AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A particle falling under gravity
describes \( 80 f t \) in a certain sec. How
long does it take to describe next \( 112 f t \)
\( ?\left[\boldsymbol{g}=\boldsymbol{3} 2 \boldsymbol{f} \boldsymbol{t} \boldsymbol{s}^{-2}\right] \)
\( \mathbf{A} \cdot 1 s \)
B . \( 2 s \)
c. \( 3 s \)
D. \( 4 s \)
Subject: Chemistry
At \( 527^{\circ} C \) temperature the activation energy is \( 54.7 \mathrm{KJ} / \) mole. The value of
Arrhenius factor is \( 4 \times 10^{10} \). The rate
constant will be
A \( \cdot 12.28 \times 10^{11} \)
B . \( 10^{7} \)
c. \( 12.28 \times 10^{17} \)
D. \( 14.58 \times 10^{-13} \)
Subject: Chemistry
A conductance cell was filled with 0.01
molar KCl. Its resistance was found to
be 150 ohm at \( 25^{\circ} \mathrm{C} \). The conductivity
was observed to be \( 0.00177 S c m^{-1} . \) The
cell was when washed and filled with
0.05 molar solution of NaCl whose
resistance was found to be 325 ohm.
Conductivity of NaCl solution is:
B. \( 9.168 \times 10^{-4} \mathrm{Scm}^{-1} \)
c. \( 8.169 \times 10^{-4} \mathrm{Scm}^{-1} \)
D. None of these
Subject: Physics
A sphere of mass \( m \) is moving with a velocity \( (4 \hat{i}-\hat{j}) m / s \) hits a frictionless and rebounds with a velocity \( (\hat{\mathbf{i}}+ \) \( \mathbf{3} \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} . \) The coefficient of restitution
between the sphere and the surface is :
A \( \cdot 2 / 5 \)
в. \( 4 / 9 \)
c. \( 9 / 16 \)
D. \( 4 / 25 \)
Subject: Physics
A capacitor of capacitance \( 2 \mu F \) is connected in the tank circuit of an
oscillator oscillating with a frequency of 1 kHz. If the current flowing in the circuit is \( 2 \mathrm{mA} \), the voltage across the capacitor will be :
A . \( 0.16 \mathrm{v} \)
B. 0.32
c. 79.5 \( v \)
D. \( 159 \mathrm{V} \)
Subject: Chemistry
In the pressence of a catalyst, the activation energy of a reaction is
lowered by \( 2 k c a l \) at \( 27^{\circ} C . \) The rate of reaction will increase by:
\( (\text {Antilog} 1.43=28) \)
A. 2 times
B. 14 times
c. 28 times
D. 20 times
Subject: Biology
Which of the following is true?
A. The continuous cycling of water among its three forms keeps the total amount of water on the earth constant even when the whole world is using it.
B. The continuous cycling of water among its three forms cannot keep the total amount of water on the earth constant even when the whole world is using it.
C. The continuous cycling of water among its three forms decreases the total amount of water on the earth when
the whole world is using it
D. The continuous cycling of water among its three forms keeps the total amount of water on the earth constant only if the whole world is not using it
Subject: Maths
An urn contains 25 balls of which 10
bear a mark ' \( X \) ' and the remaining 15
bear a mark 'Y'. A ball is drawn at
random from the urn, its mark noted
down and it is replaced. If 6 balls are drawn in this way, find the probability that
(i) All will bear mark ' \( \boldsymbol{X} \)
(ii) Not more than two will bear ' \( Y \) ' mark
Subject: Physics
The internal resistance of a primary cell
is 4 \Omega. It generates a current of \( 0.2 \mathrm{A} \) in
an external resistance of \( 21 \Omega \). The rate
of chemical energy consumed in providing the current is
A \( \cdot 0.42 \mathrm{J} \mathrm{s}^{-} 1 \)
B. 0.84 J \( s^{-1} \)
c. \( 1 J s^{-1} \)
D. 5 J \( s^{-1} \)
Subject: Maths
The following data give the amount of loans (in crores of rupees) disbursed by a bank during some years:
Year 1992 \( \quad 1993 \quad 1994 \quad 1995 \)
Loan
(in
crores \( 28 \quad 33 \quad 55 \) of
upee
Represent the above data with the help of a bar graph.
