AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If lies in the second quadrant, then the value of \( \sqrt{\left(\frac{1-\sin \theta}{1+\sin \theta}\right)}+\sqrt{\left(\frac{1+\sin \theta}{1-\sin \theta}\right)} \) is
\( \mathbf{A} \cdot 2 \sec \theta \)
в. \( -2 \sec \theta \)
\( c .2 \operatorname{cosec} \theta \)
D. noneofthese
Subject: Chemistry
Equal volumes of \( 0.1 M A g N O_{3} \) and
\( 0.2 M N a C l \) are mixed. The
concentration of \( N O_{3}^{-} \) ions in the mixture will be:
\( \mathbf{A} \cdot 0.1 M \)
B. \( 0.05 M \)
\( c \cdot 0.2 M \)
D. \( 0.15 M \)
Subject: Physics
Four particles of masses \( m, m, 2 m \) and
\( 2 m \) are placed at the four corners of a
square of side \( a \) as shown in the figure.
The magnitude of the gravitational
force acting on a particle of mass \( \boldsymbol{m} \)
placed at the centre of the square is
\( ^{\mathbf{A}} \cdot \frac{2 G m^{2}}{a^{2}} \)
в. \( \frac{G m^{2}}{\sqrt{2} a^{2}} \)
c. \( \frac{G m^{2}}{2 a^{2}} \)
\( D \)
Subject: Physics
A drunkard is walking along a straight
road. He takes 5 steps forward and 3 steps backward and so on. Each step is 1 \( \mathrm{m} \) long and takes 1 s. There is a pit on the road 11 m away from the starting point. The drunkard will fall into the pit
after:
A . 21 s
B. 29 s
c. \( 31 s \)
D. 37 s
Subject: Physics
A neutron in a nuclear reactor collides
head on elastically with the nucleus of a carbon atom initially at rest. The fraction of kinetic energy transferred from the neutron to the carbon atom is
A \( \cdot \frac{11}{12} \)
B. \( \frac{2}{11} \)
c. \( \frac{48}{121} \)
D. \( \frac{48}{169} \)
Subject: Chemistry
\( 2 N O C l(g) \leftrightharpoons 2 N O(g)+C l_{2}(g) \)
For the above reaction, which of the
following expressions gives the equilibrium constant?
\( ^{\text {A. }} \frac{[N O C l]}{[N O]\left[C l_{2}\right]} \)
\( ^{\mathrm{B}} \cdot \frac{[N O]\left[C l_{2}\right]}{[N O C l]} \)
c. \( \frac{[N O C l]^{2}}{[N O]^{2}\left[C l_{2}\right]} \)
D. \( \frac{[N O]^{2}\left[C l_{2}\right]}{[N O C l]^{2}} \)
E \( \frac{[N O C l]^{2}}{[N O]^{2}\left[C l_{2}\right]^{2}} \)
Subject: Physics
A ball falling-in a lake of depth \( 400 \mathrm{m} \) has a decrease of \( 0.2 \% \) in its volume at
the bottom. The bulk modulus of the
material of the ball is \( \left(\text { in } N m^{-} 2\right) \)
A \( \cdot 9.8 \times 10^{9} \)
B . \( 9.8 \times 10^{10} \)
c. \( 1.96 \times 10^{10} \)
D. \( 9.8 \times 10^{11} \)
E \( .1 .96 \times 10^{9} \)
Subject: Maths
If the sum \( 1+2+3+\ldots .+K \) is a
perfect square \( N^{2} \) and if \( N \) is less than
\( 100, \) then the possible values for \( K \) are:
A. only 1
B. 1 and 8
c. only 8
D. 8 and 49
E. \( 1,8, \) and 49
Subject: Chemistry
\( C H C l_{3} \) and \( H_{2} O \) from two separate
immiscible layers. \( B r_{2}(\text { orange }) \) and \( I_{2} \) (violet) are soluble in organic layer to a greater extent. In test tube \( \boldsymbol{A}(\boldsymbol{K} \boldsymbol{I}+ \)
\( \left.\boldsymbol{C H C l}_{3}+\boldsymbol{H}_{2} \boldsymbol{O}\right) \) and \( \boldsymbol{B}(\boldsymbol{K} \boldsymbol{B r}+ \)
\( \left.\boldsymbol{C H} \boldsymbol{C l}_{3}+\boldsymbol{H}_{2} \boldsymbol{O}\right), \boldsymbol{C l}_{2} \) gas is passed
then:
Given:
\( \frac{1}{2} C l_{2}+e^{-} \longrightarrow C l^{-} \quad E^{o}=1.40 \mathrm{V} \)
\( \frac{1}{2} B r_{2}+e^{-} \longrightarrow B r^{-} \quad E^{o}=1.09 \mathrm{V} \)
\( \frac{1}{2} I_{2}+e^{-} \longrightarrow I^{-} \quad E^{o}=0.62 \mathrm{V} \)
This question has multiple correct options
A. organic layer in \( A \) appear violet
B. organic layer in \( A \) appear orange
c. organic layer in \( B \) appear orange
D. organic layer in \( B \) first appear violet then orange
Subject: Chemistry
Which of the following set is isostructural?
