AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The free energy changes for the two reactions given below are:
\( \mathbf{a} . \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{G}=-\boldsymbol{2} 270 \boldsymbol{c} \boldsymbol{a} \boldsymbol{l} \)
b. \( S(R h o m b)+O_{2}(g)+C l_{2}(g) \longrightarrow \)
\( \boldsymbol{S O}_{2} \boldsymbol{C l}_{2}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{G}=-\mathbf{7 4 0 6 0 c a l} \)
Find \( \Delta G \) for the reaction \( S(r h o m)+ \)
\( O_{2}(g) \longrightarrow S O_{2}(g) \)
A \( . \Delta G=-71790 c a l \)
в. \( \Delta G=+71790 \) са \( l \)
c. \( \Delta G=-9670 c a l \)
D. None of these
Subject: Physics
If \( \overrightarrow{\mathrm{A}}, \overrightarrow{\mathrm{B}} \) and \( \overrightarrow{\mathrm{C}} \) are non-zero vectors, and if \( \overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}=\mathbf{0} \) and \( \overrightarrow{\mathbf{B}} \times \overrightarrow{\mathbf{C}}=\mathbf{0}, \) then the
value of \( \overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{C}} \) is:
A .
B.
c. \( \mathrm{B}^{2} \)
D. \( A C \cos \theta \)
Subject: Maths
The shape of the top of a table in a
restaurant is that of a segment of a
circle with centre \( O \) and \( \angle B O D=90^{\circ} \)
f \( B O=O D=60 \mathrm{cm} . \) The perimeter of
the table is (Take \( \pi=\mathbf{3 . 1 4} \) )
A . \( 402 \mathrm{cm} \)
в. \( 402.6 \mathrm{cm} \)
c. \( 401 \mathrm{cm} \)
D. \( 400 \mathrm{cm} \)
Subject: Maths
Tangent to parabola \( \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{x}+\mathbf{5} \) which
is parallel to \( \boldsymbol{y}=2 \boldsymbol{x}+\mathbf{7} \)
A. \( y-2 x-3=0 \)
В. \( y=x+3 \)
c. \( y-2 x+1=0 \)
D. \( y=x+1 \)
Subject: Chemistry
Which one of the following statements
İs incorrect?
A. In the aluminothermite process, aluminium acts as reducing agent
B. Lead is extracted from its chief ore by both carbon reduction and self-reduction.
C. Zinc is extracted from its chief ore by carbon reduction.
D. Extraction of gold involves the leaching of ore with cyanide solution followed by reduction with zinc.
E. In Hall-Heroult process, the electrolyte used is a molten mixture of alumina, sodium hydroxide and cryolite.
Subject: Maths
\( \operatorname{Let} \phi(\boldsymbol{x})=\frac{\boldsymbol{b}(\boldsymbol{x}-\boldsymbol{a})}{\boldsymbol{b}-\boldsymbol{a}}+\frac{\boldsymbol{a}(\boldsymbol{x}-\boldsymbol{b})}{\boldsymbol{a}-\boldsymbol{b}}, \) where
\( x \in R \) and \( a \) and \( b \) are fixed real numbers
with \( a \neq b . \) Then \( \phi(a+b) \) is equal to:
A. \( \phi(a b) \)
(i)
в. \( \phi(-a b) \)
\( \mathbf{c} \cdot \phi(a) \mid \phi(b) \)
D. \( \phi(a-b) \)
E \( . \phi(0) \)
Subject: Chemistry
A \( 5 \% \) solution of cane sugar is isotonic with \( 0.877 \% \) of \( X . \) The molecular weight of substance X is:
\( \mathbf{A} \cdot 58.98 \)
B. 119.96
\( \mathbf{c} .95 .58 \)
D . 126.98
Subject: Chemistry
The pair of amphoteric hydroxides is:
A. \( A l(O H)_{3}, L i O H \)
B. \( B e(O H)_{2}, M g(O H)_{2} \)
c. \( B(O H)_{3}, B e(O H)_{2} \)
D. \( B e(O H)_{2}, Z n(O H) \)
Subject: Chemistry
The fuel used to produce electrical energy in the space rocket Saturn \( \mathrm{V} \) used by Neil Armstrong to reach the
moon was:
A. \( C O+O_{2} \)
в. \( F_{2}+O_{2} \)
c. \( C H_{4}+O_{2} \)
D. liquid \( H_{2}+O_{2} \)
Subject: Physics
An aeroplane is moving in a circular path with a speed \( 250 \mathrm{km} / \mathrm{hr} \) in a horizontal plane. The change in magnitude of velocity in half the revolution is:
A. \( 500 \mathrm{km} / \mathrm{hr} \)
B. \( 250 \mathrm{km} / \mathrm{hr} \)
c. \( 125 \mathrm{km} / \mathrm{hr} \)
D.
