AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A bar of cross-sectional area \( \boldsymbol{A} \) is
subjected two equal and opposite tensile forces at its ends as shown in
figure. Consider a plane BB' making an
angle \( \theta \) with the length.
The ratio of tensile stress to the
shearing stress on the plane BB' is:
\( A \cdot \tan \theta \)
B. \( \sec \theta \)
\( c \cdot \cot \theta \)
\( D \cdot \cos \theta \)
Subject: Physics
An airplane pilot sets a compass course due west and maintains an air speed of \( 240 \mathrm{km} / \mathrm{h} . \) After flying for \( \frac{1}{2} h, \) he finds himself over a town that is \( 150 \mathrm{km} \) west
and \( 40 \mathrm{km} \) south of his starting point. The wind velocity (with respect to ground).
A \( \cdot 100 k m / h, 37^{\circ} \) Wof \( S \)
в. \( 100 k m / h, 37^{\circ} \) Sof \( W \)
c. \( 120 k m / h, 37^{\circ} \) Wof \( S \)
D. \( 120 k m / h, 37^{\circ} \) Sof \( W \)
Subject: Maths
The value of \( \frac{\left(1+\tan ^{2} \theta\right)}{\left(1+\cot ^{2} \theta\right)} \) is
\( \mathbf{A} \cdot \tan ^{2} \theta \)
B \( \cdot \cot ^{2} \theta \)
\( \mathbf{c} \cdot \sec ^{2} \theta \)
D. \( \operatorname{cosec}^{2} \theta \)
Subject: Maths
If \( \alpha \) and \( \beta \) are different complex
numbers with
\( |\beta|=1 \) then \( \left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right| \) is equal to
A .
B. \( \frac{1}{2} \)
\( c \cdot 1 \)
D.
Subject: Chemistry
Which of the following statements is not correct about the given reaction? \( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6} \frac{\text {Oxidation}}{\boldsymbol{\leftrightarrow}} \boldsymbol{F} \boldsymbol{e}^{3+}+\boldsymbol{C O}_{2}+\right. \)
\( \mathbf{N} \boldsymbol{O}_{\mathbf{3}}^{-} \)
A. Fe is oxidised from \( F e^{2+} \) to \( F e^{3 \text { - }} \)
B. Carbon is oxidised from \( C^{2+} \) to \( C^{4+} \).
c. \( \mathrm{N} \) is oxidised from \( N^{3} \) - to \( N^{5+} \)
D. Carbon is not oxidised
Subject: Chemistry
In which of the following compounds, \( \boldsymbol{S} \) atom has +6 oxidation state?
This question has multiple correct options
A. \( H_{2} S O_{5} \)
в. \( H_{2} S_{2} O_{8} \)
c. \( N a_{2} S_{4} O_{6} \)
D. \( H_{2} S O_{4} \)
Subject: Physics
Three masses are placed on the x-axis:
\( 300 g \) at origin, \( 500 g \) at \( x=40 c m \) and
\( 400 g \) at \( x=70 c m . \) The distance of the
centre of mass from the origin is-
\( \mathbf{A} \cdot 45 \mathrm{cm} \)
в. \( 50 \mathrm{cm} \)
\( \mathbf{c} .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)
Subject: Physics
In figure, the wires \( P_{1} Q_{1} \) and \( P_{2} Q_{2} \) are
made to slide on the rails with same
speed of \( 5 c m s^{-1} . \) In this region, a
magnetic field of \( 1 T \) exists. The electric
current in the \( 9 \Omega \) resistance is
This question has multiple correct options
A. zero if both wires slide toward left
B. zero if both wires slide in opposite directions
C. \( 0.2 m A \) if both wires move toward left
D. \( 0.2 m A \) if both wires move in opposite directions
Subject: Chemistry
By using the above informations define the electronic configuration of \( S \) atom.
