AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A body is in equilibrium under the influence of a number of forces. Each
force has a different line of action. The
minimum number of forces required is :
This question has multiple correct options
A. 2 , if their lines of action pass through the centre of mass of the body
B. 3, if their lines of action are not parallel.
\( \mathrm{c} .3 \), if their lines of action are parallel
D. \( 4, \) if their lines of action are parallel and all the forces have the same magnitude
Subject: Chemistry
For which change \( \Delta \boldsymbol{H} \neq \Delta \boldsymbol{U} \) ?
\( \mathbf{A} \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
B. \( H C l(l)+N a O H(l) \longrightarrow N a C l(l)+H_{2} 0(l) \)
\( \mathbf{c} \cdot C(s)+O_{2}(g) \rightleftharpoons C O_{2}(g) \)
D. \( N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}(g) \)
Subject: Chemistry
Among \( \boldsymbol{C H}_{4}, \boldsymbol{N H}_{3} \) and \( \boldsymbol{H}_{2} \boldsymbol{O}, \) acidity of
\( H_{2} O \) is maximum because:
A. Oxygen contains two lone pairs of electrons.
B. Bond angle on \( H_{2} O \) is less than \( 109^{\circ} 28^{\prime} \) due to \( V S E P R \)
c. oxygen is more electronegative than \( C \) or \( N \).
D. \( H_{2} O \) is an associated liquid.
Subject: Maths
The angle of a pentagon are in the ratio \( 4: 8: 6: 4: 5 . \) Find the greatest angle of
the pentagon.
\( \mathbf{A} \cdot 120^{\circ} \)
B. \( 140^{\circ} \)
\( c \cdot 160^{\circ} \)
D. 150
Subject: Chemistry
A \( 100 d m^{3} \) flask contains 10 mole each
of \( N_{2} \) and \( H_{2} \) at 777 K.After
equilibrium was reached, partial
pressure of \( \boldsymbol{H}_{2} \) was 1 at \( \boldsymbol{m} \). At this point
5 litre of \( H_{2} O_{(I)} \) was injected and gas mixture was cooled to \( 298 \mathrm{K} \). Find out
the pressure of gaseous mixture left.
Subject: Chemistry
An equimolar quantities of ethanol and
propanol is heated with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
The product formed is /are?
A. \( C_{2} H_{5} O C_{2} H_{5} \)
в. \( C_{3} H_{7} O C_{3} H_{7} \)
c. \( C_{2} H_{5} O C_{3} H_{7} \)
D. all of these
Subject: Physics
It is given that a thermodynamic
system changes from state \( A \) to state \( B \) and then back to state A. It is given that the process is reversible. Choose the
correct statements.
A. The states occurring between A to B are the same as states occurring between B to A.
B. The states occurring between A to B may be different from the states occurring between B to A
c. The energy required for transition from state \( A \) to state B is same as the energy required for the transition from state B to state A
D. The states occurring between A to B cannot be measured
Subject: Chemistry
How many of the following compound on
thermal decomposition gives \( N_{2} \) gas?
\( \left(N H_{4}\right)_{2} C r_{2} O_{7}, N H_{4} N O_{3}, N H_{4} I O_{3} \)
\( N H_{4} N O_{2}, B a\left(N_{3}\right)_{2}, B a\left(N O_{3}\right)_{2} \)
\( \left(N H_{4}\right)_{2} S O_{4},\left(N H_{4}\right)_{2} C O_{3} \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Physics
The magnitude of force (in \( N \) ) acting on a body varies with time \( t(\text { in } \mu s) \) as
shown. \( A B, B C \) and \( C D \) are straight
line segments. The magnitude of total
impulse of force on the body from \( t= \)
\( 4 \mu s \) to \( t=16 \mu s \) is :
\( \mathbf{A} \cdot 10^{-3} N s \)
B \( \cdot 10^{-2} N s \)
\( \mathbf{c} \cdot 10^{-4} N s \)
D. \( 5 \times 10^{-4} N s \)
Subject: Chemistry
The electronic configuration of an element is
\( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{6}, 3 d^{3}, 4 s^{1} . \) This
represents its
A. Excited state
B. Ground state
c. cationic form
D. Anionic form
Subject: Chemistry
The IUPAC name of \( \boldsymbol{C H}_{3}- \)
\( \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)(\boldsymbol{O H}) \boldsymbol{C H}_{2}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \) is:
A. 2,4-Dimethylpentan-2-ol
B. 2,4-dimethylpentan-4-ol
c. 2, 2-dimethylbutane
D. 2,4,4-trimethylbutan-2-ol
Subject: Physics
Velocity of a particle varies as
\( \boldsymbol{v}=\mathbf{2} \boldsymbol{t}^{3}-\mathbf{3} \boldsymbol{t}^{2} \) in \( \boldsymbol{k} \boldsymbol{m} / \boldsymbol{h} \boldsymbol{r} \)
If \( ; t=0 \) is taken at 12: 00 noon, tis in
hr
Find the time between 12: 00 noon
and 1: 00 pm at which speed is
maximum.
