AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The elements in Group 17 of the Periodic Table are called the halogens. They form stable compounds with both metals and non-metals.
The table gives some data about
\[
F_{2}, H C l \text { and } C a F_{2}
\]
\( \boldsymbol{H C l} \) \( \boldsymbol{F}_{2} \)
Boiling point/ \( K \)
\( 85 \quad 188 \)
relative form 38.0 36.5 mass
Explain why \( C a F_{2} \) has a very high boiling point.
Subject: Maths
geometric interpretation. namely, a function \( f \) defined on an interval lis
continuous on I if its graph has no 'holes' or 'jumps'.f is said to have a removable discontinuity at \( c \) if \( f(x) \) has
a limit at \( c \) but \( \lim \lim _{x \rightarrow c} f(x) \neq f(c) \)
If \( \lim _{x \rightarrow c+} f(x) \) and \( \lim _{x \rightarrow c-} f(x) \) exist
but are not equal then \( c \) is called jump discontinuity.
If \( \lim _{x \rightarrow c+} f(x) \) and \( \lim _{x \rightarrow c-} f(x) \) fail to
exist then c is called infinite
discontinuity.
\( \operatorname{Let} g(x)=\left\{\begin{array}{ll}x^{2}+5 & x<2 \\ 10 & x=2 \text { then } x=2 \\ 1+x^{3} & x>2\end{array}\right. \)
A. a point of continuity
B. is a removable discontinuity
C. is a jump discontinuity
D. is.an infinite discontinuity
Subject: Chemistry
Assertion
Benzyl bromide when kept in acetone
water produces benzyl alcohol.
Reason
The reaction follows \( S_{N} 2 \) mechanism.
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. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\}, \) then the relation \( \boldsymbol{R}= \)
\( \{(b, c)\} \) on \( A \) is
A . reflexive only
B. symmetric only
c. transitive only
D. reflexive and transitive only
Subject: Biology
Drinking water may contain dissolved calcium hydrogen-carbonate,
\( \boldsymbol{C} \boldsymbol{a}\left(\boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3}\right)_{2} . \) How many electrons are
present in a hydrogen-carbonate anion?
A . 30
B. 31
c. 32
D. 33
Subject: Chemistry
Choose the correct option.
\( \mathbf{A} \cdot \mathrm{CsH}>\mathrm{KH}>\mathrm{NaH}<\mathrm{LiH}(\text { Order of stability }) \)
B. \( H_{2} O<N H_{3}<C H_{4} \) (Order of dipole moment)
C \( \left.\cdot P H_{3}<A s H_{3}<N H_{3}<S b H_{3} \text { (Order of boiling point }\right) \)
D. \( x \ldots \ldots \ldots \ldots . . . H_{---} X, X=0>F>N>S>C \)
(Order of strength of H-bonding)
Subject: Maths
The projections of a directed line segment on the coordinate axes 12,4,3 The direction cosines of the line are
A \( \cdot \frac{12}{13},-\frac{4}{13}, \frac{3}{13} \)
B. \( -\frac{12}{13},-\frac{4}{13}, \frac{3}{13} \)
c. \( \frac{12}{13}, \frac{4}{13}, \frac{3}{13} \)
D. none of these
Subject: Physics
For periodic motion of small amplitude
\( A, \) the time period \( T \) of this particle is
proportional to
\( \mathbf{A} \cdot A \sqrt{\frac{m}{\alpha}} \)
B. \( \frac{1}{A} \sqrt{\frac{m}{\alpha}} \)
c. \( A \sqrt{\frac{\alpha}{m}} \)
D. \( A \sqrt{\frac{2 \alpha}{m}} \)
Subject: Maths
\( 9^{t h} \) term in the expansion of
\( \left(\frac{x}{a}-\frac{3 a}{x^{2}}\right)^{12} \)
A \( \cdot^{12} C_{9} \cdot 3^{9} x^{-12} a^{6} \)
В. \( ^{12} C_{6} \cdot 3^{8} x^{-16} a^{6} \)
