AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
An oil drop falls through air with a
terminal velocity of \( 5 \times 10^{-4} m / s . \) The
radius of the drop will be? Neglect density of air as compared to that of oil.
(Viscosity of air \( =\frac{18 \times 10^{-5}}{5} N-s / m^{2} \)
\( g=10 m / s^{2}, \) density of oil \( =900 \mathrm{kg} / m^{3} \)
A \( .2 .5 \times 10^{-6} m \)
В . \( 2 \times 10^{-6} m \)
c. \( 3 \times 10^{-6} m \)
D. \( 4 \times 10^{-6} \mathrm{m} \)
Subject: Maths
\( \ln \Delta A B C, \) a line is drawn parallel to
\( B C \) to meet sides \( A B \) and \( A C \) in \( D \) and
\( E \) respectively. If the area of the \( \Delta A D E \) is \( \frac{1}{9} \) times area of the \( \Delta A B C, \) then the value of \( \frac{A D}{A B} \) is equal to:
A \( \cdot \frac{1}{3} \)
B.
\( c \cdot \frac{1}{5} \)
D.
Subject: Physics
Mass \( m_{1} \) strikes \( m_{2} \) which is at rest.
The ratio of masses for which they will
collide again is : (Collisions between
ball and wall are elastic. Coefficient of
restitution between \( m_{1} \) and \( m_{2} \) is \( e \)
and all the surfaces are smooth
A \( \cdot \frac{e}{2+e} \)
B. \( \frac{2 e}{2+e} \)
\( c \)
\( D \)
Subject: Biology
Select correct combination of
statements for Lymph.
(i) It helps to maintain fluid balance of the body.
(ii) It is contained in Iymphatic vessels and lymphatic organs in mammals.
(iii) It is derived from tissue fluid.
(iv) It contains less antibodies than
plasma.
(v) It flows in both directions.
(vi) It helps to conserve proteins and remove bacteria.
A. i, ii, iii, v
B. ii, iii, iv, vi
c. i, iv, v, vi
D. iii, iv, v, vi
Subject: Maths
A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number \( 1,2,3, \dots \dots ., 12 \) as shown in figure. What is the probability that it will point to multiple of \( 4 ? \)
\( A \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D.
E. None of these
Subject: Maths
Ratio of the greatest and least focal distances of a point on the ellipse \( 4 x^{2}+9 y^{2}=36 \) is:
A. \( 4+\sqrt{5}: 4-\sqrt{5} \)
B. \( 5+\sqrt{5}: 4-\sqrt{3} \)
c. \( 3+\sqrt{5}: 3-\sqrt{5} \)
D. \( \sqrt{7}: 2 \)
Subject: Maths
Direction angle of a vector is \( 30^{\circ}, \) then
find the vector.
B. \( \sqrt{3} b \hat{i}+b \hat{j} \)
c. \( a \hat{i}+b \hat{j} \)
D. \( \sqrt{3} a \hat{i}+\sqrt{3} 3 \hat{j} \)
Subject: Physics
A point moves along a circle with a velocity \( \boldsymbol{v}=\boldsymbol{a} \boldsymbol{t}, \) where \( \boldsymbol{a}=\mathbf{0 . 5 0} \boldsymbol{m} / \boldsymbol{s}^{2} \)
The total acceleration of the point at the moment when it covered the \( n^{t h}(n= \)
0.10) fraction of the circle after the
beginning of motion in \( m / s^{2} \) is \( \frac{x}{10} . \) Find
\( \mathcal{L} \)
Subject: Physics
A wire is subjected to a tensile stress. If
A represents area of cross-section,
represents original length, I represents extension and Y is Young's modulus of elasticity, then elastic potential energy of the stretched wire is
\( \mathbf{A} \cdot U=\frac{2 L}{A Y} I^{2} \)
B \( \cdot U=\frac{A L}{2 Y} I^{2} \)
\( \mathbf{c} \cdot U=\frac{A Y}{2 L} I^{2} \)
D. \( U=\frac{1}{4} \frac{A Y}{L} I^{2} \)
Subject: Chemistry
The freezing point depression constant
for water is \( 1.86^{\circ} \mathrm{C} \boldsymbol{m}^{-1} . \) If \( 5 \mathrm{g} N a_{2} \mathrm{SO}_{4} \)
is dissolved in 45 g \( H_{2} O \), the freezing
point is changed by \( -3.82^{\circ} \mathrm{C} \)
Calculate the van't Hoff factor for
\( N a_{2} S O_{4} \)
A .0 .381
B . 2.05
\( c .2 .63 \)
D. 3.11
Subject: Physics
A uniform meter scale of mass \( 1 k g \) is placed on table such that a part of the scale is beyond the edge. If a body of
mass \( 0.25 k g \) is hung at the end of the scale then the minimum length of
scale that should lie on the table so that
it does not tilt is :
\( \mathbf{A} \cdot 90 \mathrm{cm} \)
B. \( 80 \mathrm{cm} \)
\( \mathbf{c} .70 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)
Subject: Physics
f \( \boldsymbol{E}=\mathbf{1 2} \) volts, \( \boldsymbol{X}=\mathbf{9} \Omega, \) then distance
of balance point \( P \) from end \( A \) is
A. 20 cm
B. 50 \( \mathrm{cm} \)
c. \( 70 \mathrm{cm} \)
D. Data insufficient
Subject: Physics
Wire bound resistors are made by.