B. \( 1: 00 \mathrm{pm} \)
c. 11: 00 am
D. \( 2: 00 \mathrm{pm} \)
Subject: Physics
Electric field intensity at points in between and outside two thin separated parallel sheets of infinite dimension with like charges of same surface charge density \( (\sigma) \) are and
respectively
A \( \cdot \sigma / \epsilon_{0}, \sigma / \epsilon_{0} \)
в. \( 0, \sigma / \epsilon_{0} \)
\( c .0,0 \)
D. \( \sigma / \varepsilon_{0}, 0 \)
Subject: Chemistry
Assertion
The conversion of fresh precipitate to colloidal state is called peptization.
Reason
It is caused by addition of common ions
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 copper wire of length \( 2.2 \mathrm{m} \) and a stee
wire of length \( 1.6 \mathrm{m} \). both of diameter 3.0
\( \mathrm{mm}, \) are connected end to end.When
stretched by a load, the net elongation is found to be \( 0.70 \mathrm{mm} . \) Obtain the load
applied.
Subject: Maths
When \( \overrightarrow{\boldsymbol{A}} \cdot \overrightarrow{\boldsymbol{B}}=-|\boldsymbol{A}||\boldsymbol{B}|, \) then
\( \mathbf{A} \cdot \vec{A} \) and \( \vec{B} \) are perpendicular to each other
B. \( \vec{A} \) and \( \vec{B} \) Act in the same direction
C . \( \vec{A} \) and \( \vec{B} \) Act in the opposite direction
D. \( \vec{A} \) and \( \vec{B} \) can act in any direction
Subject: Chemistry
In which of the following, the oxidation number of oxygen has been arranged in increasing order?
A. \( B a O_{2}<K O_{2}<O_{3}<O F_{2} \)
в. \( O F_{2}<K O_{2}<B a O_{2}<O_{3} \)
c. \( B a O_{2}<O_{3}<O F_{2}<K O_{2} \)
D. \( K O_{2}<O F_{2}<O_{3}<B a O_{2} \)
Subject: Physics
The weight of a person on a planet \( A \) is about half that on the Earth. He
can jump upto \( 0.4 \mathrm{m} \) height on the surface of the Earth. How high he can jump on the planet \( A \) ?
\( \mathbf{A} \cdot 0.4 \mathrm{m} \)
B. \( 0.2 \mathrm{m} \)
c. \( 0.8 \mathrm{m} \)
D. \( 1.6 \mathrm{m} \)
Subject: Physics
A plane electromagnetic wave of frequency \( 28 M H z \) travels in free space along the positive x-direction. At a particular point in space and time, electric field is \( 9.3 V / m \) along positive y-direction. The magnetic field (in T) at that point is
A \( \cdot 3.1 \times 10^{-8} \) along positive z-direction
B . 3.1 \( \times 10^{-8} \) along negative z-direction
C. \( 3.2 \times 10^{7} \) along positive z-direction
D. 3.2 \( \times 10^{7} \) along negative z-direction
Subject: Physics
A car acquires a velocity of 72 kmph in
10 \( s \) starting from rest. Calculate its
average velocity :
\( A \cdot 0 \)
B. \( 5 m s^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 15 \mathrm{ms}^{-1} \)
Subject: Chemistry
Which of the following is a redox
reaction:
A \( \cdot 2 \operatorname{Na}\left[A g(C N)_{2}\right]+Z n \rightarrow N a_{2}\left[\operatorname{Zn}(C N)_{4}\right]+2 A g \)
в. \( B a O_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+H_{2} O_{2} \)
c. \( N_{2} O_{5}+H_{2} O \rightarrow 2 H N O_{3} \)
D. \( A g N O_{3}+K I \longrightarrow A g I+K N O_{3} \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is a function satisfying
\( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x} \boldsymbol{y}) \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and
\( f\left(\frac{3}{4}\right)=\left(\frac{3}{4}\right), \) then \( f\left(\frac{9}{16}\right)= \)
\( A \cdot \frac{3}{4} \)
B. \( \frac{9}{16} \)
c. \( \frac{\sqrt{3}}{2} \)
D.
