3} \) undergoes hydrolysis.
Reason
Chlorine possesses vacant d-orbitals.
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
A letter is known to have come either
from \( \boldsymbol{T} \boldsymbol{A} \boldsymbol{T} \boldsymbol{A} \boldsymbol{N} \boldsymbol{A} \boldsymbol{G} \boldsymbol{A} \boldsymbol{R} \) or \( \boldsymbol{C A L} \boldsymbol{C U T T A} \)
On the envelope just two consecutive
letters \( T A \) are visible. What is the
probability that the letter came from \( \boldsymbol{T} \boldsymbol{A} \boldsymbol{T} \boldsymbol{A} \boldsymbol{N} \boldsymbol{A} \boldsymbol{G} \boldsymbol{R} ? \)
A \( .1 / 11 \)
в. \( 7 / 9 \)
c. \( 4 / 11 \)
D. \( 7 / 11 \)
Subject: Physics
A large conducting plane has surface charge density \( 10^{-2} C / m^{2} . \) Find the
electrostatic energy stored in a cubical volume of side \( 1 \mathrm{cm} \) in the front plane.
A. 1.4
B. \( 2.8 J \)
c. \( 5.6 J \)
D. none of these
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y}, \boldsymbol{x}-\boldsymbol{y})=\boldsymbol{x} \boldsymbol{y}, \) then the
arithmetic mean of \( \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y}) \) and \( \boldsymbol{f}(\boldsymbol{y}, \boldsymbol{x}) \)
is
Subject: Maths
The coordinates of the fixed point of the
chord cut off by \( 2 x-5 y+18=0 \) by
the circle \( x^{2}+y^{2}-6 x+2 y-54=0 \)
are
A \( .(1,4) \)
в. (2,4)
c. (4,1)
()
D. (1,1)
Subject: Maths
Write the first three terms of the AP
when a and d are as given below:
\( \boldsymbol{a}=\mathbf{5}, \boldsymbol{d}=\mathbf{3}, \) then first three terms are
\( \mathbf{5}, \mathbf{8}, \mathbf{1 1} \)
If true then enter 1 and if false then
enter 0
Subject: Physics
In situation \( 2, \) if \( h_{2} \) is further decreased
then
A. cylinder will not move up an remains at its original position
B. for \( h_{2}=h / 3 \) cylinder again starts moving up
C. for \( h_{2}=h / 4 \) cylinder again starts moving up
D. for \( h_{2}=h / 5 \) cylinder again starts moving up
Subject: Maths
To draw a pair of tangents to a circle which are inclined to each other at an
angle \( 35^{\circ}, \) it is required to draw tangents at the end points of those two radii of the circle, the angle between which is
A . \( 105^{\circ} \)
B. 70
c. \( 145^{\circ} \)
D. \( 150^{\circ} \)
Subject: Maths
The projection of a directed line segment on the co-ordinate axes are
\( 12,4,3, \) then the direction cosines of
the line are
A \( \cdot \frac{-12}{13}, \frac{-4}{13}, \frac{-3}{13} \)
В. \( \frac{12}{13}, \frac{4}{13}, \frac{3}{13} \)
c. \( \frac{12}{13}, \frac{-4}{13}, \frac{3}{13} \)
D. \( \frac{12}{13}, \frac{4}{13}, \frac{-3}{13} \)
Subject: Physics
A long straight wire is carrying current
\( \boldsymbol{I}_{1}=\mathbf{2} / \mathbf{5} \boldsymbol{A} \) in \( +\mathbf{z} \) direction.The \( \mathbf{x}-\mathbf{y} \) plane
contains a closed circular loop carrying
current \( \boldsymbol{I}_{2}=\mathbf{5} / \mathbf{2} \boldsymbol{A} \) and not encircling
the straight wire, then the force (in newton) on the loop will be ? (Radius of
the circular loop \( \boldsymbol{R}=\mathbf{3} / \mathbf{4 m} \) ).