A. Winding the wires of an alloy viz, \( \mathrm{Cu} \), Al, \( \mathrm{Ag} \)
B. Winding the wires of an alloy viz, Si, Tu, Fe
C. Winding the wires of an alloy viz, Ge, Au, Gr
D. Winding the wires of an alloy viz, manganin, constantan, nichrome
Subject: Physics
The resistance of carbon filament at
\( 0^{0} C \) is \( 104 \Omega . \) It is connected in series to
an iron wire. The temperature coefficient of resistivity of carbon and
iron are -0.0003 and +0.0052 per degree Celsius respectively. What must be the resistance of iron wire so that the
combined resistance does not change with temperature?
A . 15
B. 6
c. 1.5
D. 156
Subject: Maths
\( P \) and \( Q \) are two points whose coordinates are \( \left(a t^{2}, 2 a t\right) a n d\left(\frac{a}{t^{2}}, \frac{-2 a}{t}\right) \) respectively
and \( \mathrm{S} \) in the point \( (\mathrm{a}, 0) . \) show that \( \frac{1}{S P}+\frac{1}{S Q} \) is independent of \( t \)
Subject: Physics
Match the following:
List - 1 List - 2
a) Burning candle
e) line spectrum
f) continuous
b) Sodium vapour \( \quad \) spectrum
c) Bunsen flame
g) bond spectrum
g) Dark lines in solar
h) Absorption spectrum \( \quad \) spectrum
\( A \cdot a-g, b-e, c-f, d-h \)
B. \( a-g, b-f, c-e, d-h \)
C. \( a-f, b-g, c-e, d-h \)
D. \( a-f, b-e, c-g, d-h \)
Subject: Maths
Commutative law states that
\( \mathbf{A} \cdot \vec{a}-\vec{b}=\vec{b} \vec{a} \)
В . \( \vec{a}+\vec{b}=\vec{b}-\vec{a} \)
c. \( \vec{a}+\vec{b}=\vec{b}+\vec{a} \)
D. None of the above
Subject: Physics
A Proton of mass \( 1.6 \times 10^{-27} \) kg goes
round in a circular orbit of radius \( 0 . \)
metre under a centripetal force of \( 6 \times \)
\( 10^{-14} N \) then the frequency of revolution
of proton is about?
A . \( 1.25 \times 10^{6} \mathrm{rps} \)
в. \( 2.50 \times 10^{6} \)rps
c. \( 3.75 \times 10^{r} r p s \)
D. \( 5 \times 10^{6} r p s \)
Subject: Physics
In Young's double slit experiment, the
two slits act as coherent sources of
equal amplitude 'a' and of wavelength \( \lambda \)
In another experiment with the same
set up, the two slits are sources of equal
amplitude 'a' and wavelength \( \lambda \), but
have \( 90^{\circ} \) phase difference. The ratio of intensity of light at the midpoint of the screen in the first case to that in the
second case is
\( \mathbf{A} \cdot 2: 1 \)
B. 1: 2
c. 3: 4
D. 4: 3
Subject: Chemistry
Which statements are correct about
lactose?