\( \mathbf{A} \cdot \mathrm{XeF}_{2}, \mathrm{IF}_{2}^{-} \)
В. \( \mathrm{NH}_{3}, \mathrm{BF}_{3} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{2-}, \mathrm{SO}_{3}^{2} \)
D. \( \mathrm{PCl}_{5}, \mathrm{Cl}_{5} \)
Subject: Chemistry
Assertion
Interhalogen compounds are more reactive than halogens (except fluorine).
Reason
They all undergo hydrolysis giving halide ion derived from the smaller
halogen and anion derived from larger
halogen.
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
In the given reaction, products are
\( A \)
and \( \mathrm{H}_{2} \)
B.
and \( \mathrm{CH}_{3} \mathrm{Br} \)
\( c \)
and \( \mathrm{CH}_{3} \mathrm{OH} \)
\( D \)
and \( \mathrm{CH}_{3} \mathrm{Br} \)
Subject: Maths
The differential equation \( (3 x+4 y+ \)
1) \( \boldsymbol{d} \boldsymbol{x}+(\boldsymbol{4} \boldsymbol{x}+\boldsymbol{5} \boldsymbol{y}+\mathbf{1}) \boldsymbol{d} \boldsymbol{y}=\boldsymbol{0} \) represents
a family of
A. Circles
B. Parabolas
c. Ellipses
D. Hyperbolas
Subject: Chemistry
Assertion
The main reason of ozone layer
depletion is believed to be the release of
chlorofluorocarbon compounds known
as freons.
Reason
CFCs are transporting agents for continuously generating chlorine radicals into the stratosphere.
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 \( \sin ^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\dots \dots \infty\right)+ \)
\( \cos ^{-1}\left(x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4}-\dots \dots\right)= \)
\( \frac{\pi}{2} \) and \( 0<x<\sqrt{2} \) then \( x= \)
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot-\frac{1}{2} \)
D. -
Subject: Physics
A sphere A moving with a speed u and rotating with an angular velocity \( \omega \) makes a head-on elastic collision with
an identical stationary sphere B. There is no friction between the surface of \( A \)
and B. Disregard gravity. Then which of the following statements is/are true? This question has multiple correct options
A. A will stop moving but continue to rotate with an angular velocity \( \omega \)
B. A will come to rest and stop rotating.
c. B will move with a speed u without rotating
D. B will move with a speed u and rotate with an angular velocity \( \omega \)
Subject: Chemistry
How many minutes will it takes to plate
out \( 5.2 \mathrm{g} \) of \( \mathrm{Cr} \) from a \( \boldsymbol{C r}_{2}\left(\boldsymbol{S O}_{4}\right)_{3} \)
solution using a current of 9.65 A? (Atomic weight of \( \mathrm{Cr}=52.0 \) )
A . 200
B. 50
\( c \cdot 100 \)
\( D \cdot 103 \)
Subject: Physics
Magnetic flux linked with a stationary loop resistance \( \boldsymbol{R} \) varies with respect to
time during the time period \( T \) as
follows:
\( \phi=a t(T-t) \)
The amount of heat generated in the loop during that time (inductance of the coil is negligible) is
A \( \cdot \frac{\alpha T}{3 R} \)
В. \( \frac{a^{2} T^{2}}{3 R} \)
\( ^{\mathbf{C}} \cdot \frac{a^{2} T^{2}}{R} \)
D. \( \frac{a^{2} T^{3}}{3 R} \)
Subject: Physics
A ball of mass \( 5 k g \) experience a force
\( F=2 x^{2}+x . \) Work done in displacing
the ball by \( 2 \mathrm{m} \) is then
A \( \cdot \frac{22}{3} J \)
в. \( \frac{44}{3} J \)
c. \( \frac{32}{3} J \)
D. \( \frac{16}{3} J \)
Subject: Chemistry
Assertion
The cell potential of mercury cell is \( 1.35 V, \) which remains constant.