Subject: Maths
If the order of \( \mathbf{A} \) is \( \mathbf{4} \times \mathbf{3}, \) the order of \( \mathbf{B} \)
is \( 4 \times 5 \) and the order of \( C \) is \( 7 \times 3 \), then
the order of \( \left(\mathbf{A}^{T} \mathbf{B}\right)^{T} \mathbf{C}^{T} \) is
A. \( 4 \times 5 \)
в. \( 3 \times 7 \)
c. \( 4 x 3 \)
D. \( 5 \times 7 \)
Subject: Maths
Prove that the general equation \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{h} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{g} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{f} \boldsymbol{y}+\boldsymbol{c}= \)
0
represents two parallel straight lines if \( h^{2}=a b \) and \( b g^{2}=a f^{2} \)
Prove also that the distance between
them is
\( \frac{2 \sqrt{g^{2}-a c}}{a(a+b)} \)
Subject: Physics
A ball falls vertically onto a floor with
momentum \( p \) and then bounces repeatedly, the coefficient of restitution is \( e . \) The total momentum imparted by
the ball to the floor is
A \( \cdot \rho(1+e) \)
B. \( \frac{1}{1-e} \)
\( ^{c} \rho\left(\frac{1+e}{1-e}\right) \)
\( ^{\mathrm{D}} \rho\left(1-\frac{1}{e}\right) \)
Subject: Physics
A solid conducting sphere having a charge \( Q \) is surrounded by an uncharged concentric conducting hollow spherical
shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be
\( V . \) If the shell is now given a charge of \( 3 Q \)
the new potential difference between the same two surfaces is :
A. \( V \)
B. 2 \( V \)
\( c \cdot 4 v \)
D. \( -2 V \)
Subject: Physics
A uniform rod of mass \( m \) and length \( l \) is resting on a smooth horizontal surface.
A particle of mass \( m / 2 \) travelling with a
speed \( v_{0} \) hits the rod normally and
elastically. Then,
This question has multiple correct options
A \( \cdot \) final velocity of the particle is \( -\frac{2}{15} v_{0} \)
B. final velocity of the particle is \( -\frac{1}{15} v_{0} \)
c. angular velocity of the rod \( \frac{8 v_{0}}{5 e} \)
D. angular velocity of the rod \( \frac{6 v_{0}}{5 \ell} \)
Subject: Chemistry
In a study of equilibrium
\( \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)
Starting with 2 mole \( S O_{2} \) and 1.5 mole
\( O_{2} \) in 5 litre flask.Equilibrium mixture
required 0.4 mole \( K M n O_{4} \) in acidic
medium.Hence \( \boldsymbol{K}_{\boldsymbol{C}} \) is:
A. 0.2
B. 5.0
c. 675.0
D. None of these
Subject: Physics
Two blocks of same mass \( (4 \mathrm{kg}) \) are placed according to diagram. Initial velocities of bodies are \( 4 \mathrm{m} / \mathrm{s} \) and \( 2 \mathrm{m} / \mathrm{s} \)
and the string is taut. Find the impulse
on 4 kg when the string again becomes
taut.
