AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Choose the correct answer from the
alternatives given.

A plane EM wave travelling along zdirection is described by \( \overrightarrow{\boldsymbol{E}}= \) \( E_{0} \sin (k z-\omega t) \hat{i} \) and \( B=B_{0} \sin (k z- \)
\( \omega t) \hat{j} \)
A. the avrage energy density of the wave is given by \( u_{a v}=\frac{1}{4} \varepsilon_{0} E_{0}^{2}+\frac{1}{4} \frac{B_{0}^{2}}{\mu} \)
B. The time averaged intensity of the wave is given \( I_{a v}= \) \( \frac{1}{2} c \varepsilon_{0} E_{0}^{2} \)
c. Both (a) and (b)
D. None of these
Subject: Chemistry
The enthalpies of formation of \( \boldsymbol{C O}_{2(\boldsymbol{g})}, \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \) and \( \boldsymbol{C}_{2} \boldsymbol{H}_{4(\boldsymbol{g})} \) are
respectively -393.5,-286 and \( +52.3 k J m o l^{-1} . \) The enthalpy change
for the combustion of \( C_{2} H_{4(g)} \) is :
A . \( 1306 k J m o l^{-1} \)
В. \( 1411.3 \mathrm{kJmol}^{-1} \)
c. \( -509.7 k J m o l^{-1} \)
D. \( -731.5 k J m o l^{-1} \)
Subject: Maths
Five years ago, Shikha was thrice as old as Rani. 10 years later, Shikha will be twice as old as Rani. How old are they now?
A. Rani 20 yrs, Shikha 50 yrs
B. Shikha 20 yrs, Rani 50 yrs
c. Shikha 80 yrs, Rani 30 yrs
D. Shikha 30 yrs, Rani 80 yrs
Subject: Physics
Current in a coil of self-inductance
\( 2.0 H \) is increasing as \( i=2 \sin t^{2} . \) The
amount of energy spent during the period when the current changes from 0
to \( 2 A \) is:
A . 15
в. 2 J
\( c .3 J \)
D. \( 4 J \)
Subject: Maths
Find the value of \( x, y, z \) if \( \left[\begin{array}{ll}\mathbf{4} & \mathbf{3} \\ \boldsymbol{x} & \mathbf{5}\end{array}\right]=\left[\begin{array}{ll}\boldsymbol{y} & \boldsymbol{z} \\ \mathbf{1} & \mathbf{5}\end{array}\right] \)
Subject: Physics
A particle performs S.H.M. with amplitude \( 25 c m \) and period \( 3 s . \) The minimum time required for it to move
between two points \( 12.5 \mathrm{cm} \) on either
side of the mean position is
A . \( 0.6 s \)
B. \( 0.5 s \)
c. \( 0.4 s \)
D. \( 0.2 s \)
Subject: Chemistry
Assertion
The oxidation state of \( S \) in \( H_{2} S_{2} O_{8} \) is 6
Reason
Maximum oxidation state of \( S \) is 6
because the maximum oxidation state
of an element is its number of valence
electron.
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
Describe the shape and Magnetic
property of \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{+2} \)
\( \left[\boldsymbol{C O}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{+3} \&\left[\boldsymbol{N} \boldsymbol{i} \boldsymbol{C l}_{4}\right]^{-2} \)
Subject: Maths
dentify a possible graph for function \( \boldsymbol{f} \)
given by
\( \boldsymbol{f}(\boldsymbol{x})=\sqrt{(\boldsymbol{x}-\mathbf{2})}+\mathbf{1} \)
\begin{tabular}{|l|l|l|l|}
\hline \( \mathrm{a} \) & & & \( \mathrm{b} \) & \\
\hline & & & & \\
\hline & & & & \\
\hline \( \mathrm{c} \) & & & \( \mathrm{d} \) & \\
& & & & \\