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4} \)
B . \( 1 s^{2} 1 p^{6} d^{6} 2 s^{2} \)
c. \( 1 s^{2} 1 p^{6} 1 d^{10} \)
D. \( 1 s^{2} 1 p^{6} 2 p^{6} 2 d^{2} \)
Subject: Chemistry
Oxidation state of +1 for phosphorous is
found in :
A \( . \mathrm{H}_{3} \mathrm{PO}_{3} \)
в. \( \mathrm{H}_{3} \mathrm{PO}_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{PO}_{2} \)
D. \( \mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7} \)
Subject: Physics
A kettle with \( 2 L \) water at \( 27^{\circ} C \) is
heated by operating coil heater power
\( 1 k W \$ . \) The heat is lost to the
atmosphere at constant rate \( 160 \mathrm{J} / \mathrm{s} \) when its lid is open. In how much time
will water heated to \( 77^{\circ} C \) with the lid
open \( ? \) (specific heat of water \( = \)
\( \left.4.2 k J /^{\circ} C-k g\right) \)
A. 8 min 20 s
B. 6 min 2 sec
\( c .14 \) min
D. 7 min
Subject: Chemistry
Assertion
\( N \) -atom in \( N H_{3} \) is \( s p^{3} \) hybridised and
bond angle is \( 107^{\circ} \)
Reason
\( l p-b p \) repulsion (VSEPR) decreases
bond angle to \( 107^{\circ} \)
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
If \( S \) is the set containing values of \( x \)
satisfying \( [\boldsymbol{x}]^{2}-\mathbf{5}[\boldsymbol{x}]+\boldsymbol{6} \leq \mathbf{0}, \) where \( [\boldsymbol{x} \)
denotes greatest integer function then \( S \) contains :
в. (2,4]
c. [2,3]
D. [2,4]
Subject: Chemistry
The relationship between osmotic pressure at \( 273 \mathrm{K} \) when 10 g glucose
\( \left(P_{1}\right), 10 \) g urea \( \left(P_{2}\right) \) and 10 g sucrose
\( \left(P_{3}\right) \) are dissolved in \( 250 \mathrm{mL} \) of water is
A \( . P_{1}>P_{2}>P_{3} \)
в. \( P_{3}>P_{1}>P_{2} \)
c. \( P_{2}>P_{1}>P_{3} \)
D. \( P_{2}>P_{3}>P_{1} \)
Subject: Chemistry
Assertion
The foreign substances such as soaps, polymers, metal oxides can be used to stabilize an emulsion.
Reason
Sometimes, demulsifiers are used to
destabilize the emulsions when their
presence is undesired.
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
Aqua-regia dissolves gold.
which is correct?
A. Aqua regia, or nitro-hydrochloric acid is a highly corrosive mixture of acids, a fuming yellow or red solution.
B. The mixtures is formed by freshly mixing concentrated nitric acid and hydrochloric acid hoptimally in a volume ratio of 1: 3
C. it can dissolve the noble metalsgold and platinum
D. all of these
Subject: Maths
If \( f(x)=x^{3}+3 x^{2}+12 x-2 \sin x \)
such that \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) then
A. \( f(x) \) is one-one and onto
B. \( f(x) \) is many one onto
c. \( f(x) \) is one-one and into
D. \( f(x) \) is many one into
Subject: Maths
If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are mutually perpendicular vectors of equal magnitudes, If the angles which the vector \( 2 \vec{a}+\vec{b}+2 \vec{c} \) makes with the vectors \( \vec{a} \) is \( \cos ^{-1} \sqrt{\frac{2}{m}} \) Find \( \boldsymbol{m} \)
Subject: Maths
Suppose that \( f \) is differentiable for all
\( \boldsymbol{x} \in \boldsymbol{R} \) and that \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \leq 2 \) for all \( \boldsymbol{x} . \) If
\( f(1)=2 \) and \( f(4)=8, \) then \( f(2) \) has
the value equal to
A . 3
B. 4
\( c \cdot 6 \)
D. 8
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\log \left(1+\boldsymbol{x}^{2}\right) \) and \( \boldsymbol{A} \) be a
constant such that \( \frac{|\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{f}(\boldsymbol{y})|}{|\boldsymbol{x}-\boldsymbol{y}|} \leq \boldsymbol{A} \)
for all \( x, y \) real and \( x \neq y . \) Then the least
possible value of \( \boldsymbol{A} \) is
A. Equal to 1
B. Bigger than 1 but less than 2
c. Bigger than 0 but less than 1
D. Bigger than 2
Subject: Physics
Show that the effective capacitance, \( C \) of a series combination, of three
capacitors, \( C_{1}, C_{2} \) and \( C_{3} \) is given by
\( \boldsymbol{C}=\frac{C_{1} C_{2} C_{3}}{\left(C_{1} C_{2}+C_{2} C_{3}+C_{3} C_{1}\right)} \)
Subject: Maths
If the probability of \( x \) to fail in the
examination is 0.3 and that for \( Y \) is 0.2
then the probability that either \( \boldsymbol{X} \) or \( \boldsymbol{Y} \) fail in the examination is
A . 0.5
B. 0.44
\( c .0 .6 \)
D. None of these
Subject: Maths
A discrete random variable \( X, \) can take
all possible integer values from 1 to \( K \)
each with a probability \( 1 / K . \) Its mean is
\( \mathbf{A} \cdot K \)
в. \( K+1 \)
c. \( K / 2 \)
D. \( K / 4 \)
Subject: Maths
\( \mathrm{n} \Delta A B C, \mathrm{AD} \) bisects \( \angle B A C \) and \( \mathrm{AD}= \)
DC. If \( \angle A D B=100^{\circ} \), then find \( \angle A B D \).