Reason

In mercury cell, the electrolyte is a paste of \( K O H \) and \( Z n O \)
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: Maths
Find the roots of each of the
following quadratic equations by the method of completing the squares
\( 2 x^{2}-5 x+3=0 \)
A. \( x=2, x=-7 \)
В. \( x=-1, x=3 \)
c. \( x=1, x=\frac{3}{2} \)
D. \( x=1, x=\frac{1}{2} \)
Subject: Physics
Two sound sources of sound are placed
along the diameter of a circle of radius
\( \boldsymbol{R}(\boldsymbol{R}>>\mathbf{4} \boldsymbol{\lambda}) \) How many minima will be
heard as one moves along the perimeter
of circle?
\( A \cdot 16 \)
В. 12
\( c \cdot 4 \)
\( D \)
Subject: Chemistry
A metal \( M \) which is not affected by
strong acids like conc.
\( H N O_{3}, \) conc. \( H_{2} S O_{4} \) and conc. solution
of alkalies like \( N a O H, K O H \) forms
\( M C l_{3} \) which finds use for toning in
photography. The metal \( M \) is :
A . \( A g \)
в. \( H g \)
c. \( A u \)
D. \( C u \)
Subject: Biology
Which of the following statements is
true about RBCs in humans?
A. They carry about \( 20-25 \) per cent of \( C O_{2} \)
B. They transport 99.5 per cent of \( O_{2} \)
C. They transport about 80 per cent oxygen only and the rest 20 per cent of it is transported in dissolved state in blood-plasma.
D. They do not carry \( C O_{2} \) at all.
Subject: Chemistry
At \( 473 \mathrm{K} \), equilibrium constant, \( K_{c} \) for
decomposition of phosphorus pentachloride, \( \boldsymbol{P} \boldsymbol{C l}_{5} \) is \( \boldsymbol{8} . \boldsymbol{3} \times \boldsymbol{1 0}^{-3} . \) If
decomposition is depicted as:
\( \boldsymbol{P C l}_{5(g)} \rightleftharpoons \boldsymbol{P C l}_{3(g)}+\boldsymbol{C l}_{2(g)} ; \triangle_{r} \boldsymbol{H}^{0}= \)
\( 124.0 k m o l^{-1} \) what would be the effect
on reaction if the temperature is increased?
A. Reaction will shift in the backward direction
B. Reaction will shift in the forward direction
c. Reaction is equilibrium
D. Reaction first moves forward and then remains at equilibrium
Subject: Chemistry
Define pH? Calculate the pH of
1. \( 10^{-3} \mathrm{M} \mathrm{HCl} \)
2. \( 10^{-3} \mathrm{M} \mathrm{HCl} \)
3. \( 0.001 M \) NaOH
4. \( 0.0008 M B a(O H)_{2} \)
Subject: Maths
The first and second terms of both an
A.P. and a G.P. are same \( x \) and \( y \)
respectively where both \( x \) and \( y \) are
\( +i v e \) and \( x \) is greater than \( y . \) If \( S \) be the
sum of infinite \( G . P ., \) then prove that
sum of first \( n \) terms of \( A . P . \) is given by \( \boldsymbol{n x}-\frac{\boldsymbol{n}(\boldsymbol{n}-\mathbf{1}) \boldsymbol{x}^{2}}{\boldsymbol{2} \boldsymbol{S}} \)
Subject: Physics
A steel wire of \( 4.0 \mathrm{m} \) in length is
stretched through \( 2.0 \mathrm{mm} \). The crosssectional area of the wire is \( 2.0 m m^{2} .1 \)
Young's modulus of steel is \( 2.0 \times \) \( \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \mathbf{m}^{\mathbf{2}} \) find
(i) the energy density of
wire
(ii) the elastic potential energy stored in the wire.