\hline & & & & \\
& & & \\
\hline
\end{tabular}
A. graph a
B. graph b
c. graph c
D. graph d
Subject: Chemistry
The IUPAC name of the compound with
formula \( \mathrm{C}_{n} \mathrm{H}_{2 n+2} \) having the lowest
possible molecular mass and capable of showing enantiomerism, is :
A. 3-Methyl hexane
B. 2,3-Dimethyl pentane
c. Methane
D. Both (a) and (b)
Subject: Maths
If \( \bar{E} \) and \( \bar{F} \) are complementary events of E and F respectively and if \( 0< \)
\( \boldsymbol{P}(\boldsymbol{F})<1, \) then
This question has multiple correct options
A \( \cdot P(E / F)+P(\bar{E} / F)=1 \)
B . \( P(E / F)+P(E \bar{F})=1 \)
c. \( P(\bar{E} / F)+P(E \bar{F})=1 \)
D . \( P(E \bar{F})+P(\bar{E} \bar{F})=1 \)
Subject: Maths
тре
(I) Quadrılateral MUKE
\( M O=6 \mathrm{cm} \)
\( \boldsymbol{O} \boldsymbol{R}=\mathbf{4 . 5} \boldsymbol{c m} \)
\( \angle M=60^{\circ} \)
\( \angle O=105^{\circ} \)
\( \angle R=105^{\circ} \)
(ii) Quadrilateral \( \boldsymbol{P} \boldsymbol{L} \boldsymbol{A} \boldsymbol{N} \)
\( \boldsymbol{P L}=\boldsymbol{4} \boldsymbol{c m} \)
\( \boldsymbol{L} \boldsymbol{A}=\mathbf{6 . 5} \boldsymbol{c m} \)
\( \angle \boldsymbol{P}=\mathbf{9 0}^{\circ} \)
\( \angle A=110^{\circ} \)
\( \angle N=85^{\circ} \)
(iii) Parallelogram \( \boldsymbol{H} \boldsymbol{E} \boldsymbol{A} \boldsymbol{R} \)
\( \boldsymbol{H} \boldsymbol{E}=\mathbf{5} \boldsymbol{c m} \)
\( \boldsymbol{E} \boldsymbol{A}=\boldsymbol{6} \boldsymbol{c m} \)
\( \angle \boldsymbol{R}=\mathbf{8} \mathbf{5}^{\circ} \)
(iv) Rectangle \( \boldsymbol{O} \boldsymbol{K} \boldsymbol{A} \boldsymbol{Y} \)
\( \boldsymbol{O} \boldsymbol{K}=\mathbf{7} \boldsymbol{c m} \)
\( \boldsymbol{K} \boldsymbol{A}=\mathbf{5} \boldsymbol{c m} \)
Subject: Physics
Two positive charges \( \boldsymbol{q}_{1}=20 C \) and
\( q_{2}=6 C \) are separated by diameter of
3 \( m \). Then what is the force produced by
them?
\( A \cdot 80 N \)
B. \( 53.3 N \)
\( c .56 N \)
D. \( 72.5 N \)
Subject: Maths
\( \sinh \left(\cosh ^{-1} x\right)= \)
A \( \cdot \sqrt{x^{2}+1} \)
B. \( \frac{1}{\sqrt{x^{2}+1}} \)
c. \( \sqrt{x^{2}-1} \)
D. \( \frac{1}{\sqrt{x^{2}-1}} \)
Subject: Maths
The value of determinant \( \left|\begin{array}{lll}1 / a & b c & a^{3} \\ 1 / b & c a & b^{3} \\ 1 / c & a b & c^{3}\end{array}\right| \)
A \( \cdot a^{2} b^{2} c^{2}(a-b)(b-c)(c-a) \)
B. 0
c \( \cdot(a-b)(b-c)(c-a) \)
D. None of the above
Subject: Physics
A body of mass \( 3 \mathrm{kg} \) collides elastically with another body at rest and then continues to move in the original direction with one half of its original speed. What is the mass of the target body?
\( A \cdot 1 \mathrm{kg} \)
B. 2.5 \( \mathrm{kg} \)
\( c \cdot 2 k g \)
\( D .5 \mathrm{kg} \)
Subject: Physics
toppr
Q Type your question
Why
acceleration of block \( \boldsymbol{A} \) and \( \boldsymbol{B} \). Which
graph best represents acceleration \( a_{1} \)
and \( a_{2} \) of block \( A \) and \( B \) respectively
with time?
\( A \)
B.
\( c \)
D.