Subject: Chemistry
The atom \( A, B, C \) have the configuration \( A \rightarrow[Z(90)+n(146)], B \rightarrow[Z(92)+ \)
\( \mathrm{n}(146)], \mathrm{C} \rightarrow[\mathrm{Z}(90)+\mathrm{n}(148)] \) So that
(a) \( A \) and \( C- \) Isotones
(b) A and C -
Isotopes
(c) \( A \) and \( B \) - Isobars
(d) \( B \) and \( c- \)
Isobars
(e) \( \mathrm{B} \) and \( \mathrm{C} \) - Isotones
The wrong statements are:
A. a, bonly
B. c, d, e only
c. a \( , c, d \) only
D. a, d, e only
Subject: Maths
If \( \boldsymbol{x}=\mathbf{3} \) and \( \boldsymbol{y}=-\mathbf{2}, \) the value of \( \boldsymbol{x}^{\boldsymbol{x}}+ \)
\( \boldsymbol{y}^{\boldsymbol{y}} ? \)
A . 27
B. 9
c. 8
D. none of the above
Subject: Maths
Solve the differential equation \( \left(x^{2}-\right. \) \( \left.\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{x}-\boldsymbol{x} \boldsymbol{y} \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
A \( \cdot y^{2}\left(x^{2}-2 y^{2}\right)=k \)
B . \( x^{2}\left(x^{2}-2 y^{2}\right)=k \)
C \( \cdot y^{2}\left(2 x^{2}-y^{2}\right)=k \)
D. \( x^{2}\left(2 x^{2}-y^{2}\right)=k \)
Subject: Chemistry
IUPAC name of, \( \boldsymbol{H}_{\mathbf{2}} \boldsymbol{N}-\boldsymbol{C} \boldsymbol{H}_{\mathbf{2}}-\boldsymbol{C} \boldsymbol{H}_{2}- \)
\( \boldsymbol{C H}_{3} \) is:
A. propan-1-amine
B. propanamine-1,2
c. dipropane-1,2-amine
D. diamino-1, 2-propane
Subject: Physics
In which of the following cases can the average velocity of a particle in a timeinterval can be found by using geometry only given the velocity-time graphs?
A. Velocity-time graph is a set of straight line with different slopes
B. Velocity-time graph is a straight line with constant slope and no discontinuities
c. velocity-time graph is a set of straight lines with same slopes but with discontinuities
D. Average velocity can always be found by using geometry only
Subject: Maths
If \( f\left(\frac{3 x-4}{3 x+4}\right)=x+2, x \neq-\frac{4}{3}, \) and
\( \int \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}=\boldsymbol{A} \log |\mathbf{1}-\boldsymbol{x}|+\boldsymbol{B} \boldsymbol{x}+\boldsymbol{C} \)
then the ordered pair \( (A, B) \) is equal to
(where \( C \) is a constant of integration)
\( ^{A} \cdot\left(\frac{8}{3}, \frac{2}{3}\right) \)
B \( \cdot\left(-\frac{8}{3}, \frac{2}{3}\right) \)
\( ^{\mathbf{C}} \cdot\left(-\frac{8}{3},-\frac{2}{3}\right) \)
D. \( \left(\frac{8}{3},-\frac{2}{3}\right) \)
Subject: Maths
\( f\left|\begin{array}{ccc}\mathbf{6} i & -\mathbf{3} i & \mathbf{1} \\ \mathbf{4} & \mathbf{3} i & -\mathbf{1} \\ \mathbf{2 0} & \mathbf{3} & \boldsymbol{i}\end{array}\right|=\boldsymbol{x}+\boldsymbol{i} \boldsymbol{y}, \) then
A \( . x=3, y=0 \)
B. \( x=1, y=3 \)
c. \( x=0, y=3 \)
D. \( x=0, y=0 \)
Subject: Physics
A vertical hollow cylinder of height \( 1.52 \mathrm{m} \) is fitted with a movable piston of
negligible mass and thickness. The lower
half portion of the cylinder contains an
ideal gas and the upper half is filled with
mercury. The cylinder is initially at \( 300 \mathrm{K} \)
When the temperature is raised half of