A \( .24 \mathrm{N}-\mathrm{s} \)
B. \( 6 N- \) s
\( c \cdot 4 N-s \)
D. 2 N-s
Subject: Maths
An urn contains one black ball and one
green ball. A second urn contains one
white and one green ball. One ball is
drawn at random from each urn.Find the
probability of getting at least one green ball.
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D.
Subject: Chemistry
In the synthesis of n-alkyl tert-alkyl ether by Williamson's method the reactants used are:
B. \( 1^{\circ} R X \) and \( 3^{\circ} \)RONa
\( \mathrm{c} \cdot 3^{\circ} R X \) and \( 3^{\circ} R O N a \)
D. \( 1^{\circ} R X \) and \( 1^{\circ} R O N a \)
Subject: Physics
For a positively charged particle moving
in a \( x \) -y plane initially along the \( x \) -axis, there is a sudden change in its path due to the presence of electric and/or magnetic fields beyond P. The curved path is shown in the \( x \) -y plane and is found to be non-circular.Which one of
the following combinations is possible?
A \( \cdot \vec{E}=0, \vec{B}=b \hat{i}+c \hat{k} \)
в. \( \vec{E}=a \hat{i}, \vec{B}=c \hat{k}+a \hat{i} \)
c. \( \vec{E}=0, \vec{B}=c \hat{j}+b \hat{k} \)
D. \( \vec{E}=a \hat{i}, \vec{B}=c \hat{k}+b \hat{j} \)
Subject: Physics
An electric bulb is designed to draw
power \( P_{0} \) at voltage \( V_{0} . \) If the voltage is
\( v, \) it draws a power \( P, \) then
\( ^{A} \cdot P=\left(\frac{V}{V_{0}}\right) P_{0} \)
в. \( P=\left(\frac{V_{0}}{V}\right) P_{0} \)
\( ^{\mathrm{c}} P=\left(\frac{V_{0}}{V}\right)^{2} P_{0} \)
\( P=\left(\frac{V}{V_{0}}\right)^{2} P_{0} \)
Subject: Physics
An electrical device operate at 12 A current and \( 120 \mathrm{V} \) D.C. If it is connected
with \( 250 \mathrm{V} \) and \( 30 \mathrm{Hz} \) AC. then power consumption:
A. 625 w
B. 1250 W
\( c . \) 6250 \( w \)
D. zero
Subject: Chemistry
Which of the following represents a bronsted acid-base reaction?
\( \mathbf{A} \cdot 3 O_{2}(g) \rightleftharpoons 2 O_{3}(g) \)
B. \( O H^{-}+H_{3} O^{+} \rightleftharpoons 2 H_{2} O \)
\( \mathbf{c} \cdot B a C l_{2} \cdot 2 H_{2} O(s) \triangleq B a C l_{2}(s)+2 H_{2} O(g) \)
\( \mathbf{D} \cdot C a^{2+}+C O_{3}^{2-} \rightarrow C a C O_{3}(s) \)
\( \mathbf{E} \cdot F e+C u^{2+} \rightleftharpoons F e^{2+}+C u \)
Subject: Biology
Which of the following are correctly matched ?