Subject: Physics
Phase difference \( (\phi) \) and path
difference \( (\delta) \) are related by :
A \( \cdot \frac{2 \pi}{\lambda} \delta \)
в. \( \frac{\pi}{2 \lambda} \delta \)
\( c \cdot \frac{\lambda}{2 \pi} \delta \)
D. \( \frac{2 \lambda}{\pi} \)
Subject: Chemistry
For reaction \( , 2 A+B \rightleftharpoons 2 C, K=x \)
Equilibrium constant for \( \boldsymbol{C} \rightleftharpoons \boldsymbol{A}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{B} \)
will be:
\( A \)
в. \( \frac{x}{2} \)
c. \( \frac{1}{\sqrt{x}} \)
D. \( \sqrt{x} \)
Subject: Maths
Find composite of \( f \) and \( g \) and express
it by formula:
\( \boldsymbol{f}=\{(\mathbf{1}, \mathbf{3}),(\mathbf{2}, \mathbf{4}),(\mathbf{3}, \mathbf{5}),(\mathbf{4}, \mathbf{6})\} \)
\( \boldsymbol{g}=\{(\mathbf{3}, \mathbf{6}),(\mathbf{4}, \mathbf{8}),(\mathbf{5}, \mathbf{1 0}),(\mathbf{6}, \mathbf{1 2})\} \)
Subject: Physics
We have \( 20 \mathrm{Kg} \) of a block of a substance at its melting point. The substance has a latent heat of fusion of 1500 Joules per
kilogram and a specific heat at of 2500 Joules per kilogram degree Celcius. How much heat is needed to change the block entirely into a liquid?
A. 30000
B. 750 J
c. 1250
D. 3000 J
E. 8000
Subject: Chemistry
One method of producing \( N H_{3} \) is by
heating ammonium chloride, \( N H_{4} C l \)
with \( C a O \)
\( \mathbf{2} N \boldsymbol{H}_{4} \boldsymbol{C l}+\boldsymbol{C a O} \rightarrow \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{C a} \boldsymbol{C l}_{2}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Explain why the reaction of \( N H_{4} C l \)
with \( C a O \) produces ammonia.
Subject: Chemistry
Useful buffer range of weak acid
\( \boldsymbol{H} \boldsymbol{A}\left(\boldsymbol{K}_{a}=\mathbf{1 0}^{-5}\right) \) is:
\( \mathbf{A} \cdot 5 \) to 7
B. 4 to 6
c. 3 to 5
D. none of these
Subject: Chemistry
Assertion
Fluorine has only-1 oxidation state in
compounds.
Reason
Fluorine has maximum
electronegativity and electron-affinity.
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 \( \boldsymbol{x}+\boldsymbol{y} \) if \( \left[\begin{array}{cc}-2 & 0 \\ 3 & 1\end{array}\right]\left[\begin{array}{l}-1 \\ 2 x\end{array}\right]+ \)
\( \left[\begin{array}{c}-2 \\ 1\end{array}\right]=2\left[\begin{array}{l}y \\ 3\end{array}\right] \)
Subject: Physics
\( \mathbf{A}-\mathbf{4} . \mathbf{8 0} \mu \mathbf{C} \) charge is moving at a
constant velocity of \( 6.80 \times 10^{5} m / s \) in
the \( +x \) direction relative to a reference frame.At the instant when the point
charge is at the origin,what is the magnetic field vector it produces at the following points \( x=0, y=0.500 \mathrm{m}, z=0 ? \)
Subject: Chemistry
An ion is an atom with an electric
charge due to a loss or gain of an electron.
Which of the following is the electron configuration of a ground state of the most common alkali metal ion?
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} \)
B. \( 1 s^{2} 2 s^{\text {। }} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} s s^{2} 3 p^{6} 3 d \)
Subject: Physics
Suld
and mass \( 1 \mathrm{kg} \) are placed (fixed)
symmetrically about a movable
central charge of magnitude \( 5 \times \)
\( 10^{-5} C \) and mass 0.5 kg as shown. The
charge at \( P_{1} \) is removed. The
acceleration of the central charge is:
\( \left[\text { Given } \boldsymbol{O} \boldsymbol{P}_{1}=\boldsymbol{O} \boldsymbol{P}_{2}=\boldsymbol{O} \boldsymbol{P}_{3}=\boldsymbol{O} \boldsymbol{P}_{4}=\right. \)
\( \left.O P_{5} 1 m ; \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \text { in SI units }\right] \)
A \( .9 m s^{-2} \) upwards
B. \( 9 m s^{-2} \) downwards
C \( .4 .5 \mathrm{m} \mathrm{s}^{-2} \) upwards
D. \( 4.5 m s^{-2} \) downwards
Subject: Maths
A coin is tossed three times, where
(i) \( E: \) head on third toss, \( F: \) heads on
first two tosses
(ii) \( E: \) at least tow heads, \( F: \) at most
two heads
(iii) \( E: \) at most two tails, \( F: \) at least
one tail
Determine \( \boldsymbol{P}(\boldsymbol{E} \mid \boldsymbol{F}) \)
A. 0.42,0.50,0.85
В. 0.50,0.42,0.85
c. 0.85,0.42,0.30
D . .0.42, 0.46, 0.47
Subject: Biology
Match list I with list II and choose the
correct answer.