the mercury comes out of the cylinder. Then the temperature is (the thermal
expansion of mercury to be negligible)
\( A \cdot 437 \mathrm{K} \)
B. 337.5 K
c. \( 275 \mathrm{k} \)
D. 137.K
Subject: Maths
If \( \alpha \) is the angle subtended at \( P\left(x_{1}, y_{1}\right) \)
by the circle \( S=x^{2}+y^{2}+2 g x+ \)
\( 2 f y+c=0, \) then
This question has multiple correct options
A \( \cdot \cot \alpha=\frac{\sqrt{S_{1}}}{\sqrt{g^{2}+f^{2}-c}} \)
B. \( \cot \alpha / 2=\frac{\sqrt{S_{1}}}{\sqrt{g^{2}+f^{2}-c}} \)
\( ^{\mathrm{c}} \tan \alpha=\frac{2 \sqrt{g^{2}+f^{2}-c}}{\sqrt{S_{1}^{1}}} \)
D. \( \quad \alpha=2 \tan ^{-1}\left(\frac{\sqrt{g^{2}+f^{2}-c}}{\sqrt{S_{1}}}\right) \)
Subject: Chemistry
One mole of helium gas is heated in a vessel with variable volume so that the
pressure is fixed at 1 atmosphere. When the temperature increased from \( 273 \mathrm{K} \) to \( 274 \mathrm{K}, \) it was found that \( 21 J \) of heat energy was absorbed. The value of \( \Delta U, \) and \( \Delta H, \) respectively, are:
A. 4.4 Jand \( 12.7 \mathrm{J} \)
B. 12.7Jand21J
c. 21 Jand \( 29.3 \mathrm{J} \)
D. 29.3Jand21J
Subject: Chemistry
At \( 300 \mathrm{K}, \) the density of a certain gaseous molecule at 2 bar is double to
that of dinitrogen \( \left(N_{2}\right) \) at 4 bar. The
molar mass of gaseous molecule is :
A \( \cdot 112 g \) mol \( ^{-1} \)
B . \( 224 g \) mol \( ^{-1} \)
c. \( 28 g \) mol \( ^{-1} \)
D. \( 56 g \) mol\( ^{-1} \)
Subject: Maths
The plane \( 2 x-(1+\lambda) y+3 z=0 \)
passes through the intersection of the
planes
A. \( 2 x-y=0 \) and \( y+3 z=0 \)
в. \( 2 x-y=0 \) and \( y-3 z=0 \)
c. \( 2 x+3 z=0 \) and \( y=0 \)
D. None of the above
Subject: Maths
If \( \boldsymbol{A}=[\boldsymbol{a} \boldsymbol{i} \boldsymbol{j}] \) is a matrix of order \( 2 x \boldsymbol{2} \)
such that \( |A|=15 \) and cij represents
the co factor of aij then find \( a_{21} c_{21}+ \)
\( \boldsymbol{a}_{22} \boldsymbol{c}_{22} \)
Subject: Physics
An air tight container having a lid with
negligible mass and an area of \( 8 \mathrm{cm}^{2} \) is
partially evacuated. If a \( 48 \mathrm{N} \) force is required to pull the lid off the
container and the atmospheric
pressure is \( 1.0 \times 10^{5} \) Pa, the pressure in the container before it is opened must
be:
A . \( 0.6 a t m \)
B. \( 0.5 a t m \)
c. \( 0.4 a t m \)
D. \( 0.2 a t m \)
Subject: Physics
A satellite is revolving in a circular
equatorial orbit of radius \( \boldsymbol{R}=\mathbf{2} \times \mathbf{1 0}^{\mathbf{4}} \)
\( \mathrm{km} \) from east to west. Calculate the
interval after which it will appear at the same equatorial town. Given that the
radius of the earth \( =6400 \mathrm{km} \) and
g(acceleration due to gravity) \( =10 \mathrm{m} \) \( s^{-2} \)
Subject: Physics
A solid sphere, a thin hoop, and a solid cylinder all roll down an incline plane
from rest. All three have a mass, \( m \) and
a radius, \( r \) and all start at the same
position on the ramp. Which of the following correctly describes the order in which they would reach the bottom of the ramp?
