AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A particle moves in a way such that its
position can be expressed with \( \boldsymbol{x}(\boldsymbol{t})= \) \( t^{2}+t-3 \) and with \( y(t)=t^{3}-\frac{1}{t-1} \)
with being time in seconds. \( x(t) \) and
\( \boldsymbol{y}(t) \) are both in meters.
Initially, how far away is the particle from the origin?
A. \( 0.00 m \)
в. \( 1.00 m \)
c. \( 1.56 m \)
D. \( 2.83 m \)
E. \( 3.16 m \)
Subject: Maths
The equation of the diagonal through origin of the quadrilateral formed by the \( \operatorname{lines} \boldsymbol{X}=\mathbf{0}, \boldsymbol{Y}=\mathbf{0}, \boldsymbol{X}+\boldsymbol{Y}-\mathbf{1}=\mathbf{0} \)
and \( 6 x+Y-3=0 \) is :
A \( .4 x-3 y=0 \)
В. \( 3 x-2 y=0 \)
c. \( x=y \)
D. \( x+y=0 \)
Subject: Physics
Masses \( 8 \mathrm{kg}, 2 \mathrm{kg}, 4 \mathrm{kg} \& 2 \mathrm{kg} \) are placed
at the corners \( P, Q, R \& S \) respectively of a square PQRS of side 80cm. The
distance of \( x \) co-ordinate centre of mass
from P will be?
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. 30cm
c. \( 40 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)
Subject: Biology
Arrange the following in correct sequence with reference to sexual reproduction in Rhizopus
I. Formation of germ tube.
II. Formation of zygophores.
III. Formation of warty wall layer of
zygospore.
IV. Secretion of trisporic acid.
The correct sequence is
\( \mathbf{A} \cdot \mid \mathbf{V}, \) ॥ᅵ, И, 1
B. IV, II, III, I
c. ॥, ।, ।V, ॥॥
D. I, III, II, IV
Subject: Chemistry
(a) For what kinetic energy of a neutron will the associated de

Broglie wavelength be \( 1.40 \times 10^{-10} \mathrm{m} ? \)
(b) Find the de Broglie wavelength of a neutron in thermal equilibrium with
matter having an average kinetic energy of \( (3 / 2) k T \) at \( 300 K \)
Subject: Maths
Form the given figure, find the values of
\( x \) and \( y \) respectively.
A \( \cdot 47^{\circ}, 66^{\circ} \)
B \( \cdot 66^{\circ}, 48^{\circ} \)
\( \mathbf{c} \cdot 68^{\circ}, 47^{\circ} \)
D. \( 47^{\circ}, 68^{\text {? }} \)
Subject: Physics
An air conditioner is rated
\( 240 V, 1.5 k W . \) The air conditioner is
switched on for 8 hours each day. How much electrical energy is consumed in
30 days?
\( \mathbf{A} \cdot 360 k W h \)
B. \( 8.64 \mathrm{kW} \) h
\( \mathbf{c} \cdot 120 k W h \)
D. \( 240 \mathrm{kW} \) h
Subject: Physics
One mole of steam is condensed at
\( 100^{\circ} \mathrm{C} \) the water is cooled to \( 0^{\circ} \mathrm{C} \) and
frozen to ice. Which of the following statements are correct, given heat of vapourization and fusion are \( 540 c a l / g m \) and \( 80 c a l / g m \) (average
heat capacity of liquid water \( =1 \) cal
\( \boldsymbol{g} \boldsymbol{m}^{-1} \boldsymbol{d} \boldsymbol{e} \boldsymbol{g} \boldsymbol{r} \boldsymbol{e} e^{-1} \boldsymbol{\} \)
This question has multiple correct options
A. Entropy change during the condensation of steam is \( -26.06 c a l /^{o} C \)
B. Entropy change during cooling of water from \( 100^{\circ} \mathrm{C} \) to \( 0^{o} C \) is \( -5.62 c a l /^{o} C \)
C. Entropy change during freezing of water at \( 0^{\circ} \mathrm{C} \) is \( -5.27 c a l /^{o} C \)
D. Total entropy change is -36.95 cal\( /^{\circ} \mathrm{C} \)
Subject: Physics
A ray of light traveling in water is
incident on its surface open to the air.