C \( .^{12} C_{4} \cdot 3^{8} x^{-12} a^{4} \)
D. none of the above
Subject: Physics
A stationary body explodes into two
fragments of masses \( m_{1} \) and \( m_{2} . \) If
momentum of one tangent is \( p \), the
minimum energy of explosion is
A \( \cdot \frac{p^{2}}{2\left(m_{1}+m_{2}\right)} \)
B. \( \frac{p^{2}}{2 \sqrt{m_{1} m_{2}}} \)
c. \( \frac{p^{2}\left(m_{1}+m_{2}\right)}{2 m_{1} m_{2}} \)
D. \( \frac{p^{2}}{2\left(m_{1}-m_{2}\right)} \)
Subject: Maths
If the \( (\boldsymbol{m}+\mathbf{1}) \) th \( ,(\boldsymbol{n}+\mathbf{1}) \) th and \( (\boldsymbol{r}+\mathbf{1}) \)
th terms of an A.P are in G.P and \( m, n, r \)
are in H.P, then the ratio of the first
term of the A.P to its common difference
in terms of \( n \) be \( n / k \).Find \( -k ? \)
Subject: Chemistry
A current of 9.65 A is passed through an aqueous solution of \( N a C l \) using suitable electrodes for 1000 sec. Given
that 1 faraday equals 96500 coulombs
the amount of \( N a O H(\text { mol wt. } 40) \)
formed on electrolysis is:
A . 2.0 g
B. 8.0 g
c. \( 4.0 \mathrm{g} \)
D. \( 1.0 \mathrm{g} \)
Subject: Chemistry
Basic character of fluorides increases
in the order:
A \( \cdot X e F_{6}<X e F_{4}<X e F_{2} \)
B. \( X e F_{2}<X e F_{4}<X e F_{6} \)
c. \( X e F_{2}=X e F_{4}<X e F_{6} \)
D. \( X e F_{2}>X e F_{4}<X e F_{6} \)
Subject: Maths
\( f(x)=\left|\begin{array}{lll}a^{-x} & e^{x \ln a} & x^{2} \\ a^{-3 x} & e^{3 x \ln a} & x^{4} \\ a^{-5 x} & e^{5 x \ln a} & 1\end{array}\right|, \) then
A. \( f(x) \cdot f(-x)=0 \)
B. \( f(x)-f(-x)=0 \)
c. \( f(x)+f(-x)=0 \)
D. None of these
Subject: Maths
Calculate variance for following data:
\( \begin{array}{llll}\text { Length } & \mathbf{1 7 0 0}- & \mathbf{1 9 0 0}- & \mathbf{2 1 0 0}- \\ \text { of wire } & \mathbf{1 9 0 0} & \mathbf{2 1 0 0} & \mathbf{2 3 0 0}\end{array} \)
Number 10 16 20
\( \mathbf{A} \cdot 55,822.22 \)
B . 55,238.51
c. 55832.55
D. 56,823.50
Subject: Maths
Show that
\( \sin ^{2}(\theta+A)+\sin ^{2}(\theta+B) \)
\( 2 \cos (A-B) \sin (\theta+A) \sin (\theta+B) \)
is independent of \( \boldsymbol{\theta} \boldsymbol{o r}=\sin ^{2}(\boldsymbol{A}- \)
\( \boldsymbol{B}) \)
Subject: Chemistry
In the following reaction:
\( \boldsymbol{x} \boldsymbol{Z} \boldsymbol{n}+\boldsymbol{y} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{d} \boldsymbol{i} l) \longrightarrow \)
\( \boldsymbol{a} \boldsymbol{Z} \boldsymbol{n}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+\boldsymbol{b} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{c} \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{O}_{3} \)
What is the sum of the coefficients
\( (a+b+c) ? \)
Subject: Physics
A pendulum clock keeps correct time at
\( 20^{\circ} \mathrm{C} . \) The correction to be made during
summer per day where the average
temperature is \( 40^{\circ} C,\left(\alpha=10^{-5} /^{\circ} C\right) \)
will be:
A. 5.64 sec
B. 6.64 sec
c. 7.64 sec
D. 8.64 sec
Subject: Physics
Two cylindrical rod have area of cross-
section \( \boldsymbol{A}_{\mathbf{1}} \boldsymbol{A}_{\mathbf{2}} . \) If \( \boldsymbol{A}_{\mathbf{1}} \) is greater than \( \boldsymbol{A}_{\mathbf{2}} \)
Then which of the following is correct?