1. Arsenic poisoning - Black-foot disease
2. Secondary effluent treatment Biological process
3. Pyrolysis - Waste disposal
4. Tubifex - Water pollution indicator
5. Biomagnification - Degradable
pollutants
A. 1,2,3 and 5
B. 1,3,4 and 5
c. 2,3,4 and 5
D. 1,2,4 and 5
E. 1,2,3 and 4
Subject: Physics
Two rods \( P \) and \( Q \) are considered such
that Young's modulus of elasticity of rod \( P \) is twice that of the other while the
density of rod \( Q \) is eighteen times that of rod P. If a sound wave is allowed to
transverse \( 2 \mathrm{m} \) distance through each rod, then by how many times the time taken through \( P \) is less than that of \( Q ? \)
A. 2 times
B. 3 times
c. 4 times
D. 5 times
Subject: Physics
Three planets of same density and with
radii \( \mathbf{R}_{1}, \mathbf{R}_{2} \) and \( \mathbf{R}_{3}, \) such that \( \mathbf{R}_{1}= \)
\( 2 \mathrm{R}_{2}=3 \mathrm{R}_{3}, \) have gravitation fields on
the surfaces \( \mathrm{E}_{1}, \mathrm{E}_{2}, \mathrm{E}_{3} \) and escape velocities \( \mathbf{v}_{\mathbf{1}}, \mathbf{v}_{\mathbf{2}}, \mathbf{v}_{\mathbf{3}} \) respectively, Then
This question has multiple correct options
A \( \cdot \frac{\mathrm{E}_{1}}{\mathrm{E}_{2}}=\frac{1}{2} \)
в. \( \frac{\mathrm{E}_{1}}{\mathrm{E}_{3}}=3 \)
c. \( \frac{v_{1}}{v_{2}}=2 \)
D. \( \frac{v_{1}}{v_{3}}=\frac{1}{3} \)
Subject: Physics
If a vector \( A \) is given as \( A=4 \hat{i}+3 \hat{j}+ \) \( 12 \hat{k}, \) then the angle subtended with the
x-axis is :
\( ^{\mathbf{A}} \cdot \sin ^{-1}\left[\frac{4}{13}\right] \)
B. \( \sin ^{-1}\left[\frac{3}{13}\right] \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left[\frac{3}{13}\right] \)
D. \( \cos ^{-1}\left[\frac{4}{13}\right] \)
Subject: Physics
A series LCR circuit with \( R=20 \Omega, L=1.5 \) \( \mathrm{H} \) and \( \mathrm{C}=35 \mu \mathrm{F} \) is connected to a
variable-frequency \( 200 \mathrm{V} \) ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one
complete cycle?
Subject: Maths
The function
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{r}
\boldsymbol{x}^{2}-\boldsymbol{a} \boldsymbol{x}+\mathbf{3}, \boldsymbol{x} \text { is ratio } \\
\boldsymbol{2}-\boldsymbol{x}, \quad \boldsymbol{x} \text { is irratio }
\end{array}\right.
\]
is continuous at exactly two points then
the possible values of ' \( a \) ' are
\( A \cdot(2, \infty) \)
В \( \cdot(-\infty, 3) \)
c. \( (-\infty,-1) \cup(3, \infty) \)
D. \( R \)
Subject: Chemistry
A slice of banana weighing 2.502 g was burnt in a bomb calorimeter producing
a temperature rise of \( 3.05^{\circ} \mathrm{C} \). The combustion of \( 0.316 \mathrm{g} \) of benzoic acid in the same calorimeter produced a
temperature rise of \( 3.24^{\circ} \mathrm{C} \). The heat of combustion of benzoic acid at constant
volume is \( -3227 k J \) mol\( ^{-1} . \) If the
average banana mass is 125 g, the kilojoules of energy can be obtained from 1 average banana is: (nearest integer value)
Subject: Physics
A car, starting from rest, accelerate at
the rate \( f \) through a distance \( s, \) then continuous at constant speed for the
some time \( t \) and the decelerates at the
rate \( \boldsymbol{f} / 2 \) to come to rest. If the total
distance is \( 5 s, \) then prove that \( s=\frac{1}{2} f t^{2} \)
A . 24
B . 25
c. 30
D. 20
Subject: Chemistry
The species having tetrahedral shape is
\( - \)
A \( \cdot\left[P d C l_{4}\right]^{2-} \)
B . \( \left[N i(C N)_{4}\right]^{2} \)
c. \( \left[P d(C N)_{4}\right]^{2} \)
\( \mathbf{D} \cdot\left[N i C l_{4}\right]^{2-} \)
Subject: Physics
The two ends of a train moving with uniform acceleration pass a certain point with velocities 6 kmph and 8 kmph respectively. What is the velocity with which the middle point of the train
passes the same point?