The angle of incidence is \( \theta, \) which is
less than the critical angle. Then there
will be
A. Only a reflected ray and no refracted ray
B. Only a refracted ray and no reflected ray
C. A reflected ray and a refracted ray and the angle between them would be less than \( 180^{\circ}-2 \theta \)
D. A reflected ray and a refracted ray and the angle between them would be greater than \( 180^{\circ}-2 \theta \)
Subject: Maths
Consider the following statements in respect of the function \( \boldsymbol{f}(\boldsymbol{x})=\sin \left(\frac{\mathbf{1}}{\boldsymbol{x}}\right) \)
for \( \boldsymbol{x} \neq \mathbf{0} \) and \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \)
1. \( \lim _{x \rightarrow 0} f(x) \) exists
2. \( f(x) \) is continuous at \( x=0 \)
Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Physics
A transverse sinusoidal wave is
generated at one end of a long horizontal string by a bar that moves the end up and down through a distance
by \( 2.0 \mathrm{cm} . \) The motion of bar is continuous and is repeated regularly
125 times per sec. If the distance between adjacent wave crests is
observed to be \( 15.7 \mathrm{cm} \) and the wave
is moving along +ve x-direction, and at \( \boldsymbol{t}=\mathbf{0}, \) the element of the string at \( \boldsymbol{x}=\mathbf{0} \)
is at mean position \( y=0 \) and is
moving downwards, the equation of the
wave is best described by : \( (u s e \pi= \)
\( \mathbf{3 . 1 4}) \)
A \( \cdot y=(1 c m) \sin [(40.0 r a d / m) x-(785 r a d / s) t] \)
B . \( y=(2 c m) \sin [(40.0 r a d / m) x=(785 r a d / s) t] \)
c. \( y=(1 c m) \cos [(40.0 r a d / m) x-(785 r a d / s) t] \)
D. \( y=(2 c m) \cos [(40.0 r a d / m) x-(785 r a d / s) t] \)
Subject: Physics
in a certain region of free space a non-
uniform electric field which depends on
X-coordinates is given by \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{0} \boldsymbol{x} \hat{\boldsymbol{i}} \)
What is the total amount of electric
potential energy contained within the
cube of sides of length L as shown
below?
A \( \cdot \frac{1}{5} \varepsilon_{0} E_{0}^{2} L^{5} \)
B \( \cdot \frac{1}{5} \varepsilon_{0} E_{0}^{2} L^{6} \)
C \( \cdot \frac{1}{6} \varepsilon_{0} E_{0}^{2} L^{6} \)
D \( \cdot \frac{1}{2} \varepsilon_{0} E_{0}^{2} L^{5} \)
Subject: Biology
Hibernating animals have tissues containing mitochondria with a
membrane protein that accelerates
electron transport while blocking the synthesis of ATP.What is the
consequence of this?
A. Energy is saved because glycolysis and the citric acid cycle shuts down
B. The energy of respiration is converted into heat
c. Hibernating animals can synthesize fat instead of wasting energy of respiration
D. Pyruvate is converted to lactic acid by anaerobic fermentation
Subject: Chemistry
The electrolytes usually used in the electroplating of gold and silver, respectively are:
A \( \cdot\left[A u(O H)_{4}\right]^{-} \)and\( \left[A g(O H)_{2}\right] \)
B . \( \left[A u(C N)_{2}\right]^{-} a n d\left[A g\left(c l_{2}\right]^{-}\right. \)
C \( \left.\cdot\left[A u(N H)_{3}\right)_{2}\right]^{+} a n d\left[A g(C N)_{2}\right] \)
D. \( \left[A u(C N)_{2}\right]^{-} a n d\left[A g(C N)_{2}\right]^{-} \)
Subject: Physics
Green light wavelength \( 5460 \AA \) is incident on an air-glass interface. If the refractive index of glass is \( 1.5, \) the wavelength of light in glass would be \( \left(\boldsymbol{C}=\mathbf{3} \times \mathbf{1 0}^{\mathbf{8}} \quad \boldsymbol{m} \boldsymbol{s}^{-\mathbf{1}}\right) \)
A. \( 3640 \AA \)
в. 5460 ,
c. \( 4861 \dot{h} \)
D. None of these
Subject: Physics
The thermal capacity of \( 40 g \) of aluminium (specific heat =
\( 0.2 \mathrm{calg}^{-10} \mathrm{C}^{-1} \) ) is :
A \( \cdot 40 \) cal \( ^{\circ} C^{-1} \)
B . 160 cal \( ^{\circ} C^{-} \)
c. 200 cal' \( C^{-1} \)
D. 8 cal \( ^{\circ} \mathrm{C}^{-1} \)
Subject: Chemistry
\( K_{p} \) is how many times equal to \( K_{c} \) for the given reaction?