A. First the hoop, then cylinder, then sphere
B. First the cylinder, then hoop, then sphere
c. First the sphere, then hoop, then cylinder
D. First the sphere, then cylinder, then hoop
E. First the cylinder, then the sphere, then the hoop
Subject: Chemistry
The stability of dihalides of \( \mathrm{Si}, \mathrm{Ge}, \mathrm{Sn} \) and Pb increases steadily in the
sequence:
\( A \cdot \operatorname{Gex}_{2} \ll \operatorname{six}_{2} \ll \sin x_{2} \ll \operatorname{Pb} x_{2} \)
B. \( \operatorname{six}_{2} \ll \operatorname{Gex}_{2} \ll \operatorname{Pb} x_{2} \ll \sin x_{2} \)
c. \( \operatorname{six}_{2} \ll \cos x_{2} \ll \operatorname{sn} x_{2} \ll \operatorname{pbx}_{2} \)
D. \( P b x_{2} \ll \operatorname{sn} x_{2} \ll G e x_{2} \ll \operatorname{six}_{2} \)
Subject: Physics
If A vessel of thermal capacity 30
calories contains \( 170 g \) of water at
\( 30^{\circ} \mathrm{C} . \) If on dropping a solid at \( 93^{\circ} \mathrm{C} \)
into the calorimeter, then temperature
of mixture becomes \( 33^{\circ} \mathrm{C} \), find the
thermal capacity of solid.
Subject: Maths
At present a firm manufacturing 2000 items it is estimated that the rate of
change of production (P) with respect to additional number of workers \( (x) \) is
given by \( \frac{d P}{d x}=100-12 \sqrt{x} . \) If the firm employes
25 more workers then the new
production is?
A . 2500
в. 3000
c. 3500
D. 4500
Subject: Maths
For a set of positive numbers, consider
the following statements:
1. If each number is reduced by \( 2, \) then the geometric mean of the set may not always exists.
2. If each number is increased by 2 , then the geometric mean of the set is increased by 2 Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Chemistry
The pair of amphoteric oxides is:
A. \( V O, C r_{2} O_{3} \)
в. \( V_{2} O_{5}, C r_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{V} \mathrm{O}_{2}, \mathrm{Cr}_{2} \mathrm{O}_{3} \)
D. \( V_{2} O_{5}, C r O_{3} \)
Subject: Maths
\( \bar{a}, \bar{b}, \bar{c} \) are three non-zero vectors such that any two of them are non-collinear. If \( \bar{a}+\bar{b} \) is collinear with \( \bar{c} \) and \( \bar{b}+\bar{c} \) is
collinear with \( \bar{a} \), then what is their sum?
A . -1
B. 0
c. 1
D. 2
Subject: Physics
A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing
down at \( 22^{0} \) with the horizontal. The
horizontal component of the earth's magnetic field at the place is known to be \( 0.35 G . \) Determine the magnitude of
the earth's magnetic field at the place.