\( A .7 \mathrm{kmph} \)
B. \( 2 \sqrt{5} \) kmph
c. \( 2 \sqrt{10} \mathrm{kmph} \)
D. 7.5 kmph
Subject: Physics
A particle moving with certain velocity collides elastically with another particle at rest. If it were head on collision, the
K.E. transferred by the colliding particle is \( 100 \% \) when its mass is equal to the
A. the mass of the stationary particle
B. twice the mass of the stationary particle
c. half the mass of the stationary particle
D. \( 1 / 4 \) times the mass of the stationary particle
Subject: Chemistry
Photochromic glass, used for sunglasses, darkens when exposed to bright light and becomes more transparent again when the light is less bright. The darkness of the glass is related to the
concentration of silver atoms.
The following reactions are involved. reaction \( 1 A g^{+}+C l^{-} \rightleftharpoons A g+C l \)
reaction 2 \( \boldsymbol{C u}^{+}+\boldsymbol{C l} \rightarrow \boldsymbol{C u}^{2+}+\boldsymbol{C l}^{-} \)
reaction 3 \( C u^{2+}+A g \rightarrow C u^{+}+A g^{+} \)
Which statement about these reactions
is correct?
A \( \cdot C u^{+} \) and \( C u^{2+} \) ions act as catalysts
B. \( C u^{+} \) ions act as an oxidising agent in reaction 2
c. Reaction 3 increases the darkness of the glass
D. silver atoms are reduced in reaction 3
Subject: Physics
The minimum speed of wind necessary for the satisfactory working of a wind generator to produce electricity is about:
A. \( 15 \mathrm{km} / \mathrm{h} \)
B. 20 \( \mathrm{m} / \mathrm{h} \)
\( c \cdot 12 m / s \)
D. \( 50 \mathrm{km} / \mathrm{h} \)
Subject: Maths
What will be \( \angle X O Y \) if arc \( A B= \) arc
\( X Y \) and \( \angle A O B=60^{\circ} ? \)
\( A \cdot 30^{\circ} \)
B. \( 45^{\circ} \)
\( c \cdot 50^{\circ} \)
D. 60
Subject: Chemistry
Empirical formula of a compound is
\( C H_{2} O . \) If its molecular weight is 180
then the molecular formula of the
compound is?
A. \( C_{6} H_{12} O_{6} \)
B. \( C_{5} H_{10} O_{5} \)
\( \mathbf{c} \cdot C_{3} H_{6} O_{3} \)
D. \( C_{4} H_{8} O_{4} \)
Subject: Maths
\( \lim _{n \rightarrow \infty} n\left[\frac{1}{(n+1)(n+2)}+\frac{1}{(n+2)(n+}\right. \)
is equal to
\( ^{A} \cdot \log \left(\frac{3}{2}\right) \)
в. \( \log \left(\frac{5}{2}\right) \)
c. \( \log \left(\frac{1}{2}\right) \)
D. \( \log \left(\frac{7}{4}\right) \)
Subject: Physics
A range of galavanometer is ' \( V \) ', when
\( 50 \Omega \) resistance is connected in series.
Its range gets doubled when \( 500 \Omega \) resistance is connected in series.
Galvanometer resistance is
\( \mathbf{A} \cdot 100 \Omega \)
в. 200\Omega
c. \( 300 \Omega \)
D. \( 400 \Omega \)
Subject: Maths
In a circle of radius \( 21 \mathrm{cm}, \) an arc
subtends an angle of \( 60^{\circ} \) at the centre.