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
A \( \cdot \frac{1}{R^{2} T^{2}} \)
В \( \cdot R^{2} T^{2} \)
c. \( \frac{R}{T} \)
D. \( R T \)
Subject: Biology
Assertion
During apoplastic movement of water,
water travels through the cells and their
cytoplasm.
Reason
The symplastic movement of water
occurs exclusively through the
intercellular spaces and the walls of the cells.
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
\( \boldsymbol{R}-\boldsymbol{C O O H} \frac{N D_{3}}{\Delta}(\boldsymbol{A}) \frac{B r_{2}, \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}}{\Delta} \)
\( (B) \stackrel{N a N O_{2}+H C l}{\longrightarrow}(C) \)
What is \( A, B \) and \( C ? \)
A \( \cdot(A) R C O N D_{2} ;(B) R N H_{2} ;(C) \) ROH
B . \( (A) R C O N D_{2} ;(B) R N D_{2} ;(C) R O D \)
c. \( (A) R C O N H D ;(B) R N H D ;(C) \) ROH
D. None of these
Subject: Chemistry
The rate of the reaction starting with
initial concentrations \( 2 \times 10^{3} M \) and
\( 1 \times 10^{3} M \) are equal to \( 2.40 \times \)
\( 10^{4} M s^{1} \) and \( 0.60 \times 10^{4} M s^{1} \)
respectively. Calculate the order of reaction with respect to reactant:
Subject: Chemistry
The radial probability distribution curve obtained for an orbital wave function
\( (\mathbf{\Psi}) \) has \( \mathbf{3} \) peaks and 2 radial nodes. The
valence electron of which one of the
following metals does this wave
function \( (\Psi) \) correspond to?
A . \( C o \)
в. \( L i \)
c. \( K \)
D. Na
Subject: Physics
If the mass of the planet is \( 10 \% \) less than that of the earth and radius of the
planet is \( 20 \% \) greater than that of the earth the weight of 40 kg person on that planet is
A. \( 10 \mathrm{kg} \) wt
B. 25 kg wt
c. \( 40 \mathrm{kg} \) wt
D. \( 60 \mathrm{kg} \) wt
Subject: Physics
A hollow cylinder has a charge \( q \)
coulomb within it. If \( \phi \) is the electric flux in units of voltmeter associated
with the curved surface \( B \), the flux
linked with the plane surface \( A \) in units
of voltmeter will be
A \( \cdot \frac{q}{\epsilon_{0}}-\phi \)
B \( \cdot \frac{1}{2}\left(\frac{q}{\epsilon_{0}}-\phi\right) \)
c. \( \frac{q}{2 \epsilon_{0}} \)
D. \( \frac{\phi}{3} \)
Subject: Physics
The binding energy per nucleon of \( C^{12} \) is
\( E_{1} \) and that of \( C^{13} \) is \( E_{2} . \) The energy
required to remove one neutron from
\( C^{13} \) is
A \( \cdot 12 E_{1}+12 E_{2} \)
в. \( 13 E_{2}-12 E_{1} \)
c. \( 12 E_{2}-13 E_{1} \)
D. \( 13 E_{2}+12 E_{1} \)
Subject: Physics
A body cools from \( 70^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in 8
minute. The same body cools from \( 60^{\circ} \mathrm{C} \)
to \( 50^{\circ} \mathrm{C} \) in
A. 8 minute
B. less than 8 minute
c. More than 8 minute
D. 1 or 2 or 3 , depending on the specific heat of the body
Subject: Physics
Two wires of the same material (young's modules \( Y \) ) and same length \( L \) but radii
\( R \) and \( 2 R \) respectively are joined end to
end and a weight \( W \) is suspended from
the combination as shown in the figure.