\( A \cdot 30 \)
в. 45
\( c \cdot 60 \)
D. 90
Subject: Chemistry
Marshall's acid \( \frac{H_{2} O}{\longrightarrow} A+B \)
\( \boldsymbol{A} \stackrel{\boldsymbol{H}_{2}}{\rightarrow} \boldsymbol{O} \boldsymbol{B}+\boldsymbol{C} \)
If \( P \) and \( Q \) represent a maximum number of atoms that can lie in a plane of compound \( A \) and \( C \) respectively. Then, find the value of \( (\boldsymbol{P}-\boldsymbol{Q}) \)
Subject: Chemistry
Two liquids \( A \) and \( B \) form an ideal solution. The vapour pressure of pure \( \mathbf{A} \) and pure B are 66mm of Hg and 88mm of Hg, respectively. Calculate the composition of vapour \( A \) in the solution which is equilibrium and whose molar volume is \( 36 \% \)
A. 0.43
B. 0.70
c. 0.30
D. 0.50
Subject: Maths
If \( \boldsymbol{I}=\int \frac{\boldsymbol{d} \boldsymbol{x}}{\left(\boldsymbol{x}^{2}+\boldsymbol{a}^{2}\right)\left(\boldsymbol{x}^{2}+\boldsymbol{b}^{2}\right)\left(\boldsymbol{x}^{2}+\boldsymbol{c}^{2}\right)} \)
then \( I \) equals
A \( \cdot \frac{1}{b c} \tan ^{-1}(a)+\frac{1}{c a} \tan ^{-1}(b)+\frac{1}{c b} \tan ^{-1}(c)+k \)
B. \( \frac{1}{b^{2}-c^{2}} \tan ^{-1}(a)+\frac{1}{c^{2}-a^{2}} \tan ^{-1}(b)+ \)
\( \frac{1}{a^{2}-b^{2}} \tan ^{-1}(c)+k \)
\( \frac{\tan ^{-1} a+\tan ^{-1} b+\tan ^{-1} c}{a^{2}+b^{2}+c^{2}}+k \)
D. none of these
Subject: Physics
Consider the plane \( S \) formed by the dipole axis and the axis of earth. If \( P \) be the point of intersection of the geographical and magnetic equators then the declination and dip angle at point \( P \) are
A. \( 0^{\circ}, 11.3^{\circ} \)
В. \( 11.3^{\circ}, 0^{\circ} \)
c. \( 11.3^{\circ}, 11.3^{\circ} \)
D. \( 0^{\circ}, 0^{\circ} \)
Subject: Physics
A stone of mass \( m \) tied to one end of a
wire of length \( L \). The diameter of the
wire is \( D \) and it is suspended vertically. The stone is now rotated in a horizontal
plane and makes an angle \( \theta \) with the
vertical. If Young's modulus of the wire
is \( Y, \) then the increase in the length of
the wire is then
\( ^{\mathbf{A}} \cdot \frac{4 m g L}{\pi D^{2} Y} \)
B. \( \frac{4 m g L}{\pi D^{2} Y \sin \theta} \)
c. \( \frac{4 m g L}{\pi D^{2} Y \cos \theta} \)
D. \( \frac{4 m g L}{\pi D^{2} Y \tan \theta} \)
Subject: Chemistry
Aqueous solution of acetic acid
contains:
\( \mathbf{A} \cdot C H_{3} C O O^{-} \) and \( H^{+} \)
B. \( C H_{3} C O O^{-}, H_{3} O^{+} \) and \( C H_{3} C O O H \)
\( \mathbf{c} \cdot C H_{3} C O O^{-}, H_{2} O^{+} \) and \( H^{+} \)
D. \( C H_{3} C O O H, C H_{3} C O O^{-} \) and \( H^{+} \)
Subject: Maths
Draw a \( \triangle A B C, \) right - angled at \( B \) such that \( A B=3 c m, B C=4 \) cm. Now
construct a \( \triangle P B Q \) similar to \( \Delta A B C \) each of whose side is \( \frac{7}{5} \) times the
corresponding side of \( \Delta A B C \)
Subject: Physics
A police party is moving in a jeep at a
constant speed \( v \). They saw a thief at a
distance \( x \) on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant
acceleration \( a \). Which of the following relations is true if the police is able to catch the thief?
