AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Electrons in a TV tube move horizontally
South to North. Vertical component of earth's magnetic field points down. The electron is deflected towards which
direction? \( [\boldsymbol{F}=\boldsymbol{q}(\overrightarrow{\boldsymbol{v}} \times \overrightarrow{\boldsymbol{B}})] \)
A. west
B. No deflection
c. East
D. North to South
Subject: Chemistry
Assertion
Bond dissociation energy of \( \boldsymbol{F}_{2} \)
molecule is less than that of \( C l_{2} \)
molecule.
Reason
Due to inter-electronic repulsion
between \( F \) atom \( , F- \) - \( F \) bond length in \( F_{2} \)
molecule is higher than Cl- -Cl bond
Iength in \( C l_{2} \) molecule

Read the above assertion and reason
and choose the correct option regarding
it.
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
I: If \( a, b, c \) are real, the roots of \( (b- \)
\( c) x^{2}+(c-a) x+(a-b)=0 \) are real
and equal, then \( a, b, c \) are in A.P.
Il: If \( a, b, c \) are real and the roots of \( \left(a^{2}+\right. \)
\( \left.\boldsymbol{b}^{2}\right) \boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{b}(\boldsymbol{a}+\boldsymbol{c}) \boldsymbol{x}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2}=\boldsymbol{0} \) are
real and equal, then \( a, b, c \) are in H.P.
Which of the above statement(s) is(are)
true?
A. only।
B. only II
c. both I and II
Subject: Physics
Two electric resistors have equal values of resistance \( R \). Each can be operated
with a power of 320 watts\( (w) \) at 220 volts. If the two resistors are
connected in series to a 110 volts
electric supply, then the power generated in each resistor is
A . 90 watts
B. 80 watts
c. 60 watts
D. 20 watts
Subject: Chemistry
Calculate percentage degree of hydrolysis in a \( 0.1 ~ M \) solution of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N a} \)
Given that \( :\left[\boldsymbol{K}_{\boldsymbol{a}} \boldsymbol{o} \boldsymbol{f} \boldsymbol{C H}_{3} \boldsymbol{C O O H}=\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{5}}\right] \)
A . 1.0
B. 0.01
\( c \cdot 10^{-4} \)
D. None of these
Subject: Maths
If \( (5+2 \sqrt{6})^{n}=m+f \), where \( n \) and \( m \)
are positive integers and \( 0 \leq f<1 \)
then
\( \frac{1}{1-f}-f \) is equal to
A \( \cdot \frac{1}{m} \)
в. \( m \)
c. \( _{m+\frac{1}{m}} \)
D. \( _{m-} \frac{1}{m} \)
Subject: Physics
An aeroplane is in a level flight at \( 144 k m / h r \) at an altitude of \( 1000 m \)
How far from a given target a bomb be released from it to hit the target ?(take \( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2} \mathbf{)} \)
\( \mathbf{A} \cdot 566 m \)
B. \( 671.43 m \)
c. \( 471.34 m \)
D. \( 371.34 m \)
Subject: Chemistry
The electronic configuration of silicon is and that of sulphur is
A. silicon - 2, 8, 1; Sulphur - 2, 8, 6
B. Silicon - 2, 8, 4; Sulphur - 2, 8, 3
c. silicon - 2, 8, 2; sulphur - 2, 8, 6
D. silicon - 2, 8, 4; Sulphur - 2, 8, 6
Subject: Maths
Draw a circle with center \( \boldsymbol{O} \) and radius
\( 6 \mathrm{cm} . \) Take a point \( P \) outside the circle
at a distance of \( 10 \mathrm{cm} \) from \( O . \) Draw
tangents to the circle from point \( P . \) Let
the tangents intersect the circle in points \( A \) and \( B . \) Find the approximate
value of \( \angle O P B \)
A \( .37^{\circ} \)
B. \( 53^{\circ} \)
\( c \cdot 45^{\circ} \)
D. None of these
Subject: Biology
Go through the following flow chart for
division of subphylum vertebrata. Fill
the gaps \( A, B, C \) and \( D \) and select the
correct option.