Subject: Maths
The value of \( \left|\begin{array}{ccc}1+x & 2 & 3 \\ 1 & 2+x & 3 \\ 1 & 2 & 3+x\end{array}\right| \) is
A \( \cdot(x-6) x^{2} \)
в. \( (x-6) \)
c. \( x^{2}(x+6) \)
D. \( (x-6) \)
Subject: Maths
Find the difference between total
surface area \( \& \) curved surface area of a hemisphere of radius \( 21 \mathrm{cm} \)
\( \mathbf{A} \cdot 1376 \mathrm{cm}^{2} \)
B . \( 1386 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 1396 \mathrm{cm}^{2} \)
D. \( 1404 \mathrm{cm}^{2} \)
Subject: Physics
A spherical solid ball of volume \( V \) is
made of a material of density \( \rho_{1} \). It is
falling through a liquid of density
\( \rho_{2}\left(\rho_{2}<\rho_{1}\right) . \) Assume that the liquid
applies a viscous force on the ball
that is proportional to the square of its
speed \( v, \) i.e., \( F_{v i s c o u s}=k v^{2}(k>0) . \) The
terminal speed of the ball is:
A \( \cdot \sqrt{\frac{V g \rho_{1}}{k}} \)
в. \( \frac{V g\left(\rho_{1}-\rho_{2}\right)}{k} \)
c. \( \sqrt{\frac{V g\left(\rho_{1}-\rho_{2}\right)}{k}} \)
D. \( \frac{V g \rho_{1}}{k} \)
Subject: Chemistry
The degree of dissociation of
\( \boldsymbol{C a}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \) in a dilute aqueous solution
containing 7 g of salt per 100 g of water at \( 100^{\circ} \mathrm{C} \) is \( 75 \% \). The vapour pressure of solution in \( \mathrm{mm} \) is \( x, \) then find the
value of \( x / 150 \) to the nearest integer.
Subject: Physics
Particle has an initial velocity \( (\mathbf{6} \hat{\mathbf{i}}+ \)
\( 8 \hat{j}) m s^{-1} \) and \( (0.8 \hat{i}+0.6 \hat{j}) m s^{-2} \) an
acceleration. Its speed after 10 s is:
A \( \cdot 20 m s^{-1} \)
В. \( 7 \sqrt{2} \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 14 \sqrt{2} \mathrm{ms}^{-1} \)
Subject: Maths
The order of \( [\mathbf{x} \mathbf{y} \mathbf{z}]\left[\begin{array}{lll}\mathbf{a} & \mathbf{h} & \mathbf{g} \\ \mathbf{h} & \mathbf{b} & \mathbf{f} \\ \mathbf{g} & \mathbf{f} & \mathbf{c}\end{array}\right]\left[\begin{array}{l}\mathbf{x} \\ \mathbf{y} \\ \mathbf{z}\end{array}\right] \)
is
A . \( 3 \times 1 \)
B. 1x
\( c .1 \times 3 \)
D. 3x3
Subject: Physics
A glass wind screen whose inclination with the vertical can be changed is
mounted on a car. The car moves
horizontally with a speed of \( 2 m / s . A t \)
what angle \( \alpha \) with the vertical should
the wind screen be placed so that the rain drops falling vertically downwards
with velocity \( 6 m / s \) strike the wind
screen perpendicularly?