the elastic potential energy in the system in equilibrium is
A \( \cdot \frac{3 W^{2} L}{4 \pi R^{2} Y} \)
В \( \cdot \frac{3 W^{2} L}{8 \pi R^{2} Y} \)
\( ^{\mathbf{C}} \cdot \frac{5 W^{2} L}{8 \pi R^{2} Y} \)
\( ^{\mathrm{D}} \cdot \frac{W^{2} L}{\pi R^{2} Y} \)
Subject: Physics
There are two unknown charges, \( Q_{1} \) and
\( Q_{2} . \) A positive charge is placed at P.P is
closer to \( Q_{2} \) than \( Q_{1} \). If the net electric
force acting on the charge at P is zero, then conclusion is :
\[
\frac{\boldsymbol{\rho}_{1}}{\mathbf{0}} \quad \boldsymbol{P} \quad \underline{\boldsymbol{Q}}_{2}
\]
A. Both \( Q_{1} \) and \( Q_{2} \) are positive
B. Both \( Q_{1} \) and \( Q_{2} \) are negative
C. Both \( Q_{1} \) and \( Q_{2} \) have opposite signs
D. Both \( Q_{1} \) and \( Q_{2} \) have the same sign, but the
magnitude of \( Q_{1} \) is greater than the magnitude of \( Q_{2} \)
E. \( Q_{1} \) and \( Q_{2} \) have same sign, but the magnitude of \( Q_{2} \) is greater than the magnitude of \( Q_{1} \)
Subject: Physics
An elastic material of Young's modulus \( Y \) is subjected to a stress \( S \). The elastic energy stored per unit volume of the material is :
A \( \cdot \frac{S Y}{2} \)
B. \( \frac{s^{2}}{2 Y} \)
c. \( \frac{s}{2 Y} \)
D. \( \frac{2 S}{Y} \)
Subject: Physics
The radius of the earth is given \( 6.4 \times \)
\( 10^{6} m . \) What is the order of magnitude of
the size of the earth?
\( \mathbf{A} \cdot 10^{6} m \)
B . \( 6 \times 10^{6} \mathrm{m} \)
\( \mathbf{c} \cdot 10^{7} m \)
D . \( 5 \times 10^{6} m \)
Subject: Physics
Two identical trains take 3 sec to pass
one another when going in the opposite direction but only 2.5 sec if the speed of
one is increased by \( 50 \% \). The time one would take to pass the other when going in the same direction at their original speed is
A \( .10 \mathrm{sec} \)
B. 12 sec
c. 15 sec
D. 18 sec
Subject: Physics
Assertion
The pressure at the bottom of two tanks of different area of cross sections are
equal if they contain same liquid to
same height
Reason
Pressure of a liquid is hdg and is
independent of shape and width of the
container
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 ray incident at \( 15^{\circ} \) on one refracting
surface of a prism of angle \( 60^{\circ} \) suffers a
deviation of \( 55^{\circ} . \) What is the angle of
emergence?
A . \( 90^{\circ} \)
B. \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. None of these
Subject: Maths
Bag I contains 1 white, 2 black and 3 red
balls; Bag II contains 2 white, 1 black and 1 red balls; Bag III contains 4 white,
3 black and 2 red balls. A bag is chosen
at random and two balls are drawn from
it with replacement. They happen to be one white and one red. What is the
probability that they came from Bag III.
Subject: Maths
\( \lim _{n \rightarrow \infty} \frac{\sqrt{\mathbf{1}}+\sqrt{\mathbf{2}}+\ldots \ldots+\sqrt{n-1}}{\boldsymbol{n} \sqrt{\boldsymbol{n}}}=\mathbf{0} \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{3} \)
D. 0 (zero)
Subject: Physics
A coil of self-inductance \( L \) is connected
in series with a bulb B and an AC
source. Brightness of the bulb decreases when :
A. frequency of the AC source is decreased
B. number of turns in the coil is reduced
C . a capacitance of reactance \( X_{C}=X_{L} \) is included in the same circuit
D. an iron rod is inserted in the coil
Subject: Chemistry
When \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHCl}_{2} \) is treated with
\( \mathrm{NaNH}_{2} \), the product formed is
В. \( \mathrm{cH}_{3} \mathrm{c} \equiv \mathrm{cH} \)
\( D \)
Subject: Physics
A cord is wound around the
circumference of wheel of radius 'r'. The
axis of the wheel is horizontal and
moment of inertia about it is 'l'. The
weight 'mg' is attached to the end of the cord and falls from rest. After falling
through a distance 'h', the angular
velocity of the wheel will be
\( \mathbf{A} \cdot[m g h]^{1 / 2} \)
B. \( \left[\frac{m g h}{I+2 m r^{2}}\right]^{1 / 2} \)
c. \( \left[\frac{2 m g h}{I+m r^{2}}\right]^{1 / 2} \)
D. \( \left[\frac{m g h}{I+m r^{2}}\right]^{1 / 2} \)
Subject: Physics
A series of ocean waves, each \( 5.0 \mathrm{m} \)
from crest to crest, moving past the observer at a rate of 2 waves per second
What is the velocity of ocean waves?