A. A-Ostracodermi, B-Cyclostomata, C-Pisces, DTetrapoda
B. A-Cyclostomata, B-Ostracodermi, C-Pisces, DTetrapoda
C. A-Ostracodermi, B-Tetrapoda, C-Cyclostomata, DPisces
D. A-Pisces, B-Ostracodermi, C-Tetrapoda, DCyclostomata
Subject: Physics
A cars initially at rest, 330m away from a stationary observer. It begins to move towards the observer with an
acceleration of \( 1.1 m s^{-2}, \) sounding its horn continuously. 20 s later, the driver stops sounding the horn. The velocity of sound in air is \( 330 m s^{-1} \). The observer
will hear the sound of the horn for a
duration of
A . \( 20 s \)
в. \( 21 s \)
\( \mathrm{c} \cdot 20 \frac{2}{3} s \)
D・ \( 19 \frac{1}{3} s \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x} \boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{f}(\boldsymbol{y}) \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \)
f \( f^{\prime}(1)=2 \) and \( f(4)=4, \) then \( f^{\prime}(4) \)
equal to
\( \mathbf{A} \cdot \mathbf{4} \)
B.
c. \( \frac{1}{2} \)
D. 8
Subject: Chemistry
Which one of the following is correct
with respect to molar ionic
conductance of ions in aqueous
solution?
\( \mathbf{A} \cdot L i^{+}<N a^{+}<K^{+}<R b^{+} \)
B \( \cdot R b^{+}<K^{+}<N a^{+}<L i^{+} \)
\( \mathbf{c} \cdot S r^{2+}<C a^{2+}<M g^{2+}<B e^{2+} \)
D. \( N a^{+}<K^{+}<L i^{+}<R b^{+} \)
Subject: Physics
To detect light of wavelength 500nm, the photodiode must be fabricated
from, a semiconductor of minimum
bandwidth of:
A . \( 1.24 e V \)
B. \( 0.62 e V \)
c. \( 2.48 e V \)
D. \( 3.2 e V \)
E . \( 4.48 e V \)
Subject: Maths
\( \int_{0}^{\pi / 2} \frac{d x}{a^{2} \cos ^{2} x+b^{2} \sin ^{2} x} \) equals-
A . \( \pi / a b \)
B. \( 2 \pi / a b \)
c. \( a b / \pi \)
D. \( \pi / 2 a b \)
Subject: Physics
A perfect gas at \( 27^{\circ} \mathrm{C} \) heated at constant
pressure so as to double its volume. The
final temperature of the gas will be
\( \mathbf{A} \cdot 327^{0} \mathrm{C} \)
в. \( 327 K \)
\( c \cdot 600^{0} c \)
D. None
Subject: Physics
A gas bubble, from an explosion under water, oscillates with a period \( \boldsymbol{T} \) proportional to \( P^{a} d^{b} E^{c}, \) where \( P \) is the
static pressure, \( d \) is the density of water
and \( E \) is the total energy of the
explosion. The values of \( a \ldots \ldots . b \ldots . . . . . . \) and
\( \mathcal{C} \)
Subject: Physics
Find the work done to take a particle of mass \( \mathrm{m} \) from surface of the earth to a
height equal to \( 2 R \)
\( \mathbf{A} \cdot 2 m g R \)
в. \( \frac{m g R}{2} \)
c. \( 3 m g R \)
D. \( \frac{2 m g R}{3} \)
Subject: Physics
A steel ball of mass \( 0.5 \mathrm{kg} \) is dropped from a height of \( 4 \mathrm{m} \) on to a horizontal heavy steel slap. the strile the slap and reounds to its original height.
(a) calculate the impulse delivered to the ball during impact
(b) if the ball is in contact with the slab
for \( 0.002, \) find the average reaction
force on the ball during impact.