\( \mathbf{A} \cdot \tan ^{-1}(3) \)
B \( \cdot \tan ^{-1}(4) \)
c. \( \tan ^{-1}\left(\frac{1}{3}\right) \)
D. \( \tan ^{-1}\left(\frac{1}{4}\right) \)
Subject: Maths
\( f(x)=\left\{\begin{array}{ll}\frac{1-\cos x}{x^{2}}, & \text { when } x \neq 0 \\ 1, & \text { when } x=0\end{array}\right. \)
then show that \( f(x) \) is discontinuous at
\( \boldsymbol{x}=\mathbf{0} \)
Subject: Maths
If \( \boldsymbol{A}=(\mathbf{2},-\mathbf{3}, \mathbf{1}), \boldsymbol{B}=(\mathbf{3},-\mathbf{4}, \mathbf{6}) \) and \( \boldsymbol{C} \)
is a point of trisection of \( A B, \) then \( C_{y}= \)
A \( \cdot \frac{11}{3} \)
B. -11
c. \( \frac{10}{3} \)
D. \( \frac{-11}{3} \)
Subject: Physics
A current \( I \) is flowing in a straight
conductor wire of length \( L \). The magnetic induction at a point perpendicular distance \( \frac{L}{4} \) from its centre will be:
A \( \cdot \frac{4 \mu_{0} i}{\sqrt{5} \pi L} \)
в. \( \frac{\mu_{0} i}{2 \pi L} \)
c. \( \frac{\mu_{0} i}{\sqrt{2} L} \)
D. zero
Subject: Maths
Find a vector of magnitude 6 perpendicular to each of the vectors \( \rightarrow \)
\( +\vec{b} \) and \( \vec{a}-\vec{b} \)
where \( \underset{a}{\rightarrow}=\hat{i}+\hat{j}+ \)
\( \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \)
Subject: Chemistry
What is the correct representation of
reaction occurring when HCl is heated
with \( M n O_{2} ? \)
\( \mathbf{A} \cdot M n O_{4}^{-}+5 C l^{-}+8 H^{+} \rightarrow M n^{2+}+5 C l^{-}+5 H_{2} O \)
B. \( M n O_{2}+2 C l^{-}+4 H^{+} \rightarrow M n^{2+}+C l_{2}+2 H_{2} O \)
\( \mathbf{c} \cdot 2 M n O_{2}+4 C l^{-}+8 H^{+} \rightarrow 2 M n^{2+}+2 C l_{2}+4 H_{2} O \)
D. \( M n O_{2}+4 H C l \rightarrow M n C l_{4}+C l_{2}+H_{2} O \)
Subject: Chemistry
Decreasing order of reactivity of \( \boldsymbol{F}_{2} \)
\( C l F \) and \( C l F_{3} \) is :
A. \( C l F_{3}>C l F>F_{2} \)
в. \( C l F>C l F_{3}>F_{2} \)
c. \( C l F_{3}>F_{2}>C l F \)
D. \( F_{2}>C l F>C l F_{3} \)
Subject: Physics
Assertion
Two coherent point sources of light having non-zero phase difference are separated by a small distance. Then, on the perpendicular bisector of line segment joining both the point sources,
constructive interference cannot be
obtained.
Reason
For two waves from coherent point sources to interfere constructively at a
point, the magnitude of their phase
difference at that point must be \( 2 m \pi \)
(where \( m \) is a non-negative integer)
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
Which one of the following is the correct
statement?
A. Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase
B. \( \mathrm{B}_{2} \mathrm{H}_{6} .2 \mathrm{NH}_{3} \) is known as inorganic benzene
C . Boric acid is a protonic acid
D. Beryllium exhibits coordination number of six
Subject: Maths
Let \( a_{1}, a \) and \( b_{1}, b_{2}, \dots . \) be the arithmetic
progressions such that \( a_{1}=25, b_{1}= \)
75 and \( a_{1} 00+b_{100} . \) The sum of the first
one hundred terms of the progressions
\( \left(a_{1}+b_{1}\right),\left(a_{2}+b_{2}\right), \dots \dots \) is
\( A \cdot O \)
B. 100
\( c \cdot 10,000 \)
D. 5,05,000
Subject: Maths
Which of the following functions from \( \boldsymbol{A} \)
to \( B \) are one-one and onto?