This question has multiple correct options
\( \mathbf{A} \cdot\left(C_{1}-\beta\right)(O H) \) of glucose is linked with \( \left(C_{4}-O H\right) \) of galactose
B \( \cdot\left(C_{1}-\beta\right)(O H) \) of galactose is linked with \( \left(C_{4}-O H\right) \) of \( \beta \) -glucose
C. It is hydrolysed both by lase and lactase
D. It exhibits mutarotation
Subject: Physics
If two mirrors are inclined at some
angle \( \theta . \) An object is placed between the mirrors and there are 5 images formed
for an object, then \( \theta \) is may be
A \( \cdot 45^{\circ} \)
B. \( 53^{\circ} \)
\( c \cdot 63^{\circ} \)
D. \( 75^{\circ} \)
Subject: Maths
The sum of the abscissa of all the
points on the line \( x+y=4 \) that lie at a
unit distance from the line \( 4 x+3 y- \)
\( \mathbf{1 0}=\mathbf{0} \) is
A .4
B. -4
\( c .3 \)
D. - 3
Subject: Chemistry
Which of the following statement(s)
is/are not correct?
\( \mathbf{A} \cdot L a(O H)_{3} \) is less basic than \( L u(O H)_{3} \)
B. In lanthanide series, ionic radius of \( L n^{3+} \) ion
decreases.
C. \( L a \) is actually an element of transition series rather than lanthanides.
D. Atomic radii of \( Z r \) and \( H f \) are same because of lanthanide contraction.
Subject: Physics
A planet in a distant solar system is 10 times more massive than the earth and
its radius is 10 times smaller. Given
that the escape velocity from the earth
is \( 11 k m s^{-1}, \) the escape velocity from
the surface ofthe planet would be
A. \( 110 k m s^{-1} \)
B. \( 0.11 k m s^{-1} \)
c. \( 1.1 k m \mathrm{s}^{-1} \)
D. \( 11 k m s^{-1} \)
Subject: Physics
The resistance of \( n \) wires each of
resistance \( r \) ohms is \( R \), when they are connected in parallel. When these resistance are connected in series the
resultant resistance will be :-
A \( \cdot \frac{R}{n} \)
в. \( \frac{R}{n^{2}} \)
\( c \cdot n R \)
D. \( n^{2} R \)
Subject: Maths
If \( f(x) \) and \( g(x) \) are functions such that \( \boldsymbol{f}(\boldsymbol{x}+)=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{g}(\boldsymbol{y})+\boldsymbol{g}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}), \) then the
value of \( \left|\begin{array}{lll}\boldsymbol{f}(\boldsymbol{\alpha}) & \boldsymbol{g}(\boldsymbol{\alpha}) & \boldsymbol{f}(\boldsymbol{\alpha}+\boldsymbol{\theta}) \\ \boldsymbol{f}(\boldsymbol{\beta}) & \boldsymbol{g}(\boldsymbol{\beta}) & \boldsymbol{f}(\boldsymbol{\beta}+\boldsymbol{\theta}) \\ \boldsymbol{f}(\boldsymbol{\gamma}) & \boldsymbol{g}(\boldsymbol{\gamma}) & \boldsymbol{f}(\boldsymbol{\gamma}+\boldsymbol{\theta})\end{array}\right| \)
A \( \cdot f(\alpha) \cdot f(\beta) \cdot f(\gamma) \)
B.
\( \mathbf{c} \cdot g(\alpha) \cdot g(\beta) \cdot g(\gamma) \)
D. None of these
Subject: Maths
If \( C \) and \( D \) are two events such that
\( C \subset D \) and \( P(D) \neq 0, \) then the correct
statement among the following is
\( \mathbf{A} \cdot P(C \mid D)<P(C) \)
\( ^{\mathbf{B}} P(C \mid D)=\frac{P(D)}{P(C)} \)
c. \( P(C \mid D)=P(C) \)
D. \( P(C \mid D) \geq P(C) \)
Subject: Physics
The angle between two vectors \( \vec{A}= \) (4,-2,5) and \( \vec{B}=(3,1,-2) \) is:
A \( \cdot 60^{\circ} \)
в. \( 30^{\circ} \)
\( c \cdot 90^{0} \)
D. \( 45^{\circ} \)
Subject: Physics
An air-gap parallel plate capacitor is
fully charged by a battery.