Subject: Physics
Three point charges \( 3 n C, 6 n C \) and \( 9 n C \)
are placed at the corners of an
equilateral triangle of side 0.1 m. The
potential energy of the system is :
A \( .8910 n J \)
в. \( 89100 \mathrm{mJ} \)
c. \( 9910 J \)
D. \( 99100 K J \)
Subject: Chemistry
10mL of gaseous hydrocarbon on
combustion gives \( 40 \mathrm{mL} \) of \( \mathrm{CO}_{2} \mathrm{g} \) and 50
\( \mathrm{mL} \boldsymbol{H}_{2} \boldsymbol{O}(\text { vapour }) . \) The hydrocarbon is:
A \( \cdot C_{4} H_{5} \)
в. \( C_{8} H_{10} \)
\( \mathbf{c} \cdot C_{4} H_{8} \)
D. \( C_{4} H_{10} \)
Subject: Physics
A hollow conducting sphere has a net
charge of \( +Q . \) There are four labeled
points all on the inside of the sphere, as
shown above. Points A through D are
ocated progressively closer to the
center of the sphere.
Which point has the largest magnitude
of electric field?
A. Point A
B. Point B
\( c . \) Point \( c \)
D. Point D
E. All points have the \( d \)
ie
Subject: Chemistry
A nitrogenous fertilizers having more nitrogen is :
\( \mathbf{A} \cdot\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} \)
B. \( C a\left(N O_{3}\right)_{2} \)
c. \( N H_{2} C O N H_{2} \)
D. \( N H_{4} N O_{3} \)
Subject: Physics
The two charges \( 7 \mu C \) and \( -2 \mu C \) are
separated by a distance of \( 18 \mathrm{cm} . \) The work required by you to separate the two charges infinitely away from each other is:
A . 0.7
B . -0.7 J
c. 1.4
D . -1. 4 J
Subject: Physics
A monochromatic source of light
operating at \( 200 \mathrm{W} \) emits \( 4 \times 10^{20} \)
photons/second. Then the wavelength of light used is
A. 3000 \( A^{0} \)
B . \( 5000 A^{0} \)
c. \( 4000 A^{0} \)
D. \( 6000 A^{\circ} \)
Subject: Chemistry
Select the correct statements for
Ellingham diagram.

This question has multiple correct options
A. Any metal will reduce the oxide of other metals which lie above it in the Ellingham diagram
B. According to the Ellingham diagram, Al will not reduce MgO at temperature below \( 1350^{\circ} \mathrm{C} \)
C. According to the Ellingham diagram, Al will reduce
MgO at temperature below \( 1350^{\circ} \mathrm{C} \)
D. Any metal will not reduce the oxide of other metals which lie above it in the Ellingham diagram
Subject: Chemistry
A current of \( 2.0 \mathrm{A} \) is passed for 5 hours through a molten metal salt deposits 22.2 \( g \) of metal (At. mass: 177 u). The oxidation states of the metal in metal
salt is:
\( A \cdot+1 \)
\( B .+2 \)
\( c \cdot+3 \)
\( D \cdot+4 \)
Subject: Chemistry
Bond energy of \( F_{2}, C l_{2} \) and \( B r_{2} \) follow
the order:
A. \( F-F>C l-C l>B r-B r \)
в. \( C l-C l>B r-B r>F-F \)
c. \( B r-B r>C l-C l>F-F \)
D. \( C l-C l>F-F>B r-B r \)
Subject: Physics
In the given LCR series circuit. Choose the correct option/options (resistance
is nonzero).
A. Reading of Voltmeter \( V_{2} \) may be greater than source
voltage
B. Reading of voltmeter \( V_{4} \) may be equal to \( V_{1} \)
C. Reading of \( V_{4} \) may be equal to source voltage \( v \)
D. None of these
Subject: Biology
Which of the following is true/false regarding transport of substances in plants?
(i) Mass flow is the movement of
substance in bulk as a result of
pressure difference.
(ii) Bulk flow is achieved only through a positive hydrostatic pressure gradient.
(iii) The apoplast system is the system of interconnected protoplasts.
(iv) Most of the water flow in the roots
occurs via the apoplast since the cortical cells are loosely packed, and offer no resistance to water movement.
A . (i) and (iv) are true; (ii) and (iii) are false
B. (i) and (ii) are true; (iii) and (iv) are false
\( c . \) (ii) and
(iii) are true; (i) and (iv) are false
D. (i), (ii) and (iv) are true; (iii) is false
Subject: Physics
A charge \( q \) is to be distributed on two conducting spheres. What should be the value of the charges on the spheres so that the repulsive force between them is maximum when they are placed at a fixed distance from each other in air?