A . 0.12
B. 1.23
\( c \cdot 4.56 \)
D. 0.38
Subject: Physics
The position \( x \) of a particle varies with
time \( t \) a \( a t^{2}-b t^{3} . \) The acceleration of
particle will be zero at time \( t \) is equal to
A \( \cdot \frac{a}{b} \)
в. \( \frac{2 a}{3 b} \)
c. \( \frac{a}{3 b} \)
D. zero
Subject: Chemistry
An orange solid \( (X) \) on heating, gives a colourless gas (Y) and a only green residue (Z). Gas (Y) on treatment with
Mg, produceds a white solid
substance
A. \( M g_{3} N_{2} \)
2
в. \( M g O \)
c. \( M g_{2} O_{3} \)
D. \( M g C l_{2} \)
Subject: Maths
If the line \( x-1=0 \) is the directrix of
the parabola \( y^{2}-k x+8=0, \) then one
of the values of \( k \) is
A \( .1 / 8 \)
B. 8
\( c \cdot 4 \)
D. \( 1 / 4 \)
Subject: Physics
The normal operating voltage and current for a light-emitting diode are:
\( \mathbf{A} \cdot 60 V \) and \( 20 m A \)
B. \( 5 V \) and \( 50 m A \)
c. \( 1.7 V \) and \( 20 m A \)
D. \( 0.7 V \) and \( 60 m A \)
Subject: Physics
A charge of \( 10 \mu C \) is placed at the origin of \( (x-y) \) coordinate system. The potential difference between two points \( (0, a) \) and
\( (a, 0) \) in volts is
\( \mathbf{A} \cdot 9 \times 10^{4} / a \)
B . \( 9 \times 10^{4} / a \sqrt{2} \)
c. \( 9 \times 10^{4} 2 a \)
D.
Subject: Physics
A ring takes time \( t_{1} \) in slipping down an inclined plane of length \( L \), whereas it
takes time \( t_{2} \) in rolling down the same
plane. The ratio of \( t_{1} \) and \( t_{2} \) is :
B . \( 1: 2^{\frac{1}{2}} \)
\( c \cdot 1: 2 \)
D. \( 1: 2^{\frac{1}{7}} \)
Subject: Chemistry
The Van't Hoff factor of \( 0.1 \mathrm{M} \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} \)
solutions is \( 2.74 . \) The degree of dissociation will be
A . 91.3\%
B. 87\%
c. \( 100 \% \)
D. 74\%
Subject: Physics
A physical quantity \( x \) can be dimensionally represented in terms of \( M, L \) and \( T \) is \( x=M^{a} L^{b} T^{c} . \) The
quantity time
A. may be dimensionally represented in terms of \( x, M \) and \( L \) if \( c \neq 0 \)
B. may be dimensionally represented in terms of \( x, M \) and \( L \) if \( c=0 \)
c. may be dimensionally represented in terms of \( x, M \) and \( L \), irrespective of \( c \)
D. may be dimensionally represented in terms of \( x, M \) and \( L \)
Subject: Maths
The line passes through \( \left(-1, \frac{\pi}{2}\right) \) and perpendicular to the line \( \sqrt{3} \sin \theta+ \) \( 2 \cos \theta=\frac{4}{r} \) is:
A \( .2=\sqrt{3} r \cos \theta-2 r \sin \theta \)
в. \( 5=2 \sqrt{3} r \sin \theta+4 r \cos \theta \)
c. \( 2=\sqrt{3} r \cos \theta+2 r \sin \theta \)
D. \( 8=2 \sqrt{3} r \sin \theta-4 r \cos \theta \)
Subject: Physics
A sphere A impinges directly on an identical sphere \( \mathrm{B} \) at rest. If e is the coefficient of restitution then the ratio
of the velocities of \( A \) and \( B \) after impact
is
A \( \cdot \frac{1+e}{1-e} \)
в. \( \frac{1-e}{1+e} \)
c. \( \frac{e}{1-e} \)
D. \( \frac{e}{1+e} \)
Subject: Maths
Given that \( \vec{A} \times \vec{B}=\vec{B} \times \vec{C}=\overrightarrow{0} \) if \( \overrightarrow{A B C} \)
are not null vectors, Find the value of \( \vec{A} \times \vec{C} \)
A \( . \vec{A} \times \vec{B} \)
B. \( \overrightarrow{0} \)
c. \( \vec{c} \times \vec{B} \)
D. \( \vec{C} \times \vec{A} \)
Subject: Maths
For two given events \( \boldsymbol{A} \) and \( \boldsymbol{B}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
is :
This question has multiple correct options
A. not less than \( P(A)+P(B)-1 \)
B. not greater than \( P(A)+P(B) \)
c. equal to \( P(A)+P(B)-P(A \cup B) \)
D. equal to \( P(A)+P(B)+P(A \cap B) \)
Subject: Chemistry
Which of the underlined atoms in the
molecules shown below have \( s p \)
hybridization?