The area of the segment formed by the corresponding chord of the arc is :
A \( .42 \mathrm{cm}^{2} \)
В. 421.73 \( c m^{2} \)
c. \( 429.43 \mathrm{cm}^{2} \)
D. \( 40 \mathrm{cm}^{2} \)
Subject: Physics
1 volt is equal to
A .1 Joule
B. \( \frac{1 \text { Joule}}{1 \text { Coulomb }} \)
c. \( \frac{1 \text { Joule}}{1 \text { meter }} \)
D. \( \frac{1 \text { Newton }}{1 \text { Coulomb }} \)
Subject: Maths
\( \mathrm{ff} \mathbf{A}=\left[\begin{array}{lll}1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}1 & -2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \quad \) and
\( A B=I_{3}, \quad \) then \( \quad x+ \)
\( \boldsymbol{y} \quad \boldsymbol{i s} \quad \boldsymbol{e q u a l} \quad \boldsymbol{t o} \)
Subject: Physics
toppr
Q Type your question
uniform area of cross-section is
attached with the particle. The other end of the band is suspended from a
rigid support. A force \( \boldsymbol{K}\left(\boldsymbol{l}^{\prime 2}-\boldsymbol{l}^{2}\right)^{1 / 2} \) is
required to stretch the band to a length
\( l^{\prime} . \) The particle is moved to a distance \( S \)
(where \( S<<l \) ) and then released.
taking \( K=\frac{M g}{S} \) and \( \mu \) as the
coefficient of friction between the
particle and the groove, the velocity of
particle when passing through the
initial position is:
\( ^{A} \cdot\left(\frac{g S}{3 l}(2 S-3 \mu l)\right)^{1 / 2} \)
B. \( \left[\frac{g S}{3 l}(3 S-3 \mu l)^{1 / 2}\right] \)
c. \( \frac{g S}{l}(3 S-2 \mu l)^{1 / 2} \)
\( ^{\mathrm{D}}\left[\frac{g S}{2 l}(3 S-2 \mu l)\right]^{1 / 2} \)
Subject: Maths
If \( \sin x+\sin ^{2} x=1 \) then the value of
\( \cos ^{2} x+\cos ^{4} x \) is equal to
\( A \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{3 \sqrt{3}} \)
D. \( \frac{3 \sqrt{5}-5}{2} \)
Subject: Chemistry
One gas bleaches the colour of flowers by reduction while the other gas by
oxidation. The two gases are,
respectively:
A \( \cdot \cos 2 l_{2} \)
в. \( H_{2} S \& B r_{2} \)
\( \mathrm{c} \cdot \operatorname{SO}_{2} \& C l_{2} \)
D. \( N H_{3} \& S O_{3} \)
Subject: Physics
In a process a neutron which is initially at rest, decays into a proton, an electron and an antineutrino. The ejected
electron has a momentum of \( \boldsymbol{p}_{1}= \)
\( 2.4 \times 10^{-26} k g m / s \) and the antineutrino
has \( p_{2}=7.0 \times 10^{-27} k g m / s . \) Find the
recoil speed of the proton if the electron and the antineutrino are ejected (a) along the same direction (b) in mutually perpendicular directions
(Mass of the proton \( \boldsymbol{m}_{\boldsymbol{p}}=\mathbf{1 . 6 7} \times \mathbf{1 0}^{-\mathbf{2 7}} \)