Subject: Maths
If \( \boldsymbol{I}=\int_{0}^{a} \sqrt{\frac{\boldsymbol{a}-\boldsymbol{x}}{\boldsymbol{a}+\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x}, \boldsymbol{a}>\mathbf{0}, \) then \( \boldsymbol{I} \)
equals
A \( \cdot \frac{1}{2}\left(a-\frac{\pi}{2}\right) \)
B \( \cdot \frac{a}{2}(\pi-1) \)
c. \( \frac{1}{\sqrt{2}} a(\pi-1) \)
D. \( a\left(\frac{\pi}{2}-1\right) \)
Subject: Physics
A \( 10 k W \) drilling machine is used to drill a bore in a small aluminium block
of mass \( 8 k g . \) Find the rise in
temperature of the block in 2.5 minutes,assuming \( 50 \% \) power is used up in heating the machine itself or lost to the surroundings.
(Specific heat of aluminium= \( \left.0.91 J g^{-1 o} C^{-1}\right) \)
\( \mathbf{A} \cdot 100^{\circ} C \)
в. \( 103^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 150^{\circ} \mathrm{C} \)
D. \( 155^{\circ} \mathrm{C} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{4}}{\mathbf{3}} \boldsymbol{x}^{3}-\mathbf{4} \boldsymbol{x}, \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{2} . \) Then
the global minimum value of the function is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( -8 / 3 \)
c. -4
D. none of these
Subject: Maths
\( \int \frac{d x}{x(1+\sqrt[3]{x})^{2}} \) is equal to
A \( \cdot\left(\log \frac{x^{1 / 3}}{1+x^{1 / 3}}+\frac{1}{1+\sqrt[3]{x}}\right)+c \)
B. \( 3\left(\log \frac{1+\sqrt[3]{x}}{\sqrt[3]{x}}+\frac{1}{1+\sqrt[3]{x}}\right)+c \)
\( ^{\mathrm{C}} \cdot\left(\log \frac{x^{1 / 3}}{1+x^{1 / 3}}-\frac{1}{1+\sqrt[3]{x}}\right)+c \)
D. \( 3\left(\log \frac{1+\sqrt[3]{x}}{\sqrt[3]{x}}-\frac{1}{1+\sqrt[3]{x}}\right)+c \)
Subject: Maths
The area enclosed between the curves
\( \mathbf{y}=\mathbf{a x}^{2} \) and \( \mathbf{x}=\mathbf{a y}^{2}(\mathbf{a}>\mathbf{0}) \) is 1 sq. unit,
then the value of a is
A. \( 1 / \sqrt{3} \)
в. \( 1 / 2 \)
c. 1
D. \( 1 / 3 \)
Subject: Chemistry
The equilibrium constant for the
following reaction is \( 64 . H_{2} O(l)+ \)
\( \boldsymbol{C O}(\boldsymbol{g}) \leftrightharpoons \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) . \) If the rate
constant for the forward reaction is 160
the rate constant for the backward
reaction is:
A . 0.4
B . 2.
c. 6.2
D. 10.24
Subject: Maths
Find the median for the following data.
\( \begin{array}{lllll}\text { Height } & \mathbf{5}- & \mathbf{1 0}- & \mathbf{1 5}- & \mathbf{2 0}- \\ (\mathrm{ft}) & \mathbf{1 0} & \mathbf{1 5} & \mathbf{2 0} & \mathbf{2 5}\end{array} \)
No. of
trees
Subject: Physics
The block of mass \( m_{2}=10 \mathrm{kg} \) is given
a sharp impulse so that it acquires a velocity \( v_{0}=30 m / s \) towards right. Find the velocity of the centre of mass.
\[
\left.\boldsymbol{m}_{2}=\mathbf{5} \boldsymbol{k} \boldsymbol{g} \text { and } \boldsymbol{k}=\boldsymbol{3 0} \boldsymbol{N} / \boldsymbol{m}\right)
\]
A. \( 5 \mathrm{m} / \mathrm{s} \)
в. \( 10 \mathrm{m} / \mathrm{s} \)
c. \( 15 \mathrm{m} / \mathrm{s} \)
D. 20 \( m / s \)
Subject: Physics
The velocity of the object over the
interval (2,4) is :
A. \( 10 \mathrm{m} / \mathrm{s} \)
\( B .5 \mathrm{m} / \mathrm{s} \)
c. \( 20 \mathrm{m} / \mathrm{s} \)
D. \( 15 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
What is the \( p H \) of \( 0.1 M N a H C O_{3} ? \)
(Given \( \boldsymbol{K}_{\mathbf{1}}=\mathbf{4 . 5} \times \mathbf{1 0}^{-\mathbf{7}}, \boldsymbol{K}_{\mathbf{2}}=\mathbf{4 . 5} \times \)
\( 10^{-11} \) for carbonic acids.