A. \( 2.5 \mathrm{m} / \mathrm{s} \)
B. \( 5.0 \mathrm{m} / \mathrm{s} \)
\( c \cdot 8.0 \mathrm{m} / \mathrm{s} \)
D. \( 10.0 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Match the compounds given in column I with oxidation states of carbon given in column II and mark the apropriate
choice.
\( (A) \)
(B) The the \( \begin{array}{llll}\text { Column I } & & \text { Column II } \\ & & \\ C_{6} H_{12} O_{6} & \text { (i) } & +3 \\ & C H C l_{3} & \text { (ii) } & -3 \\ & C H_{3} C H_{3} & \text { (iii) } & +2 \\ & (C O O H)_{2} & \text { (iv) } & 0\end{array} \)
(c)
(D)
\( A \)
\( (A) \rightarrow(\text { iv }),(B) \rightarrow(\text { iii }),(C) \rightarrow(\text { ii }),(D) \rightarrow(i) \)
B. \( (A) \rightarrow(\text { i }),(B) \rightarrow(\text { ii }),(C) \rightarrow(\text { iii }),(D) \rightarrow(\text { iv }) \)
C. \( (A) \rightarrow(\text { ii }),(B) \rightarrow(\text { iii }),(C) \rightarrow(\text { iv }),(D) \rightarrow(i) \)
\( D \cdot(A) \rightarrow(\text { iii }),(B) \rightarrow(\text { ii }),(C) \rightarrow(i),(D) \rightarrow(\text { iv }) \)
Subject: Physics
The excess pressure across a soap bubble of radius \( r \) is \( p=\frac{4 \sigma}{r}, \) where \( \sigma \)
is the surface tension of soap solution.
What is the excess pressure across an
air bubble of the same radius \( r \) formed
inside a container of soap solution?
A \( \cdot \frac{\sigma}{r} \)
в. \( \frac{2 \sigma}{r} \)
c. \( \frac{4 \sigma}{r} \)
D. none of these
Subject: Maths
The solution of the differential equation \( x \frac{d y}{d x}=\frac{y}{1+\log x} \) is :
A. \( y=\log x+C \)
в. \( y=\frac{C}{1+\log x} \)
c. \( y=C(x+\log x) \)
D. \( y=x+\log (C x) \)
E . \( y=C(1+\log x) \)
Subject: Chemistry
The enthalpy of vaporization of water at \( 100^{\circ} \mathrm{C} \) is \( 40.63 \mathrm{KJ} \) mol\( ^{-1} \). The value \( \Delta \boldsymbol{E} \)
for this process would be:
A . 37.53 К J \( m o l^{-1} \)
B. 39.08 К J mol \( ^{-1} \)
c. 42.19 К и \( m o l^{-1} \)
D. 43.73 К」 \( m o l^{-1} \)
Subject: Physics
A \( 500 W \) heating unit is designed to operate on a \( 115 \mathrm{V} \) line. If line voltage
drops to \( 110 V \) line, the percentage drop in heat output will be:
A. \( 7.6 \% \)
B. \( 8.5 \% \)
c. \( 8.1 \% \)
D. 10.2 \%
Subject: Maths
Diameter of the largest sphere which can be carved out from a cube of side \( x \)
\( \mathrm{cm} \) is equal to This question has multiple correct options
A. one third of sum of all edges
B. One twelfth of sum of all edges
c. one half of sum of length of diagonals
D. \( \frac{1}{\sqrt{3}} \) times of length of any diagonal
Subject: Physics
In a circuit, the frequency is \( \boldsymbol{f}=\frac{\mathbf{1 0 0 0}}{\mathbf{2} \pi} \)
\( \mathrm{Hz} \) and the inductance is 2 henry, then
the reactance will be
\( A \cdot 200 \Omega \)
в. 200 \( \mu \) \Omega
c. \( 2000 \Omega \)
D. 2000 \( \mu \Omega \)
Subject: Maths
If tangents \( \boldsymbol{T} \boldsymbol{A} \) and \( \boldsymbol{T} \boldsymbol{B} \) from a point \( \boldsymbol{T} \)
to a circle with centre \( O \) are inclined to
each other at an angle of \( 70^{\circ}, \) then find
\( \angle A O B \) (in degrees)
Subject: Physics
Which of the following statements are
true? For a particle on the surface of the
earth.