Subject: Physics
Mass of proton \( =1.00760 a m u, \) mass
of neutron \( =1.00899 a m u, \) mass of
deuterium nucleus \( =2.0147 a m u . \) Then
binding energy is :
в. \( 1.76 a m u \)
c. \( 1.76 M e V \)
D. \( 10^{15} \) joules
Subject: Maths
If \( a_{1}, a_{2}, a_{3} \dots \dots \dots a_{n} \) are in A.P.with
common difference \( d, \) then
\( \tan \left[\tan ^{-1}\left(\frac{d}{1+a_{1} a_{2}}\right)+\tan ^{-1}\left(\frac{d}{1+a_{2} a_{3}}\right)+\right. \)
\( \dots \dots \dots \dots \dots+ \)
\( \left.\tan ^{-1}\left(\frac{d}{1+a_{n-1} a_{n}}\right)\right]=? \)
A \( \cdot \frac{(n-1) d}{a_{1}+a_{n}} \)
B. \( \frac{(n-1) d}{1+a_{1} a_{n}} \)
c. \( \frac{n d}{1+a_{1} a_{n}} \)
D. \( \frac{a_{n}-a_{1}}{a_{n}+a_{1}} \)
Subject: Chemistry
If the \( H^{+} \) concentration is decreased
from \( 1 M \) to \( 10^{-4} M \) at \( 25^{\circ} C \) for the
couple \( M n O_{4}^{-} / M n^{2+}, \) then the
oxidising power of the \( M n O_{4}^{-} / M n^{2+} \) couple decreases by :
\( \mathbf{A} \cdot-0.18 V \)
B. \( 0.18 V \)
c. \( 0.38 V \)
D. \( -0.38 V \)
Subject: Chemistry
The vapour pressure of a certain liquid is given by the equation:
\( \log _{10} P=3.54595-\frac{313.7}{T}+ \)
\( \mathbf{1} . \mathbf{4 0 6 5 5} \log _{\mathbf{1 0}} \boldsymbol{T} \)
where \( P \) is the vapour pressure in \( \mathrm{mm} \) and \( T=K \) elvin temperature. Determine
the molar latent heat of vaporisation at
\( \boldsymbol{T}=\mathbf{8 0} \boldsymbol{K} \)
Subject: Maths
The image of the point \( \boldsymbol{P}(\boldsymbol{\alpha}, \boldsymbol{\beta}, \gamma) \) by
the plane \( l x+m y+n z=0 \) is the point \( \boldsymbol{Q}\left(\boldsymbol{\alpha}^{\prime}, \boldsymbol{\beta}^{\prime}, \boldsymbol{\gamma}^{\prime}\right) . \) Then
A \( \cdot \alpha^{2}+\beta^{2}+\gamma^{2}=l^{2}+m^{2}+n^{2} \)
B . \( \alpha^{2}+\beta^{2}+\gamma^{2}=\alpha^{2}+\beta^{2}+\gamma^{2} \)
\( \mathbf{c} \cdot \alpha \alpha^{\prime}+\beta \beta^{\prime}+\gamma \gamma^{\prime}=0 \)
D \( \cdot l\left(\alpha-\alpha^{\prime}\right)+m\left(\beta-\beta^{\prime}\right)+n\left(\gamma-\gamma^{\prime}\right)=0 \)
Subject: Maths
\( \int \frac{1}{\sqrt{1-4 x^{2}}} d x= \)
\( A \cdot \sin ^{-1} 2 x+c \)
B. \( \frac{1}{2} \sin ^{-1} 2 x+c \)
c. \( \left(\sin ^{-1} 2 x\right)^{2}+c \)
D. \( \frac{1}{2}\left(\sin ^{-1} 2 x\right)^{2}+c \)
Subject: Physics
In which of the following option could represent the ball increasing its speed?
\( A \)
\[
\text { (A) } . \quad \bullet \quad \bullet \quad \bullet \quad \text { ・ }
\]
B.
\[
\text { (B) } \bullet \bullet \quad \bullet
\]
\( \mathbf{c} \)
(C)
D.
(D)
\[
\bullet
\]
E .