A \( \cdot \frac{q}{2} \) and \( \frac{q}{2} \)
в. \( \frac{q}{4} \) and \( \frac{3 q}{4} \)
c. \( \frac{q}{3} \) and \( \frac{2 q}{3} \)
D. \( \frac{q}{5} \) and \( \frac{4 q}{5} \)
Subject: Maths
\( \sum_{i=l}^{n}\left(x_{i}-a\right)= \)
\( ^{\mathrm{A}} \cdot \sum_{i=l}^{n} x_{i}-n a \)
В. \( _{n a-\sum_{n}^{i=l} x_{i}} \)
c. \( _{n a-\sum_{n}^{i=l} x_{i}+n a} \)
D. None of these
Subject: Maths
\( \operatorname{Let} \overrightarrow{\boldsymbol{a}}=2 \hat{\hat{\boldsymbol{i}}}+\boldsymbol{\lambda}_{1} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\boldsymbol{4} \hat{\boldsymbol{i}}+(\boldsymbol{3}- \)
\( \left.\lambda_{2}\right) \hat{j}+6 \hat{k} \) and \( \vec{c}=3 \hat{i}+6 \hat{j}+\left(\lambda_{3}-1\right) \hat{k} \)
be three vectors such that \( \vec{b}=2 \vec{a} \) and \( \vec{a} \)
is perpendicular to \( \vec{c} \). Then a possible
value of \( \left(\lambda_{1}, \lambda_{2}, \lambda_{3}\right) \) is?
\( ^{\mathbf{A}} \cdot\left(\frac{1}{2}, 4,-2\right) \)
в. \( \left(-\frac{1}{2}, 4,0\right) \)
c. (1,3,1)
D. (1,5,1)
Subject: Maths
Let \( x_{1}, x_{2}, \ldots, x_{n} \) be \( n \) observations such
that \( \sum x_{i}^{2}=400 \) and \( \sum x_{i}=80 . \) Then a
possible value of \( n \) among the following is :
A. 15
B. 18
\( c \cdot 12 \)
D.
Subject: Physics
In a one-dimensional collision between
two particles, their relative velocity is \( \overrightarrow{v_{1}} \) before the collision and \( \overrightarrow{v_{2}} \) after
collision:
A. \( \overrightarrow{v_{1}}=\overrightarrow{v_{2}} \) if the collision is elastic
B. \( \overrightarrow{v_{1}}=-\overrightarrow{v_{2}} \) if the collision is elastic
c. \( |\overrightarrow{v_{2}}|=|\overrightarrow{v_{1}}| \) in all cases
D. \( \overrightarrow{v_{1}}=-k \overrightarrow{v_{2}} \) in all cases, where \( k \geq 1 \)
Subject: Physics
Draw a ray diagram showing the formation of the image by a point object on the principal axis of a spherical convex surface separating
two media of refractive indices \( n_{1} \) and
\( n_{2}, \) when a point source is kept in
rarer medium of refractive index \( n_{1} \) Derive the relation between object and image distance in terms of refractive index of the medium and
radius of curvature of the surface.
Hence obtain the expression for lens-
maker's formula in the case of
thin convex lens.
Subject: Chemistry
Balance the following equations by ion electron method.
\( \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{N} \boldsymbol{O}_{2}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Maths
The arithmetic mean of \( 1+\sqrt{2} \) and \( 7+ \) \( \mathbf{5} \sqrt{\mathbf{2}} \) is \( \sqrt{\boldsymbol{a}}+\sqrt{\boldsymbol{b}} . \) Then \( \boldsymbol{a}-\boldsymbol{b}= \)
A . -
B.
\( c \cdot 2 \)
\( D \cdot-2 \)
Subject: Maths
Assertion
If two triangles have same perimeter, then they are congruent.
Reason
If under a given correspondence, the three sides of one triangle are equal to the three sides of the other triangle,
then the two triangles are congruent.
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 are correct
Subject: Chemistry
Observe the given adsorption isotherm carefully and choose the correct option.