A \( \cdot v^{2}<a x \)
В. \( v^{2}<2 a x \)
c. \( v^{2}>2 \) ах
D. \( v^{2}=a x \)
Subject: Maths
A balloon which always remains spherical, is being inflated by pumping in 900 cubic centimetres of gas per second. The rate at which the radius of
the balloon is increasing when the radius is \( 15 \mathrm{cm} \) is.
A \( \cdot \frac{1}{\pi} c m / s e c \)
B \( \cdot \frac{2}{\pi} c m / \) sec
c. \( \pi c m / s e c \)
D. \( \frac{\pi}{2} \mathrm{cm} / \mathrm{sec} \)
Subject: Chemistry
The mechanism of the reaction
\( \mathbf{2} N \boldsymbol{O}+\boldsymbol{O}_{2} \rightarrow \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2} \) is:
\( N O+N O \underset{k_{-1}}{\Gamma} N_{2} O_{2}(\text { fast }) ; N_{2} O_{2}+ \)
\( O_{2} \stackrel{k_{2}}{\longrightarrow} 2 N O_{2}(s l o w) \)
The rate constant of the reaction is :
\( A \cdot(A) k_{2} \)
B . (В) \( k_{2} k_{1}\left(k_{-1}\right) \)
c. (с) \( k_{2} k \)
D.
(D) \( k_{2}\left(\frac{k_{1}}{k_{-1}}\right) \)
Subject: Physics
The equation \( y=4 \sin \pi\left[200 t-\left(\frac{x}{25}\right)\right] \)
represents a transverse wave that
travels in a stretched wire, where \( \boldsymbol{x}, \boldsymbol{y} \)
are in \( c m \) and \( t \) in second.
Its wavelength and velocity are
A \( \cdot 0.5 m, 25 m s^{-1} \)
B . \( 0.5 m, 50 m s^{-1} \)
c. \( 1 m, 50 m s^{-1} \)
D. \( 1 m, 25 m s^{-1} \)
Subject: Maths
Identify the formula for the \( n^{t h} \) term of
the sequence \( 54,18,6 \dots \)
\( ^{\mathrm{A}} \cdot_{54}\left(\frac{1}{3}\right)^{n-1} \)
\( ^{\text {В }} \). \( _{6}\left(\frac{1}{3}\right)^{n-1} \)
c. \( _{3}\left(\frac{1}{3}\right)^{n} \)
D. \( _{54}\left(\frac{1}{3}\right)^{n} \)
Subject: Chemistry
Assertion: Copper sulphate solution can be stored in a zinc vessel.
Reason: \( \boldsymbol{E}_{\boldsymbol{C u}^{2+} \mid \boldsymbol{C u}}^{\ominus}= \)
\( \mathbf{0 . 3 4} \boldsymbol{V}, \boldsymbol{E}_{Z n^{2+} \mid \mathbf{Z} n}^{\ominus}=-\mathbf{0 . 7 6} \boldsymbol{V} \)
\( \boldsymbol{E}_{A \boldsymbol{g}^{\oplus} \mid A \boldsymbol{g}}^{\ominus}=\mathbf{0 . 8 0} \boldsymbol{V} \)
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Chemistry
Choose the correct statements -
This question has multiple correct options
A. A change in one unit in the pH corresponds to a tenfold change in concentration
B. Solution of \( \mathrm{pH} 1 \) or more are considered strongly acidic
C. Solutions with pH less than 7 but greater than 1 are weakly acidic.
D. A solution of \( \mathrm{pH} 6 \) is 100,000 times less acidic than a solution of \( \mathrm{pH} 1 \)
Subject: Chemistry
Calculate the solubility of AgCl in \( 0.2 \mathrm{M} \)
\( -N H_{3} \) solution
Given : Ksp of \( \mathrm{AgCl}=2 \times 10, \mathrm{Kf} \) of \( A g\left(N H_{3}\right) 2^{+}=8 \times 10^{6} \)
Subject: Physics
A heater coil connected to a \( 220 \mathrm{V} \) has a
resistance of 150 oh \( m \). How long will it
take for this coil to heat \( 1 k g \) of water
from \( 20^{0} C \) to \( 60^{0} C \), assuming that all
heat is taken up by water.