(u) \( C H_{2} C H C H_{3} \)
(v) \( C H_{2} \) CCHCl
\( (w) C H_{3} C H_{2}^{+} \)
\( (x) H-C=C-H \)
\( (y) C H_{3} C N \)
(z) \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C} \underline{\boldsymbol{N}} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{z}} \)
A. \( x \) and \( z \)
B. \( x, y \) and \( z \)
c. u, w and \( x \)
D. \( v, x \) and \( y \)
Subject: Maths
The minimum value of the function \( f(x) \)
\( =\int_{0}^{x} \frac{d \theta}{\cos \theta}+\int_{x}^{\pi / 2} \frac{d \theta}{\sin \theta} \) where \( x \in\left[0, \frac{\pi}{2}\right], \) is
A \( .2 \ln (\sqrt{2}+1) \)
в. \( \ln (2 \sqrt{2}+2) \)
c. \( \ln (\sqrt{3}+2) \)
D. \( \ln (\sqrt{2}+3) \)
Subject: Chemistry
An experiment was conducted by a
student and he obtained 3 values viz.
1.65,1.68 and \( 1.71, \) during three repetitive trials, respectively. After sometime, the student got the true value, which was 2.37 So, in the contrast to the real value, the
experiments' results should be characterized as:
A. not accurate and not precise
B. accurate but not precise
c. not accurate but precise
D. accurate, precise, but unreliable
Subject: Biology
Three of the following pairs of the human skeletal parts are correctly matched with their respective inclusive skeletal category and one pair is not matched. Identify the non-matching pair.
A. Malleus and stapes \( \rightarrow \) Ear ossicles
B. Sternum and ribs \( \rightarrow \) Axial Skeleton
C. Clavicle and glenoid cavity \( \rightarrow \) Pelvic girdle
D. Humerus and ulna \( \rightarrow \) Appendicuar skeleton
Subject: Chemistry
Which of the following oxidation numbers is not correctly matched?
A \( \cdot P \) in \( N a H_{2} P O_{4}=+5 \)
B. \( N i \) in \( \left[N i(C N)_{6}\right]^{4-}=+2 \)
\( \mathbf{c} \cdot P \) in \( M g_{2} P_{2} O_{7}=+6 \)
D. \( C r \) in \( \left(N H_{4}\right)_{2} C r_{2} O_{7}=+6 \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{rr}\mathbf{4} & \boldsymbol{x}+\mathbf{2} \\ \mathbf{2} \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{1}\end{array}\right] \) is symmetric
then what is x equal to?
\( \mathbf{A} \cdot \mathbf{5} \)
B. 3
\( c \cdot-1 \)
D. -
Subject: Chemistry
The rate law for the reaction below is
given by the expression \( \boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}] \)
\( A+B \rightarrow \) Product
If the concentration of \( B \) is increased
from 0.1 to 0.3 mole, keeping the value
of \( A \) at 0.1 mole, the rate constant will
be:
\( \mathbf{A} \cdot 3 k \)
B. \( 9 k \)
c. \( k / 3 \)
D.