A. The resistivity of the cylinder having area of crosssection \( A_{1} \) is higher than the cylinder of cross-section \( A_{2} \)
B. The resistivity of the cylinder having area of crosssection \( A_{2} \) is higher than the cylinder of cross-section
\( A_{1} \)
C. The resistivity of the cylinder having area of crosssection \( A_{1} \) is same as the cylinder of cross-section \( A_{2} \)
D. None of the above
Subject: Physics
A long wire is bent into the shape
PQRST as shown in the following
Figure with \( Q R S \) being a semicircle
with centre \( O \) and radius \( r \) metre. \( A \)
current of \( I \) ampere flows through it in
the direction \( \boldsymbol{P} \rightarrow \boldsymbol{Q} \rightarrow \boldsymbol{R} \rightarrow \boldsymbol{S} \rightarrow \boldsymbol{T} \)
Then, the magnetic induction at the
point \( O \) of the figure in vacuum is
\( ^{\mathbf{A}} \cdot_{\mu_{0} i}\left[\frac{1}{2 \pi r}+\frac{1}{4 r}\right] \)
В \( \cdot \mu_{0} i\left[\frac{1}{2 \pi r}-\frac{1}{4 r}\right] \)
c. \( \frac{\mu_{0} i}{4 r} \)
D. \( \frac{\mu_{0} i}{\pi r} \)
Subject: Maths
A member of these family with positive
gradient making an angle of \( \frac{\pi}{4} \) with the line \( 3 x-4 y=2, \) is
A. \( 7 x-y-5=0 \)
B. \( 4 x-3 y+2=0 \)
c. \( x+7 y=15 \)
D. \( 5 x-3 y-4=0 \)
Subject: Physics
Q Type your question-
speed of \( 2 \mathrm{cms}^{-1} \) on a \( \mathrm{V} \) -shaped
conductor each prong of which is \( 50 \mathrm{cm} \) in length immersed in a uniform
magnetic field \( \mathbf{B}=\mathbf{0 . 4 T}, \) perpendicular
and into the \( V \) -plane shown in the

Figure. To start with, at time \( \mathbf{t}=\mathbf{0} s, \) the
mid-point \( C \) of the rod is at \( 0 . \) Then [both conductor and rod have resistance of 10
\( ^2 \) per meter
A. the current in the circuit increases from zero to \( 300 \mathrm{mA} \) during \( 20 s \)
B. the current in the circuit is \( 300 \mathrm{mA} \) fort \( \leq 20 \) s and zero fort \( >20 \) s.
c. the current in the circuit is \( 150 \mathrm{mA} \), till the rod is in contact with \( V \) -conductor
D. the current in the circuit is \( 150 \mathrm{mA} \) for \( \mathrm{t} \leq 10 \mathrm{s} \) and is \( 300 m A \) for \( 10 s<t \leq 20 s \)
Subject: Physics
A solid cylinder of mass \( \mathrm{m} \) and radius \( \mathrm{r} \) is rolling on a rough inclined plane of inclination \( \theta . \) The coefficient of friction
between the cylinder and incline is \( \mu \) Then:
This question has multiple correct options
A. frictional force is always \( \mu \) mg \( \cos \theta \)
B. friction is a dissipative force.
c. by decreasing \( \theta \), frictional force decreases
D. friction opposes translation and supports rotation
Subject: Physics
Displacement time equation of a particle executing SHM is \( x=4 \) sin\omegat +3 \( \sin \left(\omega t+\frac{\pi}{3}\right) \) here \( x \) is in centimeter and
\( t \) is in seconds. The amplitude of oscillation of the particle is approximately:
A. \( 5 \mathrm{cm} \)
B. 6 \( \mathrm{cm} \) m
\( c \cdot 7 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)
Subject: Physics
Some physical constants are given in List - I and their dimensional formulae
are given in List - II. Match the following
List - 1
A) Planck's constant
e) \( \left[M L^{-1} T^{-2}\right] \)
B) Gravitational constant
f) \( \left[M L^{1} T^{-1}\right] \)
C) Bulk modulus
g) \( \left[M L^{2} T^{-1}\right] \)
D) Linear momentum
h) \( \left[M^{-1} L^{3} T^{-2}\right] \)
A. A-h, B-g, C-e ,D-f
B. A-f, B-e, C-g, D-h
C. A-g, B-f, C-e, D-h
D. A-g, B-h, C-e, D-f
Subject: Maths
\( \operatorname{Let} g(x)=x^{6}+a x^{5}+b x^{4}+c^{3}+d x^{2} \)
\( \boldsymbol{g}(\mathbf{1})=\mathbf{1}, \boldsymbol{g}(\mathbf{2})=\mathbf{2}, \boldsymbol{g}(\mathbf{3})=\mathbf{3}, \boldsymbol{g}(\mathbf{4})=\mathbf{4} \)
A . zero
B.