A . 210 sec
B. 420 sec
\( c .520 \mathrm{sec} \)
D. None of these
Subject: Physics
The capacitive reactance of \( 50 \mu \mathrm{F} \)
capacitance at a frequency of \( 2 \times 10^{3} \)
\( \mathrm{Hz} \) will be \( _{----} \Omega \)
\( A \cdot \frac{2}{\pi} \)
B. \( \frac{3}{\pi} \)
\( c \cdot \frac{4}{\pi} \)
\( D \cdot \frac{5}{5} \)
Subject: Physics
In Rutherford's alpha scattering
experiment:

This question has multiple correct options
A. distance of closest approach is of the order of \( 10^{-14} \mathrm{m} \)
B. at the distance of closest approach, the kinetic energy of the \( \alpha- \) particle is transformed into electrostatic
potential
C. the \( \alpha- \) particles moving towards the nucleus will stop
moving and then start retracing its path
D. maximum number of \( \alpha- \) particles went straight
through the metal foil
Subject: Physics
The relation between voltage sensitivity
\( \left(\sigma_{v}\right) \) and current sensitivity \( \left(\sigma_{i}\right) \) of \( a \) moving coil galvanometer is (resistance of galvanometer is \( G \) ).
A \( \cdot \frac{\sigma_{i}}{G}=\sigma_{v} \)
в. \( \frac{\sigma_{v}}{G}=\sigma \)
c. \( \frac{G}{\sigma_{v}}=\sigma \)
D. None of the above
Subject: Maths
If \( f \) is differentiable at \( x=1 \) and
\( \lim _{h \rightarrow 0} \frac{1}{h} f(1+h)=5, f^{\prime}(1)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 3 \)
D. 4
\( E \)
Subject: Biology
DNA is a polymer of nucleotides which
are linked to each other by \( 3-5 \) phosphodiester bond. To prevent polymerisation of nucleotides, which of the following modifications would you choose?
A. Replace purines with pyrimidines.
B. Remove/Replace 3 OH group in deoxyribose.
c. Remove/Replace 2 OH group with some other group in deoxyribose.
D. Both (b) and (c)
Subject: Maths
The angle between the lines \( y-x+ \)
\( \mathbf{5}=\mathbf{0} \) and \( \sqrt{\mathbf{3}} \boldsymbol{x}-\boldsymbol{y}+\mathbf{7}=\mathbf{0} \) is/are
This question has multiple correct options
A \( \cdot 15^{\circ} \)
B. \( 60^{\circ} \)
\( \mathbf{c} \cdot 165^{\circ} \)
D. \( 75^{\circ} \)
Subject: Physics
Imagine a light planet revolving around a very massive star in a circular orbit of
radius r with a period of revolution T. If the gravitational force of attraction between the planet and the star is
proportional to \( r^{5 / 2}, \) then the square of the time period will be proportional to.
A \( \cdot r^{3} \)
в. \( r^{2} \)
\( c \cdot r^{2.5} \)
D. \( r^{3.5} \)
Subject: Chemistry
Predict the correct product when \( C l_{2} \) passed through \( \boldsymbol{H}--\boldsymbol{0}^{\mathbf{8}}--\boldsymbol{0}^{18}--\boldsymbol{H} \)
solution.
A \( \left.\cdot H^{+} C l^{-}+O_{2} \text { (both oxygen having } 18\right) \)
B. HOCl and \( H C l O_{2} \) (all oxygen having 18 )
c. \( H C l O_{4} \) and \( H C \) ( all oxygen having 18 )
D. \( C l_{2} O \) and \( H_{2} O \) (all oxygen having 18
Subject: Physics
A rectangular coil of wire of 500 turns of
area \( 10 \times 5 c m^{2} \) carries a current of \( 2 A \)
in a magnetic field of induction \( 2 \times \)
\( 10^{-3} T . \) If the plane of the coil is parallel
to the field. The torque on the coil is (in
\( N m) \)
A . 0.1
B. 0.01
c. 0.001
D.