What combination of two
measurements will allow someone to
calculate the magnitude of the electric
field in between the capacitor plates?
A. The potential difference of the battery and the area of the plates.
B. The charge on the plates and the distance between the plates.
C. The charge on the plates and the area of the plates.
D. The area of the plates and the distance between the plates
E. More than two measurements are needed to calculate the electric field in between the capacitor plates.
Subject: Physics
A transformer consisting of 300 turns in the primary and 150 turns in the
secondary gives output power of \( 2.2 k W \) .f the current in the secondary coil is
\( \mathbf{1 0} A, \) then the input voltage and current in the primary coil are :
A . \( 220 V \) and \( 10 A \)
B. \( 440 V \) and \( 5 A \)
c. \( 440 V \) and \( 20 A \)
D. 220V and 20A
Subject: Chemistry
The peptide linkage formed between
glycine \( \left(N H_{2} C H_{2} C O O H\right) \) and
alanine \( \left(N H_{2}\right)\left(C H_{3}\right) C H C O O H \) to
give glycylalanine can be shown as:
A. \( N H_{2}-C H_{2}-N H-C_{1} H-C O O H \)
\[
C H_{3}
\]
в. \( N H_{2}-C H_{2}-C O N H-_{\left\{_{H_{3}}\right.}^{C} H- \) СООН
c. \( H_{2} N C O C H_{2}-C_{C H_{3}} H-C O N H_{2} \)
D. \( H O O C-C H_{2}-N H-N H-C_{I}^{C} H-C O O H \)
Subject: Chemistry
Element A burns in nitrogen to give an ionic compound B. Compound B reacts with water to give \( C \) and \( D \). A solution of C becomes milky on bubbling carbon dioxide. Identify \( A, B, C \) and \( D: \)
A \( \cdot A=N a ; B=N a_{3} N_{2} ; C=N a(O H)_{2} ; D=N H_{3} \)
B. \( A=K ; B=K_{3} N_{2} ; C=K O H ; D=N H_{3} \)
C. \( A=C a ; B=C a_{3} N_{2} ; C=C a(O H)_{2} ; D=N H_{3} \)
D. \( A=B a ; B=B a_{3} N_{2} ; C=B a(O H)_{2} ; D=N H_{3} \)
Subject: Chemistry
\( \ln \) a \( H \) -atom, the \( n \) transition takes
place from \( \boldsymbol{L} \) to \( \boldsymbol{K} \) shell If \( \boldsymbol{R}=\mathbf{1 . 0 8} \times \)
\( 1067 m^{-1}, \) the wave length of the light
emitted is nearly:
A \( \cdot 4400 A^{\circ} \)
B . \( 1250 A^{\circ} \)
c. \( 1650 A^{\circ} \)
D. \( 1850 A^{\circ} \)
Subject: Physics
Two cells of emf's approximately \( 5 V \) and
10V are to be accurately compared
using a potentiometer of length \( 400 \mathrm{cm} \)
A. The battery that runs the potentiometer should have voltage of \( 8 \mathrm{V} \)
B. The battery of potentiometer can have a voltage of \( 15 \mathrm{V} \) and \( R \) adjusted so that the potential drop across the wire slightly exceeds \( 10 \mathrm{V} \)
C. The first portion of \( 50 \mathrm{cm} \) of wire itself should have a potential drop of \( 10 \mathrm{v} \)
D. Potentiometer is usually used for comparing resistances and not voltages
Subject: Physics
If the capacitance between two successive plates is \( C, \) then the capacitance of the equivalent system between \( A \) and \( B \) is
A \( \cdot \frac{C}{3} \)
в. \( 3 C \)
c. \( \frac{2 C}{3} \)
D. \( \frac{3 C}{2} \)
Subject: Chemistry
Assertion
The mobilities of the alkali metal ions
in aqueous solutions are: \( \boldsymbol{L} \boldsymbol{i}^{+}< \)
\( \boldsymbol{N} \boldsymbol{a}^{+}<\boldsymbol{K}^{+}<\boldsymbol{R} \boldsymbol{b}^{+}<\boldsymbol{C} \boldsymbol{s}^{+} \)
Reason
Greater the charge, smaller the radius, larger the hydration and thus heavier (hydrated) ion slower.