Subject: Physics
Match the following
a) p-type
1) Pure semiconductor semiconductor
b) Intrinsic
2) Doped with impurity semiconductor
c) Extrinsic
3) majority carriers are semiconductor \( \quad \) electrons
d) \( n \) -type
4) majority carriers are semiconductor holes
\( A \cdot a-3, b-2, c-4, d-1 \)
B. \( a-1, b-2, c-4, d-3 \)
C. \( a-4, b-1, c-2, d-3 \)
D. \( a-2, b-1, c-4, d-3 \)
Subject: Chemistry
A dye absorbs a photon of wavelength lambda and re-emits the same energy
into two photons of wavelengths of \( \lambda_{1} \)
and \( \lambda_{2} \) respectively. The wavelength
lambda is related with \( \lambda_{1} \) and \( \lambda_{2} \) as:
\( A \cdot \lambda=\frac{\lambda_{1}+\lambda_{2}}{\lambda_{1} \lambda_{2}} \)
B. \( \lambda=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}} \)
\( c \cdot \lambda=\frac{\lambda_{1}^{2} \lambda_{2}^{2}}{\lambda_{1}+\lambda_{2}} \)
D. \( \lambda=\frac{\lambda_{1} \lambda_{2}}{\left(\lambda_{1}+\lambda_{2}\right)^{2}} \)
Subject: Chemistry
\( P C l_{5} \) dissociates according to the
reaction \( \boldsymbol{P} \boldsymbol{C l}_{5} \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \cdot \mathbf{A t} \)
\( \mathbf{5} \mathbf{2 3} \boldsymbol{K}, \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{1 . 7 8} \boldsymbol{a t m} . \) Find the
density of the equilibrium mixture at a total pressure of 1 atm.
A. 2.96 g/ml
B. 4.51 \( g / m \) ।
c. 6.73 g/ml
D. 3.44 g/ml
Subject: Physics
The primary of a transformer has 400
turns while the secondary has 2000 turns. If the power output from the secondary at \( 1000 V \) is \( 12 k W, \) what is
the primary voltage?
\( \mathbf{A} \cdot 200 V \)
B. \( 300 V \)
c. \( 400 V \)
D. \( 500 V \)
Subject: Physics
Statement-1: If the Earth suddenly contracts to \( \frac{1}{n} \) th of its present size without any change in its mass.

Statement-2:The duration of the new
day will be \( \frac{24}{n} \) hrs.
A. Statement-1 is True, Statement-2 is True; Statement-2
is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Maths
If a curve \( y=f(x) \) passes through the
point (1,-1) and satisfies the differential equation, \( \boldsymbol{y}(\mathbf{1}+\boldsymbol{x} \boldsymbol{y}) \boldsymbol{d} \boldsymbol{x}= \)
\( x d y, \) then \( f\left(-\frac{1}{2}\right) \) is equal to
Subject: Maths
Factorise :
\( (2 a+b)^{3}-(a+3 b)^{3} \)
A \( \cdot(a+b)\left(7 a^{2}+13 a b+13 b^{2}\right) \)
B . \( (a-2 b)\left(7 a^{2}+17 a b+13 b^{2}\right) \)
C \( \cdot(a-b)\left(7 a^{2}+13 a b+17 b^{2}\right) \)
D. \( (2 a-b)\left(7 a^{2}+17 a b+17 b^{2}\right) \)
Subject: Maths
Factorise :
\( 121 a c-16 a^{2} b^{2} \)
A \( \cdot a\left(121 c-16 a b^{2}\right) \)
В . \( a\left(121 c+16 a b^{2}\right) \)
\( \mathbf{c} \cdot a\left(121 c-16 a c^{2}\right) \)
D. none of these
Subject: Chemistry
\( \mathbf{2} C u_{2} S+\mathbf{3} O_{2}(g) \stackrel{h e a t}{\longrightarrow} \underline{a}+\underline{b} \)
A \( \cdot a=2 C u_{2} O, b=2 S O_{2} \)
В . \( a=4 C u O_{2}, b=2 S O_{3} \)
C \( . a=2 C u O, b=4 S O_{2} \)
D. \( a=3 C u S, b=2 S O_{2} \)
Subject: Biology
The total volume of air accommodated
in the lungs at the end of forced inspiration is known as Total Capacity(TLC). TLC is equal to (where, TV= Tidal volume, IRV =
Inspiratory reserve volume, ERV Expiratory reserve volume, RV= Residual volume)
A . TLC = ERV+ IRV+TV
B. TLC= TV+RV+ERV
c. \( \mathrm{TLC}=\mathrm{ERV}+\mathrm{RV} \)
D. TLC = ERV+IRV+TV+RV
Subject: Maths
Which of the following is always true?