Subject: Maths
If statements \( p, q, r \) have truth values \( T \)
\( F, T \) respectively then which of the following statement is true
A \( \cdot(p \rightarrow q) \wedge r \)
в. \( (p \rightarrow q) \vee \sim r \)
C \( .(p \wedge q) \vee(q \wedge r) \)
D. \( (p \rightarrow q) \rightarrow r \)
Subject: Chemistry
Hydrogen molecules are:
A. monoatomic and form \( X_{2}^{2-} \) type ions
B. diatomic and form \( X_{2}^{-} \) type ions
C . diatomic and form \( X^{-} \) as well as \( X^{+} \) type ions
D. monoatomic and form \( X^{-} \) type ions
Subject: Physics
The moment of force of \( 5 N \) about a
point \( \boldsymbol{P} \) is \( 20 \mathrm{Nm} \). Calculate the
distance of point of application of the
from the point \( \boldsymbol{P} \)
\( A .3 m \)
в. \( 0.6 m \)
\( c .4 m \)
D. \( 10 m \)
Subject: Maths
In the figure, \( m \) ? \( P O Q=30 \) ? and radius \( O P \)
\( =12 \mathrm{cm}, \) then find the given area of segment PRQ (Given \( \pi=3.14) \)
A \( \cdot 1.68 c m^{2} \)
B \( \cdot 2 \cdot 46 c m^{2} \)
\( c \cdot 0.68 c m^{2} \)
D. none of these
Subject: Physics
The isothermal elasticity of a medium
is \( \mathrm{E}_{i} \) and the adiabatic elasticity in \( \mathrm{E}_{a} \)
The velocity of sound in the medium is proportional to
\( \mathbf{A} \cdot E_{j} \)
в. \( E_{a} \)
c. \( \sqrt{E_{i}} \)
D. \( \sqrt{E_{a}} \)
Subject: Maths
An ellipse passing through origin has its foci at (5,12) and \( (24,7), \) then its eccentricity is
A \( \cdot \frac{\sqrt{386}}{38} \)
B. \( \frac{\sqrt{386}}{39} \)
c. \( \frac{\sqrt{386}}{47} \)
D. \( \frac{\sqrt{386}}{51} \)
Subject: Chemistry
Assertion
A spectral line will be observed for
\( 2 P_{z}-2 P_{y} \) transition
Reason
The energy of \( 2 P_{x} \) and \( 2 P_{y} \) orbitals is
the same
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
A solution containing \( 10 g d m^{-3} \) of urea
(molecular mass \( =60 g m o l^{-1} \) ) is
isotonic with a \( 5 \% \) solution of a
nonvolatile solute. The molecular mass
of this is nonvolatile solute is:
A \( \cdot 250 g m o l^{-1} \)
в. 300 gmol-\( ^{-1} \)
c. 350 gmol-\( ^{-1} \)
D. \( 200 g \) mol \( ^{-1} \)
Subject: Maths
Solution of \( \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{y}}+\boldsymbol{m} \boldsymbol{x}=\mathbf{0}, \) where \( \boldsymbol{m}<\mathbf{0} \)
is:
A \( . x=C e^{m y} \)
B . \( x=C e^{-m y} y \)
c. \( x=m y+C \)
D. \( x=C \)
Subject: Physics
A body is allowed to fall from a height of \( 98 \mathrm{m} \) before hitting the ground the distance travelled by it in the last
second of motion \( \left(\boldsymbol{g}=\mathbf{9} . \mathbf{8 m} \boldsymbol{s}^{-2}\right) \) is
\( A .38 m \)
в. \( 40 m \)
\( c .50 m \)
D. \( 29 m \)
Subject: Maths
Find the equation of parabola with focus (5,0) and vertex (5,3)
A \( \cdot y=12(x-5)^{2}-3 \)
B . \( y-3=-(x-5)^{2} \)
c. \( y=\frac{(x-5)^{2}}{12}-3 \)
D. \( y=-\frac{(x-5)^{2}}{12}+3 \)
Subject: Chemistry
In which of the following reactions have the underlined substance been
reduced?