Read the above assertion and reason and
choose the correct statement regarding
it.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
The following equation represents a method of purification of nickel by:
\( N i+4 C O(\text {impure}) \stackrel{320 K}{\rightarrow} N i(C O)_{4} \stackrel{420 L}{\longrightarrow} \)
A. Cupellation
B. Mond's process
c. van Arkel method
D. zone refining
Subject: Physics
An electric kettle is rated \( 2.5 k W, 250 V \)
What is the cost of running the kettle
for two hours at Rs. 5.40 per unit?
A. \( R s .17 .00 \)
B. \( R s .27 .00 \)
c. \( R s .26 .00 \)
D. \( R s .16 .20 \)
Subject: Physics
In the meter bridge shown, the
resistance \( X \) has a negative
temperature coefficient of resistance.
Neglecting the variation in other
resistors, when current is passed for
some time, in the circuit balance point
should shift towards:
\( A \cdot A \)
в. \( B \)
\( c . \) First \( A \) then \( B \)
D. It will remain at
Subject: Physics
The Fahrenheit temperature \( \boldsymbol{F} \)
decreased by 32 is equal to nine-fifths of the centigrade temperature \( C . \) The correct formula framed for the above
statement will be :
A \( \cdot F+32=\frac{5}{9} C \)
В \( \cdot F-32=\frac{5}{9} C \)
c. \( _{F}+32=\frac{9}{5} C \)
D. \( _{F-32}=\frac{9}{5} C \)
Subject: Chemistry
The complete balanced equation is:
\( \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{K}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \)
A \( \cdot 3 \mathrm{H}_{2} S+2 \mathrm{K}_{2} \mathrm{CrO}_{4}+5 \mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3}+ \)
\( 2 K_{2} S O_{4}+8 H_{2} O+3 S \)
B. \( 3 H_{2} S+K_{2} C r O_{4}+5 H_{2} S O_{4} \rightarrow C r_{2}\left(S O_{4}\right)_{3}+ \)
\( K_{2} S O_{4}+8 H_{2} O+3 S \)
c. \( H_{2} S+2 K_{2} C r O_{4}+3 H_{2} S O_{4} \rightarrow C r_{2}\left(S O_{4}\right)_{3}+ \)
\( 2 K_{2} S O_{4}+8 H_{2} O+3 S \)
D. none of these
Subject: Physics
Consider the following statements A \& B and identify correct choice in the
given answers
(A) When light falls on two polaroid sheets having their axes mutually perpendicular, it is completely extinguished.
(B) When polyvinyl alcohol is subjected to a large strain the molecules get
oriented parallel to the direction of
strain and material becomes
double refractive.
A . A \& B are correct
B. Both A \& B are wrong
C. A correct B wrong
D. A wrong B correct
Subject: Biology
Match the following with reference to
adaptations.
The correct match is
A \( . \) A- II, B- \( 1 \mathrm{V}, \mathrm{C}-1 \mathrm{II}, \mathrm{D}-1 \)
B. A-III, B -II, C-I, D -V
C. \( A-11, B-111, C-1 V, D-1 \)
D. \( A-\| I, B-I V, C-1, D-V \)
Subject: Maths
Assertion
The points (2,1,5) and (3,4,3) lie on
opposite sides of the plane \( 2 x+2 y- \)
\( \mathbf{2} z-\mathbf{1}=\mathbf{0} \)
Reason
The algebraic perpendicular distance from the given points to line have opposite signs.
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 ball strikes a smooth horizontal
ground at an angle of \( 45^{\circ} \) with the vertical. What cannot be the possible angle of its velocity with vertical after the collision? (Assume \( e \leq 1 \) )
A . \( 45^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 53^{\circ} \)
D. \( 60^{\circ} \)
Subject: Physics
On to a sphere of radius \( \boldsymbol{R} / 2 \) and
density \( \rho_{2} \) with centre at \( C_{2} \) a second
solid sphere is moulded with density \( \rho_{1} \)
radius \( R \) and centre \( C_{1} \). Find the force
experienced by a point mass \( m \) at point
\( P \) at a distance \( y \) from the combination
as shown.
Subject: Chemistry
Q Type your question
"I 11
\( \left.\sqrt{\boldsymbol{c}}(\text {in } \boldsymbol{m o l} / \boldsymbol{L})^{1 / 2}\right) \) for \( \boldsymbol{K} \boldsymbol{C l} \) solution?