(i) \( \boldsymbol{f}_{1}=\{(\mathbf{1}, \mathbf{3}),(\mathbf{2}, \mathbf{5}),(\mathbf{3}, \mathbf{7})\} ; \boldsymbol{A}= \)
\( \{1,2,3\}, B=\{3,5,7\} \)
(ii) \( f_{2}=\{(2, a),(3, b),(4, c)\} ; A= \)
\( \{2,3,4\}, B=\{a, b, c\} \)
(iii) \( \boldsymbol{f}_{3}=\{(\boldsymbol{a}, \boldsymbol{x}),(\boldsymbol{b}, \boldsymbol{x}),(\boldsymbol{c}, \boldsymbol{z})\} ; \boldsymbol{A}= \)
\( \{a, b, c, d\} ; B=\{x, y, z\} \)
Subject: Maths
A cubical box has each edge \( 10 \mathrm{cm} \) and
another cuboidal box is \( 12.5 \mathrm{cm} \) long, 10
cm wide and \( 8 \mathrm{cm} \) high.
i) Which box has the greater lateral
surface area and by how much?
ii) Which box has the smaller total
surface area and by how much?
Subject: Chemistry
Which of the following statements is correct, if the intermolecular force of
attraction between the particles in liquid \( A, B, C \) is in the order \( A<B<C ? \) This question has multiple correct options
A. All the three evaporate at the same rate
B. B evaporates faster than A
c. B evaporates more readily than \( c \)
D. A evaporates more readily than
Subject: Maths
If \( f(x)=\sin ^{2} x+\sin ^{2}\left(x+\frac{\pi}{3}\right)+ \)
\( \cos x \cos \left(x+\frac{\pi}{3}\right) \) and \( g\left(\frac{5}{4}\right)=1 \)
\( \boldsymbol{g}(1)=0 \) then \( (\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})(\boldsymbol{x})= \)
\( A \)
в.
\( c \cdot \sin x \)
D. Data is insufficient
Subject: Chemistry
Calculate pH of solution obtained by
mixing \( 500 \mathrm{ml} \) of \( 0.4 \mathrm{M}, M_{1} O H \) and
1500ml of \( \frac{\mathbf{0 . 8}}{\mathbf{3}} \) molar \( \boldsymbol{N}_{\mathbf{2}} \boldsymbol{O} \boldsymbol{H} . \boldsymbol{K}_{\boldsymbol{b}_{1}}= \)
\( \mathbf{1 0}^{-\mathbf{7}} \boldsymbol{K}_{\boldsymbol{b}_{2}}=\mathbf{4} \times \mathbf{1 0}^{-\mathbf{7}} \)
Subject: Maths
If \( f: R \rightarrow R \) and \( g: R \rightarrow R \) are defined
by \( f(x)=2 x+3, g(x)=x^{2}+7, \) then
the values of \( x \) for which \( f[g(x)]=25 \)
\( A \cdot \pm 1 \)
B. ±2
\( c .\pm 3 \)
D. ±4
Subject: Maths
If the planes \( \boldsymbol{x}-\boldsymbol{c} \boldsymbol{y}-\boldsymbol{b} \boldsymbol{z}=\boldsymbol{0}, \boldsymbol{c} \boldsymbol{x}-\boldsymbol{y}+ \)
\( \boldsymbol{a} \boldsymbol{z}=\mathbf{0} \) and \( \boldsymbol{b} \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y}-\boldsymbol{z}=\mathbf{0} \) pass
through a stright line,then the value of \( a^{2}+b^{2}+c^{2}+2 a b c \) is:
A . 1
B. 2
\( c .3 \)
D. none of these
Subject: Physics
The stopping potential for the photo electrons emitted from a metal surface
of work function \( 1.7 e V \) is \( 10.4 V \)

Identify the energy levels corresponding to the transitions in hydrogen atom which will result in emission of
wavelength equal to that of incident radiation for the above photoelectric effect.
A. \( n=3 \) to 1
B. \( n=3 \) to 2
\( c \cdot n=2 \) to 1
\( D \cdot n=4 \) to 1
Subject: Maths
Equation of one of the sides of an isosceles right angled triangle whose hypotenuse is \( 3 x+4 y=4 \) and the
opposite vertex of the hypotenuse is \( (2,2), \) will be \( ? \)
A. \( x-7 y+12=0 \)
в. \( 7 x+y-12=0 \)
c. \( x-7 y+16=0 \)
D. \( 7 x+y+16=0 \)
Subject: Physics
Two pulses in a stretched string whose centers are initially \( 8 \mathrm{cm} \) apart are moving towards each other as shown in figure. The speed of each pulse is 2 \( \mathrm{cm} / \mathrm{s} . \) After 2 seconds, the total energy
of the pulses will be :
A . zero
B. purely kinetic
c. purely potential
D. partly kinetic and partly potential
Subject: Chemistry
If the solubility of the salt
\( \boldsymbol{L} \boldsymbol{i}_{3} \boldsymbol{N} \boldsymbol{a}_{3}\left(\boldsymbol{A l} \boldsymbol{F}_{6}\right)_{2} \) is \( \boldsymbol{x}, \) then its solubility
product would be:
\( \mathbf{A} \cdot 972 x^{8} \)
В . \( 1458 x^{8} \)
\( \mathbf{c} \cdot 2916 x^{8} \)