A. Carbonmonoxide + copperoxide \( \rightarrow \) carbondioxide \( + \) Carbon
copper
в. \( \frac{\text { Copperoxide }}{\text { water }}+ \) hydrochloricacid \( \rightarrow \) copperchloride \( + \)
c. Hydrogen\( + \)ironoxide\( \rightarrow \)iron \( + \)water
D. \( \underline{S t e a m}+ \)iron \( \rightarrow \) ironoxide \( + \)hydrogen
Subject: Chemistry
Select the incorrect statement.
A. If the orbitals differ largely in energy, the cost of hybridization energy becomes large
B. The hybridization in phosphorus between \( 3 s \) and \( 3 p- \) orbitals any be possible and the participation of \( 3 d \) orbitals in the hybridization with the \( 3 s \) and \( 3 p- \) orbitals in not expected because of their (i.e, \( 3 d \) orbital) much higher energy
C. The orbital participation generally requires to bond with highly electronegative elements
D. \( P H_{5} \) does not exist but \( P C l_{5}, P F_{5} \) exist through the formation of \( s p^{3} d^{2} \) hybridization
Subject: Physics
A particle of mass \( M, \) charge \( q>0 \) and
initial kinetic energy \( K \) is projected from infinity towards a heavy nucleus of charge \( Q \) assumed to have a fixed
position.
(a) If the aim is perfect, how close to the center of the nucleus is the particle when it comes instantaneously to rest?
(b) With a particular imperfect aim, the particle's closest approach to nucleus is twice the distance determined in (a)
Determine speed of particle at the closest distance of approach.
Subject: Maths
\( \operatorname{Det}\left\{\begin{array}{ccc}-2 a & a+b & c+a \\ b+a & -2 b & b+c \\ c+a & c+b & -2 c\end{array}\right\}= \)
\( A \cdot(a+b)(b+c)(c+a) \)
В . \( (a-b)(b-c)(c-a) \)
\( c \cdot 4(a+b)(b+c)(c+a) \)
D. \( 4(a-b)(b-c)(c-a) \)
Subject: Maths
Two times the interior angle of a regular polygon is equal to seven times is exterior angle. Find the interior angle of
the polygon and the number of sides in ¡t.
A. \( 130^{\circ} \) and \( n=9 \)
B. \( 140^{\circ} \) and \( n=9 \)
c. \( 160^{\circ} \) and \( n=9 \)
D. \( 170^{\circ} \) and \( n=9 \)
Subject: Physics
The polarising angle for a medium is
found to be \( 60^{\circ} . \) The critical angle of the medium is
A \( \cdot \sin ^{-1}\left(\frac{1}{2}\right) \)
B. \( \sin ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
\( ^{c} \cdot \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
D. \( \sin ^{-1}\left(\frac{1}{4}\right) \)
E \( \cdot \sin ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)
Subject: Physics
A force \( F \) is acting on an object of mass
\( m \) to give it an acceleration of \( a \). If \( m \) is
doubled and \( F \) becomes 16 th times,
what happens to \( a \) ?
A. It is divided by eight
B. It is divided by two
c. It remains unchanged
D. It is multiplied by two
E. It is multiplied by eight
Subject: Chemistry
Endothermic reactions, having \( \Delta S= \)
+ \( \boldsymbol{v} e \) may be spontaneous if:
This question has multiple correct options
A \( . \Delta H>T \Delta S \)
в. \( \Delta H<T \Delta S \)
c. \( \Delta H=T \Delta S \)
D. \( T \) is very high
Subject: Maths
The third term from the end in the
expansion of \( \left(\frac{4 x}{3 y}-\frac{3 y}{2 x}\right)^{9} \) is
A \( \cdot \) s \( _{C_{7}} \frac{3^{5}}{2} \frac{y^{5}}{x^{5}} \)
В. \( -_{-9} \sigma_{7} \frac{3^{5}}{2^{3}} \frac{y^{5}}{x^{5}} \)
c. \( _{9} C_{7} \frac{3^{5}}{2^{3}} \frac{y^{5}}{x^{3}} \)
D. none of these
Subject: Maths