This question has multiple correct options
A. The linear speed is minimum at the equator
B. The angular speed is maximum at the equator
C. The linear speed is minimum at the poles
D. The angular speed is \( 7.3 \times 10^{-5} \) rad \( s^{-1} \) at the equator
Subject: Chemistry
When 2 -butyne is treated with \( H_{2} \)
/Lindlar's catalyst, compound \( \boldsymbol{X} \) is
produced as the major product and
when treated with \( N a / \)lliq. \( N H_{3} \) it produced \( Y \) as the major product. Which of the following statements is correct?
(1) \( X \) will have higher dipole moment
and higher boiling point than \( Y \)
(2) \( Y \) will have higher dipole
moment and higher boiling point than
\( \boldsymbol{X} \)
Subject: Physics
Two cells of the same emf \( e \) but
difference internal resistances \( r_{1} \) and
\( r_{2} \) are connected in series with an
external resistance \( R \). The potential
drop across the first cell is found to be
zero. The external resistance \( \boldsymbol{R} \) is
A \( \cdot r_{1}-r_{2} \)
в. \( r_{1} / r_{2} \)
\( c \cdot r_{1} r_{2} \)
D. \( r_{1}+r_{2} \)
Subject: Maths
The sequence \( -10,-6,-2,2, \dots \dots \)
\( \mathbf{A} \cdot \) is an \( A \cdot P ., \) Reasons \( d=-16 \)
B. is an \( A . P ., \) Reasons \( d=4 \)
C. is an \( A \).P., Reasons \( d=-4 \)
D. is not an \( A . P \)
Subject: Maths
\( \ln \) an A.P., if \( m^{t h} \) term is \( n \) and the \( n^{t h} \)
term is \( \mathrm{m}, \) where \( \boldsymbol{m} \neq \boldsymbol{n} \) find the \( \boldsymbol{p}^{t h} \)
term.
A \( . m+n+p \)
в. \( m-n+p \)
c. \( m+n-p \)
\( \mathbf{D} \cdot m-n-p \)
Subject: Physics
The relation between \( t \) and distance \( x \) is
\( \boldsymbol{t}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x} \) where \( \boldsymbol{a} \) and \( \boldsymbol{b} \) are
constants. Express the instantaneous acceleration in terms of instantaneous
velocity.
Subject: Maths
For two acute angled \( \triangle A B C \) and \( \triangle P Q R \) if \( \triangle A B C \sim \triangle P Q R \) then prove
\( \operatorname{that} \frac{\operatorname{area}(\triangle A B C)}{\operatorname{area}(\triangle P Q R)}=\frac{A B^{2}}{P Q^{2}}=\frac{B C^{2}}{Q R^{2}}= \)
\( \frac{A C^{2}}{P R^{2}} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}-\boldsymbol{2} \) and \( \boldsymbol{g}(\boldsymbol{x})=\frac{\boldsymbol{x}+\mathbf{1}}{\mathbf{2}} \)
then \( \boldsymbol{g} \boldsymbol{o} \boldsymbol{f}(\boldsymbol{3})= \)
Subject: Chemistry
For describing law of multiple proportions, which among the following pair can be used?