\( \left(\boldsymbol{y}=\wedge_{m} ; \boldsymbol{x}=\sqrt{\boldsymbol{c}}\right) \)
\( A \)
B.
\( c \)
\( D \)
Subject: Chemistry
The electromagnetic radiations are:
a) Visible light
b) IR light
c) UV light
d) Microwaves
The correct order of increasing energy from lowest to highest is:
A. \( d<c<b<a \)
в. \( a<b<c<d \)
c. \( d<b<a<c \)
D. \( b<c<d<a \)
Subject: Physics
Two statements are provided. Choose
which is true and which is false.

Statement I: Image formed by half cut mirror has just half the intensity as that of the intensity of image formed by
complete mirror
Statement II: More the lateral
separation between the two halves of the mirror, less will be separation
between the two images, as show in the
given situation
A . \( T, T \)
в. \( T, F \)
Subject: Maths
If \( \sqrt{3} \tan 2 \theta+\sqrt{3} \tan 3 \theta+ \)
\( \tan 2 \theta \tan 3 \theta=1, \) then the general
value of \( \theta \) is
A \( . \quad n \pi+\frac{\pi}{5} \)
B \( \cdot\left(n+\frac{1}{6}\right) \frac{\pi}{5} \)
\( ^{c} \cdot\left(2 n \pm \frac{1}{6}\right) \frac{\pi}{5} \)
D. \( \left(n+\frac{1}{3}\right) \frac{\pi}{5} \)
Subject: Maths
If \( f(x)=3 x+10, g(x)=x^{2}-1, \) then
\( (f o g)^{-1} \) is equal to
\( ^{\mathbf{A}}\left(\frac{x-7}{3}\right)^{\frac{1}{2}} \)
B. \( \quad\left(\frac{x+7}{3}\right)^{\frac{1}{2}} \)
\( \left(\frac{x-3}{7}\right)^{\frac{1}{2}} \)
D. \( \quad\left(\frac{x+3}{7}\right)^{\frac{1}{2}} \)
Subject: Maths
\( \operatorname{Let} P=\left(\begin{array}{cc}\cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right) \) and \( x= \)
\( \left(\begin{array}{c}\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}}\end{array}\right) \cdot \operatorname{Then} P^{3} X \) is equal to
A \( \cdot\left(\begin{array}{l}0 \\ 1\end{array}\right) \)
B. \( \left(\frac{-1}{\sqrt{2}}\right) \)
\( \left(\begin{array}{c}-1 \\ 0\end{array}\right) \)
D \( \left(\begin{array}{l}-\frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}}\end{array}\right) \)
Subject: Chemistry
Equivalent weight of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \) when it
disproportionates into \( P H_{3} \) and
\( H 3 P O_{3}(\text { mol. wt. }=M) \) is :
\( \mathbf{A} \cdot M \)
в. \( \frac{M}{2} \)
c. \( \frac{M}{4} \)
D. \( \frac{3 M}{4} \)
Subject: Maths
If \( f(x)=a \cos (b x+c)+d \) then range
of \( \boldsymbol{f}(\boldsymbol{x}) \) is
A \( \cdot[d+a, d+2 a] \)
B . \( [a-d, a+d] \)
c. \( [d+a, a-d] \)
D \cdot \( [d-a, d+a] \)
Subject: Physics
\( n \) identical charged drops having charge
\( q_{0}, \) potential \( V_{0}, \) capacity \( C_{0} \) and energy
\( E_{0}, \) coalesce to form a big drop. The new
potential, charge, capacity, energy stored
will be:
B \( \cdot \frac{2}{n^{3}} V_{0} ; \frac{q_{0}}{n_{0}} ; \quad n^{\frac{1}{3}} C_{0} ; \quad n^{\frac{3}{5}} U_{0} \)
D. \( \frac{2}{n^{3}} V_{0} ; \frac{q_{0}}{n} ; n^{\frac{2}{3}} C_{0} ; n^{\frac{5}{3}} U_{0} \)
Subject: Chemistry
Assertion
Copper dissolves in dilute nitric acid but not in dilute \( \boldsymbol{H} \boldsymbol{C l} \)
Reason

Copper has positive \( \boldsymbol{E}^{\circ} \)