\( \begin{array}{lllll} & \text { List } 1 & & \text { List II } \\ \text { (A) } & \text { Hypothalamus } & \text { (1) } & \begin{array}{l}\text { Sperm } \\ \text { lysine }\end{array} \\ \text { (B) } & \text { Acrosome } & \text { (2) } & \text { Estrogen } \\ \text { (C) } & \begin{array}{l}\text { Graafian } \\ \text { follicle }\end{array} & \text { (3) } & \text { Relaxin } \\ \text { (D) } & \text { Leydig cells } & \text { (4) } & \text { GnRH } \\ \text { (E) } & \text { Parturition } & \text { (5) } & \text { Testosterone }\end{array} \)
\( A \)
(A)- (4), (B)- (1), (C)- (2), (D)- (3), (E)- (5)
B. \( (A)-(2),(B)-(1),(C)-(4),(D)-(3),(E)-(5) \)
\( c \)
(A)- (2), (B)- (1), (C)- (5), (D)- (4), (E)- (3)
D.
\( E \cdot(A)-(5),(B)-(1),(C)-C \)
(3) \( D_{D} \) (2)
(E)- (4)
Subject: Chemistry
Relative stabilities of the following
structures of \( \boldsymbol{C} \boldsymbol{H}_{2}=\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \) are
in this decreasing order:
\( A \cdot\|>1>\| \)
c. \( \|\mid>\|>1 \)
D. |>॥|| > ||
Subject: Maths
If \( P\left(E_{k}\right) \propto k \) for \( 0 \leq k \leq n, \) then the
probability that \( X \) is the only student to pass the examination is
A \( \cdot \frac{3}{n(n+1)} \)
в. \( \frac{6}{n(n+1)(2 n+1)} \)
\( c \cdot \frac{1}{n} \)
D. \( \frac{1}{n(2 n+1)} \)
Subject: Maths
If \( \boldsymbol{S}=\mathbf{1}+\frac{\mathbf{1}}{\mathbf{2}}+\frac{\mathbf{1}}{\mathbf{4}}+\frac{\mathbf{1}}{\mathbf{8}}+\frac{\mathbf{1}}{\mathbf{1 6}}+\frac{\mathbf{1}}{\mathbf{3 2}}+ \)
\( \dots \infty \)
then, the sum of the given series is 2
A. True
B. False
Subject: Maths
Obtain the differential equation whose solution is
\( \boldsymbol{y}=\boldsymbol{x} \sin (\boldsymbol{x}+\boldsymbol{A}), \mathbf{A} \) being constant
A \( \cdot\left(x y_{1}-y\right)^{2}+x^{2} y^{2}=x^{4} \)
B. \( \left(x y_{1}-y\right)^{2}-x^{2} y^{2}=x^{4} \)
c. \( \left(x y_{1}-y\right)^{2}+x^{2} y^{2}=x^{2} \)
D. \( \left(x y_{1}-y\right)^{2}-x^{2} y^{2}=x^{2} \)
Subject: Maths
From the data given below state which
group is more variable \( \boldsymbol{A} \) or \( \boldsymbol{B} \)
\( \begin{array}{llllll}\text { Marks } & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}20- \\ 30\end{array} & \begin{array}{l}30- \\ 40\end{array} & \begin{array}{l}\text { 40- } \\ \text { 50 }\end{array} & \begin{array}{l}\text { 50 } \\ 60\end{array}\end{array} \)
Group
A 32 33 17
25 \begin{tabular}{l|l|l|l} 
Group & 10 & 20 & 30 \\
B & (年) & (年)
\end{tabular}
Subject: Chemistry
Esterification of \( (-)- \) lactic acid with
methanol yields \( (+)- \) methyl lactate.
Assuming that there are no side reactions, what is true about this
reaction?
A \( \cdot \) An \( S N_{2} \) reaction has occurred, inverting the absolute configuration of the chiral centre.