(E)
Subject: Maths
A computer producing factory has only two plants \( T_{1} \) and \( T_{2} \). Plant \( T_{1} \) produces
\( 20 \% \) and plant \( T_{2} \) produces \( 80 \% \) of total
computers produced. \( 7 \% \) of computers produced in the factory turn out to be defective. It is known that \( P \) (computer
turns out to be defective given that it is
produced in plant \( T_{1} \) ) \( =10 P \) (computer
turns out to be defective given that it is
produced in plant \( T_{2} \) ). where \( P(E) \) denotes the probability of
an event \( E . \) A computer produced in the factory is randomly selected and it does not turn out ot be defective. Then the
probability that it is produced in plant
\( T_{2} \) is
A \( \cdot \frac{36}{73} \)
в. \( \frac{47}{79} \)
c. \( \frac{78}{93} \)
D. \( \frac{75}{83} \)
Subject: Physics
A particle moves along y-axis according to the equation \( y(\text { in } c m)= \)
\( 3 \sin 100 \pi t+8 \sin ^{2} 50 \pi t-6 \)
This question has multiple correct options
A. the particle performs SHM
B. the amplitude of the particle's oscillation is 5 cm
c. the mean position of the particle is at \( y=-2 \mathrm{cm} \)
D. the particle does not perform SHM
Subject: Chemistry
Which of the following cannot form oxo ion?
\( \mathbf{A} \cdot P u O_{2}^{+} \)
B. \( \mathrm{CeO}_{2}^{+} \)
\( \mathbf{c} \cdot U O_{2}^{2+} \)
D. \( N p O_{2}^{\text {th }} \)
Subject: Physics
A proton strikes another proton at rest
with speed \( V_{0} . \) Assume impact
parameter to be zero. Their closest distance of approach is (mass of proton
is \( \boldsymbol{m} \) )
\( ^{\mathbf{A}} \cdot \frac{e^{2}}{4 \pi \varepsilon m v_{0}} \)
в. \( \frac{e^{2}}{\pi \varepsilon_{0} m v_{0}^{2}} \)
c. \( \frac{e^{2}}{m v_{0}^{2}} \)
D. zero
Subject: Chemistry
\( 0.2 \mathrm{L} \) of aqueous solution of a protein contains \( 1.26 \mathrm{g} \) of the protein. The osmotic pressure of such a solution at
\( 300 \mathrm{K} \) is found to be \( 2.57 \times 10^{-3} \) bar.
Calculate the molar mass of the protein.
\( \left(\boldsymbol{R}=\mathbf{0 . 0 8 3} \boldsymbol{L} \text { bar } \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)
Subject: Maths
The acute angle \( \theta \) through which the coordinate axes should be rotated for
the point \( A(2,4) \) to attain the new
abscissa 4 is given by
A \( \cdot \tan \theta=\frac{3}{4} \)
В. \( \tan \theta=\frac{5}{6} \)
\( \mathbf{c} \cdot \tan \theta=\frac{7}{8} \)
D. None of these
Subject: Physics
A stone of mass \( m \) is tied to an elastic
string of negligble mass and spring constant k. The unstretched length of
the string is \( L \) and has negligible mass. The other end of the string is fixed to a
nail at a point P. Initially the stone is at the same level as the point P. The stone is dropped vertically from point P.
(a) Find the distance y from the top
when the mass comes to rest for an
instant, for the first time.
(b) What is the maximum velocity
attained by the stone in this drop?
(c) What shall be the nature of the
motion after the stone has reached its
lowest point?
Subject: Chemistry
The dissociation constant on n-butyric
acid is \( 1.6 \times 10^{-5} \) and the molar
conductivity at infinite dilution is
\( 380 \times 10^{-4} S m^{2} m o l^{-1} . \) The specific
conductance of the \( 0.01 \mathrm{M} \) acid solution
is:
A \( \cdot 1.52 \times 10^{-5} \mathrm{Sm}^{-1} \)
В. \( 1.52 \times 10^{-2} \mathrm{Sm}^{-1} \)
C. \( 1.52 \times 10^{-3} \mathrm{Sm}^{-1} \)
D. None
Subject: Chemistry
Five hundred milliliters of solution of 0.1
M Na Br has how many milligrams of bromine?
A. 200 \( \mathrm{mg} \)
B. 400 mg
c. \( 2,000 \mathrm{mg} \)
D. \( 4,000 \mathrm{mg} \)
E. 20,000 \( \mathrm{mg} \)