D. None of the above
Subject: Biology
Three major ways for metabolism of
pyruvic acid produced in glycolysis are
A. Lactic acid fermentation, alcoholic fermentation and aerobic respiration.
B. Oxaloacetic acid fermentation, lactic acid fermentation, aerobic fermentation.
C. Alcoholic fermentation, oxaloacetic acid fermentation, citric acid fermentation.
D. Citric acid fermentation, lactic acid fermentation, alcoholic fermentation.
Subject: Physics
A nucleus at rest undergoes \( \boldsymbol{\alpha}- \) decay
emitting an \( \alpha- \) particle of de Broglie
wavelength \( \lambda=5.76 \times 10^{-15} \mathrm{m} . \) If the
mass of the daughter nucleus is
223.610 amu and that of the \( \alpha- \)
particle is 4.002 amu, determine the
total kinetic energy in the final state, Hence, obtain the mass of parent nucleus in amu. \( (1 a m u= \) \( \left.\mathbf{9 3 1 . 4 7 0} M e V c^{-\mathbf{2}}\right) \)
Subject: Maths
The set onto which the derivative of the
function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}(\log \boldsymbol{x}-1) \) maps the
ray \( [1, \infty) \) is \( ? \)
A. \( [1, \infty) \)
(n)
в. \( (10, \infty) \)
\( c \cdot[0, \infty) \)
D. (0,0)
Subject: Maths
If \( \omega \) is an imaginary cube root of
unity,then the value of \( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} \boldsymbol{\omega}^{2} & \boldsymbol{a} \boldsymbol{\omega} \\ \boldsymbol{b} \boldsymbol{c} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{\omega}^{2} \\ \boldsymbol{c} \boldsymbol{\omega}^{2} & \boldsymbol{a} \boldsymbol{\omega} & \boldsymbol{c}\end{array}\right|, \) is
\( \mathbf{A} \cdot a^{3}+b^{3}+c^{3} \)
B . \( a^{2} b-b^{2} c \)
\( c \cdot 0 \)
D. \( a^{3} b+b^{3}+3 a b c \)
Subject: Physics
In a series resonant circuit, having L,C,R as its elements, the resonant current is
i. The power dissipated in the circuit at
resonance is
\( \mathbf{A} \cdot i^{2} l \omega \)
B . \( i^{2} R \)
c. zero
\( \mathbf{D} \cdot i^{2} C \omega \)
Subject: Chemistry
A piston exerting a pressure of 1.0 atmosphere rests on the surface of
water at \( 100^{\circ} \mathrm{C} \). The pressure is reduced to smaller extent and as a
result 10 g of water evaporates and absorbs \( 22.2 \mathrm{kJ} \) of heat. The change in internal energy is:
A . 18.24 k
B. 20.477 kJ
c. 22.05 kJ
D. 23.923 kJ
Subject: Maths
Varun is climbing steps to the top of a
monument. After climbing 15 steps, Varun stops to tie his shoe laces. If there
are 75 steps in the monument, what percent of the total number of steps has Varun climbed when he stops to tie
his shoe laces?
A . \( 90 \% \)
B. \( 60 \% \)
\( c \cdot 20 \% \)
D. \( 5 \% \)
Subject: Chemistry
What is name of the compound
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}_{2} \boldsymbol{O H} ? \)
A. 2-methylbutanol
B. 3-methylbutanol
c. 2-methylpentanol
D. Pentanol
Subject: Chemistry
Assertion
Statement-I: Molar conductivity of a weak electrolyte at infinite dilution cannot be determined experimentally.
Reason

Statement-II : Kohlrausch law help to find the molar conductivity of a weak electrolyte at infinite dilution.