B. \( A n S N_{1} \) reaction at the chiral centre has inverted the optical rotation.
C. A diastereomer has been produced; diastereomers have different physical properties, including optical rotation
D. optical rotation is not directly related to absolute configuration, so the change in sign of rotation is merely a coincidence.
Subject: Physics
How much heat energy should be added to the gaseous mixture consisting of one gram of hydrogen and one gram
helium to raise its temperature from
\( 0^{\circ} C \) to \( 50^{\circ} C \)
(a) at constant volume and
(b) at constant pressure, assuming both the gases to be ideal \( \boldsymbol{R}=\boldsymbol{2} \boldsymbol{c a l} / \boldsymbol{m o l}-\boldsymbol{K}, \boldsymbol{\gamma}_{\boldsymbol{H}_{2}}=\mathbf{1 . 4 1} \)
\( \gamma_{H_{e}}=1.67 \)
Subject: Physics
Assertion: The resistance of a
milliammeter is greater than that of
ammeter

Reason: Shunt resistance in case of
a milliammeter is more than that of
ammeter
A. Both (A) and (R) are true and
(R) is the correct explanation of A
B. Both (A) and (R) are true but (R) is not the correct explanation of A
c. (A) is true but (R) is false
D. (A) is false but (R) is true
Subject: Maths
\( \frac{\sin ^{2} A-\sin ^{2} B}{\sin A \cos A-\sin B \cos B} \) is equal to
A \( \cdot \tan (A-B) \)
B \cdot \( \tan (A+B) \)
c. \( \cot (A-B) \)
D \cdot \( \cot (A+B) \)
Subject: Maths
if \( \sin \theta=\frac{1}{2} \) and \( \cos \theta=-\frac{\sqrt{3}}{2}, \) then
the general value of \( \theta i s(n \epsilon z) \)
A \( \cdot 2 n \pi+\frac{5 \pi}{6} \)
В \( \cdot 2 n \pi+\frac{\pi}{6} \)
c. \( _{2 n \pi+\frac{7 \pi}{6}} \)
D. \( 2 n \pi+\frac{\pi}{4} \)
Subject: Maths
A fruit vendor sells fruits from his shop. Selling prices of Apple, Mango and Orange are Rs. \( 20, \) Rs. 10 and Rs. 5 each
respectively. The sales in three days are given below
\( \begin{array}{llll}\text { Day } & \text { Apples } & \text { Mangoes } & \text { Oranges } \\ 1 & 50 & 60 & 30 \\ 2 & 40 & 70 & 20 \\ 3 & 60 & 40 & 10\end{array} \)
Write the matrix indicating the total amount collected on each day and
hence find the total amount collected
from selling of all three fruits combined.
Subject: Physics
Assertion
The maximum height of a mountain on earth can be estimated from the elastic
behaviour of rocks.
Reason
At the base of mountain, the pressure is less than elastic limit of earth's
supporting material
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
A pressure of \( 100 k P a \) causes a decrease in volume of water by
\( 5 \times 10^{-3} \) percent. The speed of sound in water is
A \( \cdot \) १४१४ \( m s^{-1} \)
B. \( 1000 \mathrm{ms}^{-1} \)
c. \( 2000 \mathrm{ms}^{-1} \)
D. 3000 \( m s^{-1} \)
Subject: Chemistry
Ethylene dibromide \( \left(C_{2} H_{4} B r_{2}\right) \) and
1, 2 - dibromopropane \( \left(C_{3} H_{6} B r_{2}\right) \)
forms a series of ideal solution over the
whole range of composition. At \( 85^{\circ} C \)
the vapour pressure of these pure liquids are are \( 183 \mathrm{mmHg} \) and 127 mm \( H g \) respectively. 10gm of ethylene dibromide is
dissolved in \( 80 g m \) of \( 1,2- \) dibromo - propane. Calculate the
partial pressures of each components and the total pressure of the solution at
\( 85^{\circ} C \)
Calculate the composition of vapour in equilibrium with the above and express as mole fraction of ethylene dibromide.