c. 10
D. 727
Subject: Chemistry
Which one of the following reactions of
Xenon compounds is not feasible?
\( \mathbf{A} \cdot \mathrm{X} \mathrm{e} \mathrm{O}_{3}+6 \mathrm{HF} \rightarrow \mathrm{XeF}_{6}+3 \mathrm{H}_{2} \mathrm{O} \)
B. \( 3 \mathrm{XeF}_{4}+6 \mathrm{H}_{2} \mathrm{O} \rightarrow 2 \mathrm{Xe}+\mathrm{Xe} \mathrm{O}_{3}+12 \mathrm{HF}+1.5 \mathrm{O}_{2} \)
\( \mathbf{C} \cdot 2 \mathrm{X} \mathrm{e} \mathrm{F}_{2}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow 2 \mathrm{Xe}+4 \mathrm{HF}+\mathrm{O}_{2} \)
D. \( \mathrm{XeF}_{6}+\mathrm{RbF} \rightarrow \operatorname{Rb}\left[\mathrm{XeF}_{7}\right] \)
Subject: Maths
If for \( \boldsymbol{x} \boldsymbol{\epsilon}\left(\mathbf{0}, \frac{\mathbf{1}}{\mathbf{4}}\right), \) the derivative of
\( \tan ^{-1}\left(\frac{6 x \sqrt{x}}{1-9 x^{3}}\right) \) is \( \sqrt{x} \cdot g(x), \) then
\( g(x) \) equals.
A \( \cdot \frac{3}{1+9 x^{3}} \)
в. \( \frac{9}{1+9 x^{3}} \)
c. \( \frac{3 x \sqrt{x}}{1-9 x^{3}} \)
D. \( \frac{3 x}{1-9 x^{3}} \)
Subject: Physics
A mass of \( 30 \mathrm{kg} \) is supported on a spring of stiffness \( 60000 \mathrm{N} / \mathrm{m} \). The system is damped and the damping ratio is \( 0.4 . \) The mass is raised \( 5 \mathrm{mm} \)
and then released. Calculate the
damped frequency in Hz.
A. 6.235
B. 6.352
c. 6.523
D. 6.325
Subject: Maths
A line \( P Q \) makes intercepts of length 2
units between the lines \( y+2 x=3 \) and
\( \boldsymbol{y}+\mathbf{2} \boldsymbol{x}=\mathbf{5} . \) If the coordinates of \( \boldsymbol{P} \) are
\( (2,3), \) coordinates of \( Q \) can be
This question has multiple correct options
в. (2,3)
c. \( \left(0, \frac{9}{2}\right) \)
D. (3,2)
Subject: Physics
Assertio
A block of mass \( m \) starts moving on a
rough horizontal surface with a velocity
\( v . \) It stops due to friction between the
block and the surface after moving through a certain distance. The surface
is now tilted to an angle of \( 30^{\circ} \) with the horizontal and the same block is made
to go up on the surface with the same
initial velocity \( v \). The decrease in the
mechanical energy in the second situation is smaller than that in the
first situation.