(i) These curves indicate that at a fixed
temperature, there is a decrease in physical adsorption with increase in
pressure.
(ii) These curves always seem to approach saturation at high pressure.
(iii) \( \frac{x}{m}=k p^{1 / n}(n>1) \) is generally represented by this isotherm.
(iv) These curves indicate that at a fixed pressure, there is a decrease in physcial adsorption with increase in temperature
A. (i) and (iii) only
B. (ii) and (iv) only
\( c \)
D. All of these
Subject: Maths
In the expansion of \( \left(\boldsymbol{a} \sqrt{\boldsymbol{a}}+\frac{\mathbf{1}}{\boldsymbol{a}^{4}}\right)^{\boldsymbol{n}} \), the
coefficient in the second term exceeds
by 44 the coefficient in the first term. Find \( n \)
A . 20
B . 25
\( c .35 \)
D. 45
Subject: Physics
Assertion
When a ray of light travels from ice to water the refracted ray at the point of incidence bends towards the normal
Reason
The ray goes from rarer to denser
medium.
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 \( P, Q, R \) are collinear points such that \( \boldsymbol{P}(\boldsymbol{3}, \boldsymbol{4}), \boldsymbol{Q}(\boldsymbol{7}, \boldsymbol{7}) \) and \( \boldsymbol{P} \boldsymbol{R}=\mathbf{1 0}, \) find \( \boldsymbol{R} \)
Subject: Maths
The differential equation of the family of curves \( \boldsymbol{y}=\boldsymbol{A} \boldsymbol{e}^{\boldsymbol{3} \boldsymbol{x}}+\boldsymbol{B} \boldsymbol{e}^{\boldsymbol{5} \boldsymbol{x}}, \) where \( \boldsymbol{A} \) and
\( B \) are arbitrary constants, is
A \( \cdot \frac{d^{2} y}{d x^{2}}+8 \frac{d y}{d x}+15 y=0 \)
B. \( \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}+y=0 \)
c. \( \frac{d^{2} y}{d x^{2}}-8 \frac{d y}{d x}+15 y=0 \)
D. None of the above
Subject: Maths
Which polynomial should be added to
\( 2 x^{4}-3 x^{2}+5 x+8 \) to get \( 2 x^{2}-5 x+4 \)
\( ? \)
A \( \cdot x^{3}+5 x^{2}-x \)
B . \( 2 x^{5}+x^{2}-10 x-9 \)
c. \( -2 x^{4}+5 x^{2}-1 \)
D. \( -2 x^{4}+5 x^{2}-10 x-4 \)
Subject: Chemistry
Sequence the following steps involved generally in the extraction of a metal in pure form from its ore
(a) The metal obtained from its oxide require further purification for end use
(b) The ore should be converted to its
oxide form.
(c) The ore is beneficial to us if it is
handpicked then metal crushed and ground, and later subjected to pulverization as per the requirement
(d) The ore in the form of oxide is required to be reduced.
(e) Dressed ore is required for it to be concentrated.
A \( \cdot \operatorname{ecbd} \)
B. cebda
\( c \cdot \operatorname{cob} a d \)
D. ced b a
Subject: Maths
If \( y=x^{-\frac{1}{2}}+\log _{5} x+\frac{\sin x}{\cos x}+2^{x} \), then
find \( \frac{d y}{d x} \)
A. \( -\frac{1}{2} x^{-3 / 2}+\frac{1}{x \log _{e} 5}+\sec ^{2} x+2^{x} \log 2 \)
B. \( \frac{1}{2} x^{-3 / 2}+\frac{1}{x \log _{e} 5}+\sec ^{2} x+2^{x} \log 2 \)
c. \( -\frac{3}{2} x^{-3 / 2}+\frac{1}{x \log _{e} 5}+\sec ^{2} x+2^{x} \log 2 \)
D. \( -\frac{1}{2} x^{-3 / 2}+\frac{1}{x \log _{e} 5}+\cos ^{2} x+2^{x} \log 2 \)
Subject: Physics
An ideal gas having initial pressure \( P \) volume \( V \) and temperature \( T \) is allowed to expand adiabatically until its volume becomes \( 5.66 \mathrm{V} \) while its temperature
falls to \( T / 2 . \) How many degrees of freedom do the gas molecules have?