Subject: Maths
Let \( f \) be a twice differentiable function
[0,2] show that if \( f(0)=0, f(1)=2 \)
and \( f(2)=4 \) then there is some point
\( \boldsymbol{x}_{0} \in[\mathbf{0}, \mathbf{2}] \) such that \( \boldsymbol{f}^{\prime \prime}\left(\boldsymbol{x}_{0}\right)=\mathbf{0} \)
Subject: Maths
The angle of elevation of the top of a vertical tower from a point \( A, \) due east
of it is \( 45^{\circ} . \) The angle of elevation of the
top of the same tower from a point \( \boldsymbol{B} \)
due south of \( A \) is \( 30^{\circ} . \) If the distance
between \( A \) and \( B \) is \( 54 \sqrt{2} m, \) then
the height of the tower (in metres), is :
A. \( 36 \sqrt{3} \)
в. 108
\( c .54 \)
D. \( 54 \sqrt{3} \)
Subject: Physics
A box of weight \( 150 k g f \) has \( 1.47 k J \)
of gravitational potential energy stored in it. Find the height of the box above the ground. Take \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{N} \boldsymbol{k} \boldsymbol{g}^{-1} \)
A . \( 10 m \)
в. 4.9 т
c. \( 2.45 m \)
D. \( 1 m \)
Subject: Chemistry
If the distance between nuclei is \( 2 x \)
\( 10^{-13}, \) the density of nuclear material
is:
(mass of neuclei \( \left.=10^{-27}\right) \)
\( \begin{array}{ll}\text { A } \cdot 3.21 \times 10^{-12} & k g / m^{3}\end{array} \)
В . \( 1.6 \times 10^{-3} \mathrm{kg} / \mathrm{m}^{3} \)
D. \( 1 \times 10^{17} \mathrm{kg} / \mathrm{m}^{3} \)
Subject: Physics
One end of a cylindrical rod is grounded to a hemispherical surface of radius
\( R=20 m m . \) It is immersed in water of
refractive index \( 1.33 . \) If the refractive
index of the hemisphere is \( 1.5 . \) Find the position of an image of an object placed on the axis of the rod inside water at
\( 10 \mathrm{cm} \) from the pole.
Subject: Maths
If \( \tan \theta+\tan 4 \theta+\tan 7 \theta= \)
\( \tan \theta \tan 4 \theta \tan 7 \theta, \) then \( \theta= \)
A \( \cdot \frac{n \pi}{4} \)
в. \( \frac{n \pi}{7} \)
c. \( \frac{n \pi}{12} \)
D. \( n \pi \)
Subject: Physics
If \( \vec{A} \) is perpendicular to \( \vec{B}, \) then
\( \mathbf{A} \cdot \vec{A} \times \vec{B}=0 \)
B . \( \vec{A} \cdot[\vec{A}+\vec{B}]=A^{2} \)
c. \( \vec{A} \cdot \vec{B}=A B \)
D. \( \vec{A} \cdot[\vec{A}+\vec{B}]=A^{2}+A B \)
Subject: Chemistry
A solution containing 5 g acetic acid in 100 g \( \boldsymbol{H}_{2} \boldsymbol{O}\left(\boldsymbol{O}_{\boldsymbol{H}_{2}}^{0} \boldsymbol{O}=\mathbf{2} \boldsymbol{3} . \mathbf{7} \mathbf{5} \boldsymbol{6} \boldsymbol{m} \boldsymbol{m} \text { at } \mathbf{2} \mathbf{5}^{\boldsymbol{o}} \boldsymbol{C}\right. \)
shows a vapour pressure of \( 23.40 \mathrm{mm} \) whereas same mass of acetic acid in
\( 100 \mathrm{g} C_{6} H_{6}\left(P_{C_{6} H_{6}}^{0}=72.5 m m \text { at } 25^{\circ} C\right) \)
shows a vapour pressure of \( 70.0 \mathrm{mm} \) Assuming non-volatile nature of \( C H_{3} C O O H, \) discuss the data given to discuss hydrogen bonding:
A. acetic acid exists as a monomer
B. acetic acid exists as a dimer
c. acetic acid is dissociated
D. acetic acid exists as an anhydride