Reason
The coefficient of friction between the
block and the surface decreases with
the increase in the angle of inclination.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
Assertion
\( \mathbf{A} \)
\( 60 W \) bulb is connected in parallel with a room heater and this combination is connected across the
mains. If the \( 60 W \) bulb is replaced by a
\( 100 W \) bulb, the heat produced by the
heater will be more.BECAUSE
Reason
When resistances are connected in parallel across the mains, the heat produced is inversely proportional to the resistance
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: Chemistry
Unlike \( P b C l_{4}, P I_{4} \) and \( P B r_{4} \) are not
found because:
A. bromine and iodine are more electronegative than chlorine
B. iodine and bromine are smaller in size.
c. larger iodine and bromine are able to reduce \( P b^{4+} \)to \( P b^{2+} \) or \( P b \)
D. the statement is incorrect.
Subject: Physics
Light incident on a rotating mirror \( \mathrm{M} \) is returned to a fixed mirror N placed
\( 22.5 k m \) away from M. The fixed mirror reflects it back to M (along the same path) which in turn reflects the light again along a direction that makes an
angle of \( 27^{\circ} \) with the incident direction.
The speed of rotation of the mirror is:
A .250 rps
в. 500 rps
c. 1000 rps
D. 125 rps
Subject: Maths
A sphere of diameter \( 10 \mathrm{cm} \) weighs 44
kg. The weight of a sphere of the same material whose diameter is \( 6 \mathrm{cm} \) is
A . \( 2.64 \mathrm{kg} \)
в. \( 1.584 \mathrm{kg} \)
c. \( 0.9504 \mathrm{kg} \)
D. \( \frac{4}{3}(0.9504) k g \)
Subject: Physics
The motion of a block sliding down a frictionless ramp can be described as motion with
A. A constant speed, independent of the slope of the ramp
B. A constant speed that depends on the slope of the ramp
c. An acceleration which increases as the block slides
D. A constant acceleration less than \( 10 \mathrm{m} / \mathrm{s}^{2} \)
E. A constant acceleration greater than \( 10 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Physics
Assertion
Thin films such as soap bubble or a thin layer of oil on water show beautiful
colors when illuminated by white light.
Reason

It happens due to the interference of light reflected from the upper surface of thin film.
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
particular coastal location in Japan
seem mostly to resemble the legendary face of a Samurai. Given below are two
explanations of this observed fact. Which of these strikes you as a
scientific explanation?
(a) A tragic sea accident several centuries ago drowned a young Samurai. As a tribute to his bravery,
nature through its inscrutable ways immortalised his face by imprinting it
on the crab shells in that area.
(b) After the sea tragedy, fishermen in
that area, in a gesture of honour to their dead hero, let free any crab shell caught by them which accidentally had a shape resembling the face of a Samurai. Consequently, the particular shape of the crab shell survived longer and therefore in course of time the
shape was genetically propagated. This is an example of evolution by artificial selection.
Subject: Biology
This flower produces enormous trumpet shaped flowers, which smell of rotting meat. Each flower lasts for two days. On
the first day, it is in the female phase, attracting flies by its foul smell. On the next day, the flower changes to male phase and pollen is deposited on the pollinators. Which flower is this?
A. Dead horse arum lily
B. Flypaper flower
c. waterwheel flower
D. Pelican flower
Subject: Maths
f \( l, m, n \) are \( p^{t h}, q^{t h}, r^{t h} \) terms of \( G . P . \) al positive, then \( \left|\begin{array}{lll}\log l & p & 1 \\ \log m & q & 1 \\ \log n & r & 1\end{array}\right| \) equals
A . -
B. 2
\( c \)
\( D \)
Subject: Physics
The mass of a full bottle of cooking oil is
\( 1.30 k g \)
When exactly half of the oil has been used, the mass of the bottle plus the
remaining oil is 0.90 kg.

What is the mass of the empty bottle?
A. \( 0.40 \mathrm{kg} \)
B. \( 0.50 \mathrm{kg} \)
c. \( 0.65 \mathrm{kg} \)
D. \( 0.80 \mathrm{kg} \)
Subject: Physics
Two concentric co-planar circular loops
of radii \( r_{1} \) and \( r_{2} \) carry currents of
respectively \( i_{1} \) and \( i_{2} \) in opposite
directions (one clockwise and the other
anticlockwise.) The magnetic induction
at the centre of loops is half that due to
\( i_{1} \) alone at the centre. If \( r_{2}=2 r_{1} . \) the
value of \( i_{2} / i_{1} \) is
\( \mathbf{A} \cdot 2 \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Physics
An atomic nucleus \( A \) is composed of 84
protons and 128 neutrons. The nucleus
\( A \) emits an \( \alpha \) -particle and is
transformed into a nucleus \( B \). What is
the composition of \( \boldsymbol{B} \) ?