\( \mathbf{A} \cdot \sim(p \rightarrow q) \equiv \sim p \wedge q \)
В . \( (p \vee q) \equiv \sim p \vee \sim q \)
c. \( \sim(p \Rightarrow q) \equiv(p \wedge \sim q) \)
D. \( (p \wedge q) \equiv \sim p \wedge \sim q \)
Subject: Physics
A rigid body in shape of a triangle has
\( \boldsymbol{v}_{\boldsymbol{A}}=\mathbf{5} \boldsymbol{m} / \boldsymbol{s}^{2} \) down, \( \boldsymbol{v}_{\boldsymbol{B}}=\mathbf{1 0 m} / \boldsymbol{s} \) down
Find velocity of point \( \boldsymbol{C} \)
\( \mathbf{A} \cdot 5 \hat{i}+10 \hat{j} \)
B . \( -5 \hat{i}-10 \hat{j} \)
c. \( -5 \hat{i}+10 \hat{j} \)
D. \( 5 \hat{i}-10 \hat{j} \)
Subject: Chemistry
\( A l+M n O_{4}^{-} \rightarrow A l(O H)_{4}^{-}+M n O_{2} \)
For this reaction, element \( X \) is reduced
and element Y is oxidised. Then \( X \) and
\( Y \) are respectively:
A. \( A l \) and \( M n \)
B. \( M n \) and \( A l \)
c. \( A l \) and \( A l \)
D. Mn and \( M n \)
Subject: Physics
In the figure, the potentiometer wire \( \boldsymbol{A} \boldsymbol{B} \)
of length \( L \) and resistnace \( 9 r \) is joined
to the cell \( D \) of e.m.f and internal
resistance \( r . \) The cell \( C^{\prime} \) s emf is \( \varepsilon / 2 \) and
its internal resistance is \( 2 r \)
The galvanometer \( G \) will show no
deflection when the length \( A J \) is
A. \( 4 L / 9 \)
B. \( 5 L / 9 \)
c. \( 7 L / 18 \)
D. \( 11 L / 18 \)
Subject: Physics
\( S_{1}, S_{2}, S_{3} \) are three concentric spherical
shells as shown in figure. \( S_{1} \) and \( S_{2} \) have
charge \( 4 Q \) and \( 8 Q \) respactively
Whereas \( S_{3} \) is unchanged. Find the
ratio of the flux passing through \( S_{1} \) to
that through \( S_{3} \)
A .1: 3
B . 1: 2
\( c \cdot 2: 1 \)
\( D \cdot 1: 6 \)
Subject: Maths
If \( a, b \in Z^{+} \) then maximum value of
\( \log \left[(x-a)^{a}(x-b)^{b}\right] \) occurs at \( x= \)
\( A \cdot \frac{a+b}{2} \)
B. \( \sqrt{a b} \)
c. \( \frac{2 a b}{a+b} \)
\( D \cdot a+b \)