Subject: Physics
The electric field in a region of space is
given by \( \boldsymbol{E}=\mathbf{5} \boldsymbol{i}+\mathbf{2} \boldsymbol{j} \boldsymbol{N} / \boldsymbol{C} . \) Determine
the electric flux due to this field
through an area \( 2 m^{2} \) lying in the \( Y Z \) plane:
A . 10
B . 20
c. \( 10 \sqrt{2} \)
(
D. \( 2 \sqrt{29} \)
Subject: Maths
If \( \boldsymbol{y}=\mathbf{1}+\frac{\boldsymbol{x}}{\mathbf{1} !}+\frac{\boldsymbol{x}^{2}}{\mathbf{2 !}}+\frac{\boldsymbol{x}^{\mathbf{3}}}{\mathbf{3 !}}+\cdots, \) then
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=------ \)
Subject: Maths
The number of real solutions of
\( \tan ^{-1}(\sqrt{x(x+1)}+ \)
\( \sin ^{-1} \sqrt{\left(x^{2}+x+1\right)}=\frac{\pi}{2} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. infinite
Subject: Maths
\( \boldsymbol{x}=\mathbf{1}+\boldsymbol{a}+\boldsymbol{a}^{2}+\ldots \infty, \boldsymbol{y}=\mathbf{1}+\boldsymbol{b}+ \)
\( \boldsymbol{b}^{2}+\ldots \infty \quad \) then \( \quad \mathbf{1}+\boldsymbol{a} \boldsymbol{b}+\boldsymbol{a}^{2} \boldsymbol{b}^{2}+ \)
\( \ldots \infty= \)
Subject: Physics
A conducting rod of length \( 2 \mathrm{m} \) is placed on a horizontal table in north-south
direction. It carries a current of 5 A from
south to north. Find the direction and
magnitude of the magnetic force acting on the rod. Given that the Earth's
magnetic field at the place is \( 0.6 \times \) \( 10^{-4} T \) and angle of dip is \( \frac{\pi}{6} \)
Subject: Maths
If \( x_{1}, x_{2}, \dots ., x_{n} \) are any real number and
\( \boldsymbol{n} \) is any positive integer, then \( ? \)
B \( \cdot n \sum_{i=1}^{n} x_{i}^{2} \geq\left(\sum_{i=1}^{n} x_{i}\right)^{2} \)
c. \( n \sum_{i=1}^{n} x_{i}^{2} \geq n\left(\sum_{i=1}^{n} x_{i}\right)^{2} \)
D. None of the above
Subject: Physics
During an adiabatic compression, \( 830 J \) of work is done on 2 moles of a
diatomic ideal gas to reduce its volume
by \( 50 \% \). The change in its temperature is nearly:
\( \left(\boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right) \)
A . \( 20 K \)
в. \( 14 k \)
c. \( 40 K \)
D. \( 33 K \)
Subject: Chemistry
An iron ball has a mass of 35 gms and a speed of \( 50 \mathrm{m} / \mathrm{s} \). If the speed can be measured with in accuracy of \( 2 \% \) then the uncertainty in the position is :
A. \( 1.507 \times 10^{-34} m \)
В. \( 1.507 \times 10^{-31} m \)
c. \( 1.507 \times 10^{-33} m \)
D. \( 1.507 \times 10^{-12} m \)
Subject: Physics
A car travels a distance of \( 60 k m \) in
10min. Find its speed in SI.
\( \mathbf{A} \cdot 6 m s^{-1} \)
B. \( 0.17 m s^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 100 \mathrm{ms}^{-1} \)
Subject: Physics
Two block of equal mass are tied with a
light which passes over a masseless pulley as shown in figure. The magnitude of acceleration of centre of
mass of both the block is (neglect
friction everywhere)
A \( \cdot \frac{\sqrt{3}-1}{2} g \)
B \( \cdot(\sqrt{3}-1) g \)
c. \( \frac{g}{2} \)
D. None of these
Subject: Physics
The resistance \( R \) of a conductor varies
with temperature as shown in the given figure. If the relation between \( R \) and \( t \) is
given as,
\( \boldsymbol{R}_{t}=\boldsymbol{R}_{0}\left(1+\boldsymbol{\alpha}+\boldsymbol{\beta} \boldsymbol{t}^{2}\right), \) then
A. \( \alpha \) and \( \beta \) are negative
B. \( \alpha \) is positive but \( \beta \) is negative
\( c \cdot \alpha \) and \( \beta \) are positive
D. \( \alpha \) is negative but \( \beta \) is positive
Subject: Maths
In the expansion of \( \left(x^{3}-\frac{1}{x^{2}}\right)^{n}, n \in N \)
if the sum of the coefficient of \( x^{5} \) and
\( x^{10} \) is \( 0, \) then \( n \) is
A . 25
B. 20
c. 15
D. None of these
Subject: Maths
The ratio of income of two persons is 9:
7 and the ratio of their expenditure is
\( 4: 3 . \) If each of them manages to save
Rs. 2000 per month, find their monthly income.