A. 7
B. 5
\( c \cdot 6 \)
D.
Subject: Chemistry
A crop of wheat uses up to \( 20 \mathrm{kg} \) of nitrogen per hectare of soil. What is the mass of the fertilizer calcium nitrate
required to replace the nitrogen in a 10 hectare field?
\( (\boldsymbol{C a}=\mathbf{4 0}, \boldsymbol{N}=\mathbf{1}, \boldsymbol{O}=\mathbf{1 6}) \)
A. \( 1171.4 \mathrm{kg} \)
B. \( 1182 \mathrm{kg} \)
c. \( 1181 \mathrm{kg} \)
D. 2171 kg
Subject: Chemistry
Which of the following is not correctly
matched with respect to the processes involved in the extractive metallurgy of
the respective metal?
\( \mathbf{A} \cdot A l_{2} O_{3} \cdot 2 H_{2} O \rightarrow A l: \) Leaching, precipitation
calcination and electrolytic reduction (molten state)
B. \( A g_{2} S \rightarrow A g \) : Leaching and displacement method
C \( . P b S \rightarrow P b \) : Froth flotation process, roasting and self
reduction
D. \( K C l . M g C l_{2} .6 H_{2} O \rightarrow M g \) : Dehydration by simple heating and electrolytic reduction in aqueous phase
Subject: Physics
An L-shaped glass tube is just
immersed in flowing water such that its
opening is pointing against flowing
water. If the speed of water current is \( \mathbf{v} \)
then :
A the water in the tube rises to height \( \frac{v^{2}}{2 g} \)
B. The water in the tube rises to height \( \frac{g}{2 v^{2}} \)
c. The water in the tube does not rise at all
D. None of these.
Subject: Physics
A \( 100 m H \) inductor, a \( 25 \mu F \) capacitor
and a \( 15 \Omega \) resistor are connected in
series to a \( 120 V, 50 H z \) ac source.
Calculate
(a) impedance of the circuit at
resonance
(b) current at resonance
(c) resonant frequency
A \( . \) (a) \( 16 \Omega \) (b) \( 9 A \) (c) \( 100 H z \) \( z \)
B. (a) \( 15 \Omega \) (b) \( 8 A \) (с) \( 100 H z \)
c. \( (\text { a) } 15 \Omega \)
(b) \( 8 A \) (с) \( 120 H z \)
D. (a) \( 15 \Omega \) (b) \( 7 A \) (с) \( 100 H z \)
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{5} & \mathbf{7} \\ \mathbf{9} & \mathbf{4}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{5}\end{array}\right] \) find \( \boldsymbol{A}-\boldsymbol{B} \)
Subject: Physics
Current \( I_{o} \) flows through the solenoid of length \( L \) having \( N \) number of turns when
its connected to DC. A charged particle is projected along the axis of the solenoid
with a speed \( v_{0}, \) then the force on the
charged particle in the solenoid is:
A. Becomes zero
B. Remains same
c. Decreases
D. Increases
Subject: Maths
If \( \operatorname{lines} x-2 y+3=0,3 x+k y+7= \)
0 cut the coordinate axes in concyclic
points, then \( k=? \)
\( \mathbf{A} \cdot 3 / 2 \)
B. \( 1 / 2 \)
c. \( -3 / 2 \)
D. -4
Subject: Physics
Three elephants \( A, B \) and \( C \) are moving along a straight line with constant speed in same direction as shown in figure. Speed of \( A \) is \( 5 \mathrm{m} / \mathrm{s} \) and speed of \( \mathrm{C} \) is \( 10 \mathrm{m} / \mathrm{s} \). Initially separation between
A and B is d and between B and C is also
d. When 'B catches 'C' separation between \( A \) and \( C \) becomes \( 3 d \). Then the
speed of B will be:
\( A \cdot 15 \mathrm{m} / \mathrm{s} \)
B. \( 7.5 \mathrm{m} / \mathrm{s} \)
\( c \cdot 20 m / s \)