Subject: Chemistry
For a particular reversible reaction at
temperature \( \mathbf{T}, \boldsymbol{\Delta} \mathbf{H} \) and \( \Delta \mathbf{S} \) were found
to be both +ve. If \( \mathbf{T}_{\mathbf{e}} \) is the temperature at equilibrium, the reaction would be
spontaneous when:
A \( \cdot \mathrm{T}_{\mathrm{e}}>\mathrm{T} \)
в. \( \mathrm{T}>\mathrm{T}_{\mathrm{e}} \)
\( \mathrm{c} \cdot \mathrm{T}_{\mathrm{e}} \) is 5 times \( \mathrm{T} \)
D. \( \mathrm{T}=\mathrm{T}_{\mathrm{e}} \)
Subject: Chemistry
\( \boldsymbol{C a}, \boldsymbol{N a}, \boldsymbol{M} \boldsymbol{g}, \boldsymbol{Z} \boldsymbol{n}, \boldsymbol{F e}, \boldsymbol{H}, \boldsymbol{C u}, \boldsymbol{H} \boldsymbol{g}, \boldsymbol{A} \boldsymbol{g}, \boldsymbol{A} \)
Given elements are in order of
decreasing reactivity according to electrochemical series. Half-reaction
possible for the shown electrochemical
cell at the anode is:
A \( \cdot C u^{2+}+e^{-} \rightarrow C u+ \)
B \( \cdot Z n(s) \rightarrow Z n^{2+}+2 e^{-} \)
c. \( Z n^{2+}+2 e^{-} \rightarrow Z n(s) \)
D. \( C u(s) \rightarrow C u^{2+}+2 e^{-} \)
E \( \cdot C u^{2+}+2 e^{-} \rightarrow C u(s) \)
Subject: Physics
The coefficient of friction between the
tryes and the road is 0.25 . the maximum speed with which a car can
be driven round a curve of radius \( 40 \mathrm{m} \)
without skidding is (assume \( g=10 m s^{-2} \)
A. \( 40 \mathrm{ms}^{-1} \)
B . \( 20 m s^{-1} \)
\( \mathbf{c} \cdot 15 m s^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)
Subject: Maths
Solve the following system of linear equations using matrix method: \( 3 x+ \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{1}, \mathbf{2} \boldsymbol{x}+\mathbf{2} \boldsymbol{z}=\mathbf{0}, \mathbf{5} \boldsymbol{x}+\mathbf{5} \boldsymbol{y}+ \)
\( \mathbf{2} z=\mathbf{2} \)
Subject: Physics
Car \( X \) of mass 200 kg moving at \( 5 \mathrm{m} / \mathrm{s} \) collides with car Y of mass \( 300 \mathrm{kg} \) moving in the same direction at \( 3 \mathrm{m} / \mathrm{s} \) After the collision they move off together. What is their common velocity just after the collision?
A. \( 4.2 \mathrm{m} / \mathrm{s} \)
B. \( 5.6 \mathrm{m} / \mathrm{s} \)
\( c \cdot 3.8 m / s \)
D. \( 7.8 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
At what temperature will he atom have
the same \( r m s \) speed as \( H_{2} \) molecules have at \( 27^{0} C \) ?
A \( \cdot 127^{0} C \)
в. \( 227^{\circ} \mathrm{C} \)
c. \( 327^{\circ} \mathrm{C} \)
D. \( 27^{0} C \)
Subject: Chemistry
The equivalent conductance of NaCl at concentration \( C \) and at infinite dilution
\( \operatorname{are} \lambda_{C} \) and \( \lambda_{\infty} \) respectively. The correct
relationship between \( \lambda_{C} \) and \( \lambda_{\infty} \) is
given as: (Where the constant B is positive)
A \( \cdot \lambda_{C}=\lambda_{\infty}-(B) \sqrt{C} \)
в. \( \lambda_{C}=\lambda_{\infty}+(B) \sqrt{C} \)
c. \( \lambda_{C}=\lambda_{\infty}+(B) C \)
D. \( \lambda_{C}=\lambda_{\infty}-(B) C \)
Subject: Physics
According to Rutherford's \( \alpha \) -scattering
experiment, which of the following
statement is true?