A . NO and \( N O_{2} \)
B. \( C H_{4} \) and \( C O_{2} \)
c. \( Z n O_{2} \) and \( Z n C l_{2} \)
D. \( N H_{3} \) and \( N H_{4} C l \)
E. \( H_{2} O \) and нс
Subject: Chemistry
Reaction of \( \boldsymbol{R}-\mathbf{2}- \) butanol with \( \boldsymbol{p}- \)
toluenesulphonyl chloride in pyridine followed by reaction with \( L i B r \) gives:
A. \( R-1 \) -butyl bromide
B. \( R-2 \) -butyl tosylare
c. \( R-1 \) -butyl tosylate
D. \( R-2 \) -butyl bromide
Subject: Maths
What is the value of \( \int_{0}^{a} \frac{x-a}{x+a} d x ? \)
A. \( a+2 a \log 2 \)
в. \( a-2 a \log 2 \)
c. \( 2 a \log 2-a \)
D. \( 2 a \log 2 \)
Subject: Maths
For which values of ' \( a \) ' the different
vectors \( \bar{x}=(2 a, 3 a, 0) \) and \( \bar{y}= \)
\( (0,0,4 a) \) are orthogonal vectors
\( \mathbf{A} \cdot a \in R \)
B . \( a \in N \cup\{0\} \)
\( \mathbf{c} \cdot a \in R-\{0\} \)
\( \mathbf{D} \cdot a=0 \)
Subject: Maths
Determine range \( \boldsymbol{y}=\mathbf{3} \sin \boldsymbol{x}+ \)
\( 4 \cos (x+\pi / 3)+7 \)
A \( \cdot 7-\sqrt{5-3 \sqrt{3}}, 7+\sqrt{5-3 \sqrt{3}} \)
B・ \( 7-\sqrt{10-3 \sqrt{3}}, 7+\sqrt{10-3 \sqrt{3}} \)
c. \( _{7}-\sqrt{10+3 \sqrt{3}}, 7+\sqrt{10-3 \sqrt{3}} \)
D \( \cdot 7-\sqrt{10+3 \sqrt{3}}, 7-\sqrt{10-3 \sqrt{3}} \)
Subject: Physics
Let \( n_{1}, n_{2}, n_{3} \dots \) are the frequencies of
segments of a stretched string, then the frequency \( n \) of the string can be given
by
A \( \cdot n=n_{1}+n_{2}+n_{3}+\dots \)
B. \( n=\sqrt{n_{1} \times n_{2} \times n_{3} \times \ldots} \)
c. \( \frac{1}{n}=\frac{1}{n_{1}}+\frac{1}{n_{2}}+\frac{1}{n_{3}}+\dots \)
D. None of the above
Subject: Physics
When 60 calories of heat are supplied to \( 15 \mathrm{g} \) of water, the rise in temperature is
A \( \cdot 75^{\circ} \mathrm{C} \)
B. \( 900^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 4^{\circ} C \)
D. \( 0.25^{\circ} \mathrm{C} \)
Subject: Physics
\( A 220 V, 50 H z A C \) generator is connected to an inductor and a \( 50 \Omega \) resistance in series. The current in the
circuit is \( 1.0 A . \) What is the Potential
difference across inductor?
A. \( 102.2 V \)
в. \( 186.4 \mathrm{V} \)
c. \( 214 V \)
D. \( 170 V \)
Subject: Physics
A body travels uniformly a distance of \( (13.7 \pm 0.2) m, \) in time \( (4.0 \pm 0.3) s \)
The velocity of particle is?
A \( .(3.45 \pm 0.31) m / s \)
в. \( (3.4 \pm 0.3) \mathrm{m} / \mathrm{s} \)
c. \( (3.68 \pm 0.4) \mathrm{m} / \mathrm{s} \)
D. \( (3.6 \pm 0.42) \mathrm{m} / \mathrm{s} \)
Subject: Maths
The cross-section of a canal is
trapezium in shape. The canal is \( 12 m \) wide at the top and \( 8 m \) wide at the
bottom. If the area of the cross-section
is \( 840 s q . m, \) the depth of the canal is:
\( \mathbf{A} \cdot 8.75 m \)
в. \( 42 m \)
\( c .63 m \)
D. \( 84 m \)
Subject: Physics
A metal rod having a linear coefficient
of expansion \( 2 \times 10^{-5} /^{\circ} \mathrm{C} \) has a length 1
\( \mathrm{m} \) at \( 25^{\circ} \mathrm{C}, \) the temperature at which it is shortened by \( 1 \mathrm{mm} \) is :
\( A \cdot 50^{\circ} \mathrm{C} \)
B. \( -50^{\circ} \mathrm{C} \)
c. \( -25^{\circ} \mathrm{C} \)
D. \( -12.5^{\circ} \mathrm{C} \)
Subject: Chemistry
Classify the following reaction in one of the reaction type.
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{B r}+\boldsymbol{H O}^{-} \rightarrow \boldsymbol{C H}_{2}= \)
\( \boldsymbol{C H}_{2}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{B r} \)