A. 80 protons and 126 neutrons
B. 82 protons and 126 neutrons
c. 82 protons and 124 neutrons
D. 80 protons and 124 neutrons
Subject: Maths
If \( f(x) \) is continuous on \( [a, b] \) and \( \boldsymbol{f}(\boldsymbol{a}) \neq \boldsymbol{f}(\boldsymbol{b}), \) then for
any value \( c \) belongs \( (f(a), f(b)), \) there is at least one number
\( \boldsymbol{x}_{o} \) in \( (\boldsymbol{a}, \boldsymbol{b}) \) for which \( \boldsymbol{f}\left(\boldsymbol{x}_{\boldsymbol{o}}\right)=\boldsymbol{c} \)
A. \( f\left(x_{o}\right)=b \)
В. \( f\left(x_{o}\right)=c \)
c. \( f\left(x_{o}\right)=f(c) \)
D. \( f\left(x_{o}\right)=0 \)
Subject: Maths
Define a relation \( R \) on the set \( N \) of
natural numbers by \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{y}= \)
\( x+5, x \) is a natural number less than
\( \mathbf{4} ; \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{N}\} . \) Depict this relationship
using roster form. Write down the domain and the range.
Subject: Maths
The sum of 100 observations and the
sum of their squares are 400 and 2475 respectively. Later on, three observations, 3,4 and \( 5, \) were found to
be incorrect. If the incorrect
observations are omitted, then the variance of the remaining observations
is.
A . 8.00
B. 8.50
c. 8.25
D. 9.00
Subject: Chemistry
The value of van't Hoff factor for \( 0.1 \mathrm{M} \)
\( B a\left(N O_{3}\right)_{2} \) solution is \( 2.74 . \) The degree of dissociation is:
\( \mathbf{A} \cdot 100 \% \)
B. \( 92 \% \)
c. \( 87 \% \)
D. \( 74 \% \)
Subject: Physics
(a) A rod of length \( l \) is moved
horizontally with a uniform velocity' \( v \) ' in a direction perpendicular to its length through a region in which a uniform magnetic field is acting vertically downward. Derive the expression for the emf induced across the ends of the rod.
(b) How does one understand this
motional emf by invoking the Lorentz force acting on the free charge carriers
of the conductor? Explain.
Subject: Physics
A rubber cord of density d, Youngs modulus Y and length L is suspended vertically. If the cord extends by a length \( 0.5 \mathrm{L} \) under its own weight, then Lis
A \( \cdot \frac{Y}{2 d g} \)
в. \( \frac{Y}{d g} \)
c. \( \frac{2 Y}{d g} \)
D. \( \frac{d g}{2 Y} \)
E \( \cdot \frac{d g}{Y} \)
Subject: Chemistry
Carboxylic acids can be prepared from alcohols, nitriles or esters. Which statements are correct?
1. Both primary and secondary alcohols can be oxidised to carboxylic acids.
2. Carboxylic acids can be made from nitriles by hydrolysis.
3. Ethyl propanoate gives propanoic acid when reacted with hydrochloric
acid.