D. \( 5 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Law of multiple proportions can be illustrated by taking the example of
A. \( N a O H \) and \( K O H \)
B. \( N a C l \) and \( N a B r \)
\( c \cdot S O_{2} \) and \( S O_{3} \)
D. \( H_{2} C O_{3} \) and \( C O_{2} \)
Subject: Physics
The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The
dipole axis makes an angle of \( 11.3^{\circ} \)
with the axis of the earth. At Mumbai,
declination is nearly zero. Then
A. the declination varies between \( 11.3^{\circ} \mathrm{W} \) to \( 11.3^{\circ} \mathrm{E} \)
B. the least declination is \( 0^{\circ} \)
C. the plane defined by dipole axis and Earth axis passes through Greenwich
D. declination averaged over Earth must be always negative
Subject: Maths
A function \( f \) from the set of natural
numbers to integers defined by \( \boldsymbol{f}(\boldsymbol{n})= \)
\( \left\{\begin{array}{l}\frac{n-1}{2}, \quad \text { when } n \text { is odd } \\ -\frac{n}{2}, \quad \text { when } n \text { is even }\end{array}\right. \)
A. neither one-one nor onto
B. one-one but not onto
c. onto but not one-one
D. one-one and onto both
Subject: Maths
\( \operatorname{Let} \boldsymbol{\alpha}=\frac{-\mathbf{1}+\boldsymbol{i} \sqrt{\mathbf{3}}}{\mathbf{2}} . \) If \( \boldsymbol{a}= \)
\( (1+\alpha) \sum_{k=0}^{100} \alpha^{2 k} ; b=\sum_{k=0}^{100} \alpha^{3 k}, \) then \( a \)
and \( b \) are the roots of the quadratic equation:
A \( \cdot x^{2}-102 x+101=0 \)
B. \( x^{2}-101 x+100=0 \)
c. \( x^{2}+102 x+101=0 \)
D. \( x^{2}+101 x+100=0 \)
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C N}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{M} \boldsymbol{g} \boldsymbol{B r} \rightarrow ? \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}^{+}}{\longrightarrow} \)
Complete the reaction.
Subject: Chemistry
Which of the following compound removes both oxygen and nitrogen from the air when it is passed over it at
\( 1000^{\circ} \mathrm{C} ? \)
A. \( C a C_{2} \)
в. \( C a C l_{2} \)
\( \mathrm{c} \cdot \mathrm{CaCN}_{2} \)
D. \( \operatorname{CaSO}_{4} \)
Subject: Chemistry
Which of the following pair of compounds illustrate the law of multiple proportions? This question has multiple correct options
A. \( S O_{2} \) and \( S O_{3} \)
B. \( N O_{2} \) and \( N_{2} O \)
c. \( M g O \) and \( M g(O H)_{2} \)
D. \( N O \) and \( N_{2} O_{5} \)
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c} \) are three coplanar vectors then find the magnitude of their vector sum. It is given \( \vec{a}=4 \hat{i}-\hat{j}, \vec{b}=-3 \hat{i}+2 \hat{j}, \vec{c}=-3 \hat{j} \)
A \( \cdot \sqrt{5}, 297^{\circ} \)
B . \( \sqrt{5}, 63^{\circ} \)
c. \( \sqrt{3}, 297^{\circ} \)
D. \( \sqrt{3}, 63^{\circ} \)
Subject: Chemistry
From the electronic configuration of the given elements \( \boldsymbol{K}, \boldsymbol{L}, \boldsymbol{M} \) and \( \boldsymbol{N}, \) which
one has the highest ionization potential?
\( \mathbf{A} \cdot M=[N e] 3 s^{2} 3 p^{2} \)
B . \( L=[N e] 3 s^{2} 3 p^{3} \)
C \( \cdot K=[N e] 3 s^{2} 3 p^{1} \)
D \cdot \( N=[A r] 3 d^{10}, 4 s^{2} 4 p^{3} \)
Subject: Maths
Solve: \( \frac{\cos ^{2} 25^{\circ}+\cos ^{2} 65^{\circ}}{\sin ^{2} 59^{\circ}+\sin ^{2} 31^{\circ}}=? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. 2
\( D \)