Let a function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) satisfy the
equation \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y}) \) for
all \( x, y . \) If the function \( f(x) \) is
continuous at \( x=0, \) then
A. \( f(x)=0 \) continuous for all \( x \)
B. \( f(x) \) is continuous for all positive real \( x \)
c. \( f(x) \) is continuous for all \( x \)
D. None of these
Subject: Physics
Two masses of \( 40 \mathrm{kg} \) and \( 30 \mathrm{kg} \) are
connected by a weightless string
passing over a friction less pulley as
shown in the figure. The acceleration of
the system would be:
B. \( 0.8 \mathrm{ms}^{-2} \)
\( c \cdot 0.7 m s^{-2} \)
D. \( 0.5 \mathrm{ms}^{-2} \)
Subject: Chemistry
The correct relation between
equilibrium constant \( (K), \) standard
free energy \( \left(\Delta G^{o}\right) \) and temperature
\( (T) \) is:
\( \mathbf{A} \cdot \Delta G^{o}=R T \ln K \)
B . \( K=e^{\Delta G^{G} / 2.303 R T} \)
c. \( \Delta G^{o}=-R T \log K \)
D. \( K=10^{-\Delta G^{\circ} / 2.303 R T} \)
Subject: Physics
The particle of charge \( q \) and mass \( m \) starts moving from origin under the
action of an electric field \( \boldsymbol{E}=\boldsymbol{E}_{0} \boldsymbol{i} \) and
magnetic field \( V=V_{0} i . \) Its velocity at \( (x, 3,0) \) is \( (4 i+3 \hat{i}) . \) The value of \( x \) is :
A. \( \frac{\sqrt{3} m v_{0}}{q E} \)
в. \( \frac{25 m}{2 q E_{o}} \)
c. \( \frac{10 m}{q E_{o}} \)
D. \( \frac{25 E_{0} B_{0}}{m} \)
Subject: Physics
Two objects of same mass \( m \) are
attached at end of a light rod of length \( l \)
and rotating about axis \( O O^{\prime} \) as shown
in the figure. The moment inertia of the
system about the axis \( O O^{\prime} \) is
A \( \frac{m l^{2}}{12} \)
B. \( \frac{5 m l^{2}}{18} \)
c. \( \frac{5 m l^{2}}{24} \)
D. \( \frac{5 m l^{2}}{36} \)
Subject: Chemistry
Arrange \( C C l_{3}\left(C H_{2}\right)_{3} N H_{2}(\mathrm{a}) \)
\( C C l_{3}\left(C H_{2}\right) N H_{2}(\mathrm{b}), \) and \( C C l_{3} C H_{2} N H_{2} \)
(c) in order of decreasing basic nature
\( A \cdot C>B>A \)
B. \( C>A>B \)
\( c \cdot A>c>B \)
D. \( B>A>C \)
Subject: Chemistry
\( \boldsymbol{M}+\mathbf{8} \boldsymbol{C} \boldsymbol{N}^{-}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2} \rightarrow \)
\( \mathbf{4}\left[\boldsymbol{M}(\boldsymbol{C} \boldsymbol{N})_{2}\right]^{-}+\mathbf{4} \boldsymbol{O} \boldsymbol{H}^{-} \)
metal M is:
A. cu
в. \( \mathrm{Hg} \)
c. \( A g \)
D. Au
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\sin |\boldsymbol{x}| \) and \( \boldsymbol{g}(\boldsymbol{x})=\tan |\boldsymbol{x}| \) then
discuss the continuity of \( \boldsymbol{f}(\boldsymbol{x}) \pm \)
\( g(x) ; \frac{f(x)}{g(x)} \) and \( f(x) \cdot g(x) \)
A \( . f(x) g(x) \) and \( f(x) \pm g(x) \) are discontinuous at \( x= \)
\( (2 n+1) \frac{\pi}{2} ; n \in 1 \frac{f(x)}{g(x)} \) is discontinuous at \( x=\frac{n \pi}{2} ; n \in 1 \)
B. \( f(x) g(x) \) and \( f(x) \pm g(x) \) are continuous at \( x=(2 n+ \) 1) \( \frac{\pi}{2} ; n \in 1 \frac{f(x)}{g(x)} \) is discontinuous at \( x=\frac{n \pi}{2} ; n \in 1 \)
C. \( f(x) g(x) \) and \( f(x) \pm g(x) \) are discontinuous at \( x= \)
\( (2 n+1) \frac{\pi}{2} ; n \in 1 \frac{f(x)}{g(x)} \) is continuous at \( x=\frac{n \pi}{2} ; n \in 1 \)
D. \( f(x) g(x) \) and \( f(x) \pm g(x) \) are discontinuous at \( x= \) \( (2 n-1) \frac{\pi}{2} ; n \in 1 \frac{f(x)}{g(x)} \) is discontinuous at \( x=\frac{\pi}{2} ; n \in 1 \)