A. \( R s .18,000, \) Rs.14, 000
B. \( R s .1,000, R s .14,000 \)
c. \( R s .18,000, \) Rs.1, 000
D. None of these
Subject: Maths
If \( \overrightarrow{\boldsymbol{A}}=\boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \)
then find a unit vector along \( (\vec{A}-\vec{B}) \)
Subject: Chemistry
The value of magnetic moment of \( \boldsymbol{V}^{3+}(\boldsymbol{Z}=\mathbf{2 3}) \) is:
A \( \sqrt{2} B M \)
T
в. \( \sqrt{3} B M \)
\( \mathbf{c} \cdot 2 B M \)
D. \( \sqrt{8} B M \)
Subject: Physics
A prism of refractive index \( \sqrt{2} \) has a
reflecting angle of \( 60^{\circ} . \) At what angle
must a ray be incident on it so that it suffers minimum deviation?
A \( \cdot i=45^{\circ} \)
B . \( i=60^{\circ} \)
c. \( i=30^{\circ} \)
D . \( i=90^{\circ} \)
Subject: Maths
Let \( \bar{a}, \bar{b}, \bar{c} \) and \( \bar{d} \) be position vectors of four points \( A, B, C \) and \( D \) lying in a
plane. If \( (\bar{a}-\bar{d}) \cdot(\bar{b}-\bar{c})=0= \)
\( (\bar{b}-\bar{d}) \cdot(\bar{c}-\bar{a}), \) then \( \Delta A B C \) has \( D \) as
A . in-centre
B. circum-centre
c. ortho-centre
D. centroid
Subject: Physics
Two soap bubbles of radii \( r_{1} \) and
\( r_{2}\left(r_{a}>r_{2}\right) \) are connected by a tube
Then.
A . Air flows from the bubble of radius \( r_{1} \) to the bubble of
radius \( r_{2} \) till their size become equal
B. Air flows from the bubble of radius \( r_{1} \) to the bubble of
radius \( r_{2} \) till their sizes are interchanged
c. Air flows from smaller bubble to the bigger
D. There is no flow of air
Subject: Chemistry
Replacement of chlorine from chlorobenzene to give phenol requires
drastic conditions but chlorine of \( 2,4- \) dinitrochlorobenzene is readily replaced
because:
A. \( N O_{2} \) makes the electron rich ring at ortho and parapositions
B. \( N O_{2} \) withdraws electrons at meta position
c. \( N O_{2} \) donates electrons at meta position
D. \( N O_{2} \) withdraws electrons from ortho- and para position
Subject: Maths
The variance of the series \( \boldsymbol{a}, \boldsymbol{a}+\boldsymbol{d}, \boldsymbol{a}+ \)
\( 2 d, \ldots \ldots a+(2 n-1) d, a+2 n d, \) is
\( ^{\text {A } \cdot} \frac{n(n+1)}{2} d^{2} \)
\( ^{\text {В }} \cdot \frac{n(n-1)}{6} d^{2} \)
c. \( \frac{n(n+1)}{6} d^{2} \)
D. \( \frac{n(n+1)}{3} d^{2} \)
Subject: Maths
The eccentricity of the conic represented by \( \sqrt{(x+2)^{2}+y^{2}}+ \)
\( \sqrt{(x-2)^{2}+y^{2}}=8 \) is
A \( \cdot \frac{1}{3} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Physics
Assertion (A): According to the principle of conservation of energy all heat can be converted
into mechanical work
Reason (R): Due to various losses, it is impossible to convert all heat into
mechanical work
A. Both Assertion and Reason are true and reason is correct explanation of Assertion
B. Both Assertion and Reason are true but reason is not correct explanation of Assertion
c. Assertion is true but reason is false
D. Both assertion and reason are false
Subject: Chemistry
The IUPAC name of \( \boldsymbol{X} \boldsymbol{e}\left[\boldsymbol{P} \boldsymbol{t} \boldsymbol{F}_{\boldsymbol{6}}\right] \) is:
A. Hexafluoridoplatinate (VI) xenon
B. Xenon xenon hexafluoroplatinate (V)
c. xenon hexafluoridoplatinate (VI)
D. xenonium hexafluoridoplatinum ( V )