AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Choose the correct structure for
propane.
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-\underset{O}{\|}-O H \)
c. \( C H_{3}-O-C_{3} H_{7} \)
D. \( C H_{3}-C-C H_{3} \)
॥
监
\( o \)
E \( \cdot C H_{3}-C H_{2}-N H_{2} \)
Subject: Physics
Two positive point charges of \( 12 \mu C \) and
\( 8 \mu C \) are \( 10 c m \) apart. The work done in
bringing them \( 4 c m \) closer is
A . \( 5.8 . J \)
B. \( 5.8 e V \)
c. \( 13 . J \)
D. \( 13 e V \)
Subject: Maths
Solve graphically the following pairs of
equations
\( 4 x-y-5=0 ; x+y-5=0 \)
\( \mathbf{A} \cdot(2,3) \)
B \( \cdot(3,3) \)
\( \mathbf{c} \cdot(4,3) \)
D. None of these
Subject: Chemistry
Assertion
Liquid molecule have greater potential
energy at the melting point
Reason
Intermolecular spacing between molecules increases at melting point
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
\( \boldsymbol{n} \) is an integer. The largest integer \( \boldsymbol{m} \)
such that \( n^{m}+1 \) divides \( 1+n+n^{2}+ \)
\( \dots . . n^{127}, \) is
A . 127
B. 63
c. 64
D. 32
Subject: Chemistry
Which solutions have a concentratoin of
\( 1.0 \mathrm{M} ? \)
i. 74 grams of calcium hydroxide dissolved to make 1 liter of
Solution
ii. 74.5 grams of potassium chloride dissolved to maek 1 liter of
Solution
iii. 87 grams of lithium bromide
dissolved to make 1 liter of solution
A. i only
B. iii only
c. i and iii only
D. ii and iii only
E. i, ii and iii
Subject: Physics
In a one-dimensional collision between
two identical particles \( \boldsymbol{A} \) and \( \boldsymbol{B} . \boldsymbol{B} \) is
stationary and \( A \) has momentum \( p \)
before impact. During impact, \( B \) gives
an impulse \( J \) to \( A \). Find the coefficient
of restitution between \( A \) and \( B ? \)
Subject: Maths
Prove that:
\[
\begin{array}{ccc}
\boldsymbol{a}+\boldsymbol{b}+\mathbf{2 c} & \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{b}+\boldsymbol{c}+\mathbf{2} \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{c}+\boldsymbol{a}+\boldsymbol{2} \boldsymbol{b}
\end{array} \mid=
\]
\( \mathbf{2}(\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c})^{3} \)
Subject: Maths
The reflection of the plane \( 2 x+3 y+ \)
\( 4 z-3=0 \) in the plane \( x-y+z- \)
\( \mathbf{3}=\mathbf{0} \) is the plane
A. \( 4 x-3 y+2 z-15=0 \)
B. \( x-3 y+2 z-15=0 \)
c. \( 4 x+3 y-2 z+15=0 \)
D. none of these
Subject: Maths
The sum of 1 st \( n \) terms of the series
\( \frac{1^{2}}{1}+\frac{1^{2}+2^{2}}{1+2}+\frac{1^{2}+2^{2}+3^{2}}{1+2+3}+\dots \dots \)
\( ^{\text {A } \cdot \frac{n+2}{3}} \)
в. \( \frac{n(n+2)}{3} \)
c. \( \frac{n(n-2)}{3} \)
D. \( \frac{n(n-2)}{6} \)
Subject: Maths
\( \left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right) \dots\left(1-\frac{1}{n}\right) \)
equals
A.
B. \( \frac{2}{n} \)
c. \( \frac{3}{n} \)
D.