A. The electrons in the gold foil absorbed the alpha particles and changed energy levels.
B. Most of the alpha particles passed through the foil undeflected.
C. A few of the alpha particles knocked the nucleus completely out of the atom.
D. A large percentage of alpha pantries were turned back when striking the foil
E. The gold foil began to emit a bright-line spectrum.
Subject: Physics
A body of mass \( 6 \mathrm{kg} \) is under a force whic causes displacement in it which is given by \( s=\frac{t^{2}}{4} \mathrm{m}, \) where \( t \) is time. The work done
by the force in 2 s is
A . \( 12 J \)
в. \( 9 J \)
c. 6.5
D. 3
Subject: Physics
For a plane convex lens \( (\mu=1.5) \) having radius of curvature \( 10 \mathrm{cm} . \) It is silvered on its plane surface. Find focal length after silvering:
\( A \cdot 10 \mathrm{cm} \)
B. 20 cm
c. \( 15 \mathrm{cm} \)
D. 25 cm
Subject: Chemistry
The values of \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{C a C O}_{3} \) and \( \mathrm{CaC}_{2} \mathrm{O}_{4} \) are \( 4.7 \times 10^{-9} \) and \( 1.3 \times 10^{-9} \)
respectively at \( 25^{\circ} \mathrm{C} \). If the mixture of these two is washed with water, what is the concentration of \( C a^{2+} \) ions in
water?
A \( \cdot 5.831 \times 10^{-5} M \)
В. \( 6.856 \times 10^{-5} M \)
c. \( 3.606 \times 10^{-5} M \)
D. \( 7.77 \times 10^{-5} M \)
Subject: Physics
\( 5 g m \) of steam at \( 100^{\circ} C \) is passed into calorimeter containing liquid, Temperature of liquid rises from \( 32^{\circ} C \)
to \( 40^{\circ} \mathrm{C} . \) Then water equivalent of calorimeter and content is
A. 40 gram
B. 375 gram
c. 300 gram
D. 160 gram
Subject: Physics
Three vectors \( \overrightarrow{\boldsymbol{A}}=\boldsymbol{a} \overrightarrow{\boldsymbol{i}}+\overrightarrow{\boldsymbol{j}}+\overrightarrow{\boldsymbol{k}}, \overrightarrow{\boldsymbol{B}}=\overrightarrow{\boldsymbol{i}}+ \)
\( \boldsymbol{b} \overrightarrow{\boldsymbol{j}}+\overrightarrow{\boldsymbol{k}}, \overrightarrow{\boldsymbol{C}}=\overrightarrow{\boldsymbol{i}}+\overrightarrow{\boldsymbol{j}}+\boldsymbol{c} \overrightarrow{\boldsymbol{k}} \) are mutually
perpendicular \( (\vec{i}, \vec{j}, \vec{k} \) are unit vectors along \( X, Y, Z \) axis respectively. The respective values of \( a, b \) and \( c \) are
\( \mathbf{A} \cdot 0,0,0 \)
B. \( -\frac{1}{2},-\frac{1}{2},-\frac{1}{2} \)
c. 1,-1,1
D. \( \frac{1}{2}, \frac{1}{2}, \frac{1}{2} \)
Subject: Maths
Find the distance between the lines
\( \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{9} \) and \( \boldsymbol{6} \boldsymbol{x}+\mathbf{8} \boldsymbol{y}=\mathbf{1 5} \)
Subject: Maths
\( \int \tan ^{-1} \sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}} d x, \) where \( 0< \)
\( x<\frac{\pi}{2} \) is equal to
A. \( 2 x^{2}+C \)
B. \( x^{2}+C \)
c. \( \frac{x^{2}}{2}+C \)
D. \( \frac{x^{3}}{3}+C \)
Subject: Chemistry
Which of the following pairs of compounds have central atom with identical hybridization?
A. \( S O_{2} \) and \( S O C l_{2} \)
в. \( X e O_{3} \) and \( X e O_{2} F_{2} \)
c. \( X e F_{4} \) and \( X e O F_{4} \)
D. \( S F_{4} \) and \( X e F_{4} \)
Subject: Maths
If \( f(x)=(x-1)(x-2) \) and interval
given was \( (0,4), \) find 'c' using Langrange's mean value theorem.
A \( \cdot 2+\frac{2}{\sqrt{3}} \)
B. \( 2-\frac{2}{\sqrt{3}} \)
c. 2
D. Both A and B