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. Both Assertion and Reason are incorrect
Subject: Maths
The sum \( \frac{1}{1+1^{2}+1^{4}}+\frac{2}{1+2^{2}+2^{4}}+ \)
\( \frac{\mathbf{3}}{\mathbf{1}+\mathbf{3}^{2}+\mathbf{3}^{4}}+\ldots+\frac{\mathbf{9 9}}{\mathbf{1}+\mathbf{9 9}^{2}+\mathbf{9 9}^{4}} \) lies
between
A. 0.46 and 0.47
7
B. 0.52 and 1.0
c. 0.48 and 0.49
D. 0.49 and 0.50
Subject: Chemistry
\( \boldsymbol{B} \boldsymbol{X}_{3}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow \boldsymbol{B} \boldsymbol{X}_{3} \cdot \boldsymbol{N} \boldsymbol{H}_{3}+ \) Heat of
adduct formation \( (\Delta H) \)
The numerical value of \( \Delta H \) is found to
be maximum for:
\( A \cdot B F_{3} \)
в. \( B C l_{3} \)
\( \mathrm{c} . B B r_{3} \)
D. \( B I_{3} \)
Subject: Chemistry
For the equilibrium at \( 298 \mathrm{K} \) \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) ; G_{N_{2}}^{\ominus}_{O_{4}}= \)
\( 100 k J m o l^{-1} \) and \( G_{N O_{2}}^{\ominus}=50 k J m o l^{-1} \)
If 5 mol of \( N_{2} O_{4} \) and 2 moles of \( N O_{2} \) are taken initially in one litre container
than which statement are correct
This question has multiple correct options
A. reaction proceeds in forward direction
B . \( K_{c}=1 \)
c. \( \Delta G=-0.55 k J, \Delta G^{\ominus}=0 \)
D. At equilibrium \( \left[N_{2} O_{4}\right]=4.84 M \) and \( \left[N O_{2}\right]=0.212 M \)
Subject: Physics
A bullet fired into a fixed target loses half of its velocity after penetrating \( 3 \mathrm{cm} \) How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?
\( \mathbf{A} .3 .0 \mathrm{cm} \)
B. \( 2.0 \mathrm{cm} \)
c. \( 1.5 \mathrm{cm} \)
D. \( 1.0 \mathrm{cm} \)
Subject: Chemistry
Name the cation and anion in given reaction:
\( 2 S O_{2} \rightleftharpoons S O^{2+}+S O_{3}^{2-} \)
A \( \cdot S O^{2+}: \) Sulphide \( S O_{3}^{2-}: \) Sulpharyl
B . \( S O^{2+}: \) Sulpharyl \( S O_{3}^{2-}: \) Sulphite
c. \( S O^{2+}: \) Sulphite \( S O_{3}^{2-}: \) Sulphide
D. None of these
Subject: Chemistry
\( 14 \mathrm{g} \) of an element \( \mathrm{X} \) combines with 16 g of oxygen. On the basis of this, which of the following statement is correct?
[At.wt of oxygen \( =16] \)
A. The element \( x \) could have an atomic weight 7 and its oxide formula is \( X O \)
B. The element X could have an atomic weight 14 and its oxide formula is \( X_{2} O_{3} \)
c. The element \( x \) could have an atomic weight 7 and its oxide formula is \( X_{2} O \)
D. The element x could have an atomic weight 14 and its oxide formula is \( X O_{2} \)
Subject: Chemistry
Emf of hydrogen electrode in term of \( p H \)
is (at 1 atm pressure).
\( ^{\mathbf{A}} \cdot_{E_{H_{2}}}=\frac{R T}{F} \times p H \)
В. \( \quad E_{H_{2}}=\frac{R T}{F} \frac{1}{p H} \)
c. \( \quad E_{H_{2}}=\frac{2.303 R T}{F} p H \)
D. \( E_{H_{2}}=-0.0591 p H \)
Subject: Physics
The potential energy between electron and proton is given by \( U=\frac{K e^{2}}{3 r^{3}} \)

According to Bohr's theory, the energy in
the \( n^{t h} \) orbit of such a
hypothetical atom will be proportional to
\( \mathbf{A} \cdot n^{6} \)
B . \( n^{4} \)
c. \( n^{2} \)
D. \( n \)