A .1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct
Subject: Maths
if \( \tan 25^{\circ}=x, \) then
\( \frac{\tan 155^{\circ}-\tan 115^{\circ}}{1+\tan 155^{\circ} \tan 115^{\circ}} \) is equal to
A \( \cdot \frac{1-x^{2}}{2 x} \)
в. \( \frac{1+x^{2}}{2 x} \)
c. \( \frac{1+x^{2}}{1-x^{2}} \)
D. \( \frac{1-x^{2}}{1+x^{2}} \)
Subject: Physics
If \( K \) denotes coefficient of thermal
conductivity, \( d \) the density and \( C \) the
specific heat, the unit of \( \boldsymbol{X}, \) where \( \boldsymbol{X}= \) \( \boldsymbol{K} / \boldsymbol{d} \boldsymbol{c}, \) will be
A . \( \mathrm{cm} \) sec
B. \( c m^{2} \sec ^{-2} \)
\( \mathrm{c} \cdot_{\mathrm{cm}} \sec ^{2} \)
\( \mathbf{D} \cdot c m^{2} \sec ^{-1} \)
Subject: Maths
Quadrilateral \( A B C D \) is a square. \( P, Q \)
and \( R \) are the points on \( A B, B C \) and
\( C D \) respectively, such that \( \boldsymbol{A P}= \) \( \boldsymbol{B} \boldsymbol{Q}=\boldsymbol{C} \boldsymbol{R} . \) Hence, If \( \angle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \) is a right
angle, find \( \angle P R Q(\text { in degrees }) \)
Subject: Maths
In the expression of \( \left(2^{x}+\frac{1}{4^{x}}\right)^{n} \) ratio of
2nd and third terms is given by \( t_{3} / t_{2}= \)
7 and the sum of the co-efficients of 2 nd
and \( 3 \mathrm{rd} \) term is \( 36, \) then the value of \( x \)
is
A \( \frac{-1}{3} \)
в. \( \frac{-1}{2} \)
\( c \cdot \frac{1}{3} \)
D.
Subject: Maths
Construct a quadrilateral \( R E A D, \) when
\( \boldsymbol{R} \boldsymbol{E}=\mathbf{3 . 5 1} \mathrm{cm}, \boldsymbol{E} \boldsymbol{A}=\mathbf{4 . 3} \mathrm{cm}, \boldsymbol{A D}= \)
\( 4.8 \mathrm{cm}, \angle E=105^{\circ} \& \angle R=55^{\circ} \)
Subject: Chemistry
To \( 500 c m^{3} \) of water \( 3.0 \times 10^{-3} k g \) of
acetic acid is added. If \( 23 \% \) of acetic
acid is dissociated, what will be the depression of freezing point? \( \left[K_{f} \) and density of water are \right. \( 1.86 K k g m o l^{-1} \) and \( 0.997 g c m^{-3} \)
respectively
в. \( 0.33 K \)
c. \( 0.98 K \)
D. \( 0.68 K \)
Subject: Maths
Find the area enclosed between the
curves \( \boldsymbol{y}=\boldsymbol{x} \) and \( \boldsymbol{y}=\boldsymbol{x}^{2} \) from \( \boldsymbol{x}=\mathbf{0} \)
and \( \boldsymbol{x}=\mathbf{1} \)
Subject: Maths
The perimeter of a rhombus is \( 146 \mathrm{cm} \)
One of its diagonals is 55 cm. Then the length of the other diagonal and the area of the rhombus is
A. \( 48 \mathrm{cm}, 1320 \mathrm{cm}^{2} \)
B . \( 45 \mathrm{cm}, 660 \mathrm{cm}^{2} \)
c. \( 27.5 \mathrm{cm}, 660 \mathrm{cm}^{2} \)
D. None of these
Subject: Maths
Direction cosines of the line \( \frac{x+2}{2}= \)
\( \frac{2 y-5}{3}, z=-1 \) are
A \( \cdot \frac{4}{5}, \frac{3}{5}, 0 \)
B. \( \frac{3}{5^{\prime}}, \frac{4}{5^{\prime}} \frac{1}{5} \)
c. \( \quad-\frac{3}{5}, \frac{4}{5}, 0 \)
D. \( \frac{4}{5},-\frac{2}{5}, \frac{1}{5} \)
Subject: Physics
A railway track is banked for a speed \( \mathbf{v} \)
by making the height of the outer rail h
higher than that of the inner rail. The
distance between the rails is d. The
radius of curvature of the track is \( r \)
Then,
\( \mathbf{A} \cdot \frac{h}{d}=\frac{v^{2}}{r g} \)
B. \( \tan \left(\sin ^{-1} \frac{h}{d}\right)=\frac{v^{2}}{r g} \)
\( ^{\mathbf{C}} \tan ^{-1}\left(\frac{h}{d}\right)=\frac{v^{2}}{r g} \)
\( \mathbf{D} \cdot \frac{h}{r}=\frac{v^{2}}{d g} \)