A. statement-l is true, statement-ll is true; Statementis correct explanation for Statement-
B. Statement-lis true, Statement-II is true; Statement-1 is NOT a correct explanation for statement-
c. statement-l is true, statement-ll is false
D. Statement-I is false, Statement-II is true
Subject: Maths
Let \( A, B \) and \( C \) be the sets such that
\( \boldsymbol{A} \cup \boldsymbol{B}=\boldsymbol{A} \cup \boldsymbol{C} \) and \( \boldsymbol{A} \cap \boldsymbol{B}=\boldsymbol{A} \cap \boldsymbol{C} \)
Show that \( B=C \)
Subject: Physics
The distances of Neptune and Saturn
from the Sun are respectively \( 10^{13} \) and
\( 10^{12} \) meters and their periodic times
are respectively \( T_{n} \) and \( T_{S} \). If their orbits are assumed to be circular, the value of \( \frac{T_{n}}{T_{S}} \) is :
A. 100
в. \( 10 \sqrt{10} \)
c. \( \frac{1}{10 \sqrt{10}} \)
D. 10
Subject: Physics
The number of molecules in \( 22.4 \mathrm{cm}^{3} \) of
nitrogen gas at STP is
A \( .6 .023 \times 10^{20} \)
В. \( 6.023 \times 10^{23} \)
c. \( 22.4 \times 10^{20} \)
D. \( 22.4 \times 10^{23} \)
Subject: Physics
A \( 200 F \) capacitor is initially charged to \( 20 V \) and then shorted across a \( 5 m H \)
inductor. The angular frequency of oscillation is
A. 1000 rad\( / \)s
B. 100 rad\( / \)s
c. 10000 rad\( / \)s
D. \( 1 r a d / s \)
Subject: Physics
Calculate the gravitational force of
earth acting on an object weighting 10kg placed 1000km above the surface
of earth.
(Mass of earth \( =\mathbf{6} \times \mathbf{1 0}^{\mathbf{2 4}} \mathbf{k g} \) and radius
of earth \( \left.=\mathbf{6 . 4} \times \mathbf{1 0}^{6} \boldsymbol{m}\right) \)
A \( \cdot 0.84 \times 10^{3} N \)
В. \( 0.72 \times 10^{2} N \)
c. \( 0.65 \times 10^{6} N \)
D. \( 0.42 \times 10^{4} N \)
Subject: Physics
An object \( 15 \mathrm{cm} \) high is placed \( 10 \mathrm{cm} \) from the optical center of a thin lens. Its
image is formed \( 25 \mathrm{cm} \) from the optical
center on the same side of the lens as
the object. The height of the image is:
\( \mathbf{A} \cdot 2.5 \mathrm{cm} \)
B. \( 0.2 \mathrm{cm} \)
\( c .16 .7 \mathrm{cm} \)
D. \( 37.5 \mathrm{cm} \)
Subject: Maths
If the angle between the planes \( \boldsymbol{r} \cdot(\boldsymbol{m} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}})+\boldsymbol{3}=\boldsymbol{0} \) and \( \overline{\boldsymbol{r}} \cdot(\boldsymbol{2} \hat{\boldsymbol{i}}- \)
\( m \hat{j}-\hat{k})-5=0 \) is \( \frac{\pi}{3} \) then \( m= \)
\( A \cdot 2 \)
B. ±3
\( c \cdot 3 \)
D. - -
Subject: Physics
A wheel has angular acceleration of \( 3.0 \mathrm{rad} / \mathrm{s}^{2} \) and an intial angular speed
of 2.00 rad/s. In a time of \( 2 s \) it has rotated through an angle (in radians) of
\( \mathbf{A} \cdot \mathbf{6} \)
B. 10
c. 12
D.
Subject: Physics
Two heater coils 1 and 2 made of the
same material are connected in parallel across the mains. The length and
diameter of the wire of coil 2 are
doubled of that coil \( 1 . \) Find the ratio of
heat generated between coil land 2
A .1: 2
B. 1: 1
c. 2: 1
D. 3: 2
Subject: Maths
Let \( f(x)=x^{3}+3 x^{2}-9 x+2 . \) Then
A. \( f(x) \) has a maximum at \( x=1 \)
B. \( f(x) \) has neither a minimum nor a maximum at \( x= \) -3
c. \( f(x) \) has a minimum at \( x=1 \)
D. none of these