Subject: Physics
An AC source is connected in parallel
with an L-C-R circuit as shown. Let
\( I_{S}, I_{L}, I_{C} \) and \( I_{R} \) denote the currents
through and \( V_{S}, V_{L}, V_{C} \) and \( V_{R} \)
voltages across the corresponding
components. Then:
A \( \cdot I_{S}=I_{L}+I_{C}+I_{R} \)
В. \( V_{S}=V_{L}+V_{C}+V_{R} \)
\( \mathbf{c} \cdot\left(I_{L}, I_{C}, I_{R}\right)<I_{S} \)
D. \( I_{L}, I_{C} \) may be greater than \( I_{S} \)
Subject: Physics
How much is the work done in pulling up a block of wood weighing \( 2 k N \) for a length of \( 10 m \) on a smooth plane
inclined at an angle of \( 30^{\circ} \) with the
horizontal?
A. \( 1.732 k J \)
\( J \)
в. \( 17.32 k J \)
c. \( 10 k J \)
D. 100kJ
Subject: Chemistry
A \( 0.1 ~ M \) aqueous solution of a weak
acid is \( 2 \% \) ionized. If the ionic product
of water is \( 1 \times 10^{-14}, \) the \( \left[O H^{-}\right] \) is:
A \( \cdot 5 \times 10^{-12} \mathrm{M} \)
В. \( 2 \times 10^{-3} \) М
c. \( 1 \times 0^{-14} \mathrm{M} \)
D. none of these
Subject: Maths
\( \int \frac{e^{\cot ^{-1} x}}{1+x^{2}}\left(x^{2}-x+1\right) d x \)
\( ^{A} \cdot \frac{e^{\cot ^{-1} x}}{1+x^{2}} \)
B. \( x \cdot e^{\cot ^{-1} x} \)
\( \mathbf{c} \cdot e^{\cot ^{-1} x} \)
D. \( -e^{\cot ^{-1} x} \)
Subject: Physics
In a thermodynamic processes during each cycle, a heat engine absorbs \( 400 \mathrm{J} \) of heat from a higher- temperature source and release 300 J of heat to the
low-temperature sink. Calculate the efficiency of heat engine?
\( A \cdot 1 \)
7
B. \( \frac{1}{4} \)
\( c \cdot \frac{3}{7} \)
D. \( \frac{4}{7} \)
\( E \)
1
Subject: Maths
The eccentricity of the ellipse \( \frac{x^{2}}{a^{2}}+ \) \( \frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}=1 \) if its latus-rectum is equal to
one half of its minor axis, is
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{1}{2} \)
D. None of these
Subject: Chemistry
Assertion
When a salt such as NaCl dissolves, the
\( N a^{+} \) and \( C l^{-} \) ions leaving the crystal
lattice acquire far greater freedom.
Reason
In thermodyanamic terms, the formation of solution occurs with a
favourable change in free energy, i.e.
\( \triangle H \) has a high positive value and \( T \triangle S \)
a low negative vaiue.
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
Assertion: The strength of an oxy acid increases when the choice of the central
atom is made from down a group.
Reason: The strength of an oxy acid increases with EN value of the central
atom
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: Maths
If \( \boldsymbol{2} \boldsymbol{x}=\boldsymbol{y}^{\frac{1}{5}}+\boldsymbol{y}^{-\frac{1}{5}} \) and \( \left(\boldsymbol{x}^{2}-\mathbf{1}\right) \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+ \)
\( \lambda x \frac{d y}{d x}+k y=0, \) then \( \lambda+k \) is equal to:
A . -23
в. -24
\( c \cdot 26 \)
D. -26
Subject: Chemistry
Assertion
Super oxide ion is paramagnetic whereas peroxide ion is diamagnetic.
Reason
Super oxide ion has one unpaired electron whereas per oxide ion has no unpaired electron.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
Two point white dots are \( 1 \mathrm{mm} \) apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at
which these dots can be resolved by the eye? [Take wave length of light =500 nm]
A . \( 10 \mathrm{m} \)
B. \( 5 \mathrm{m} \)
\( c \cdot 15 m \)
D. None of these
Subject: Physics
The self inductance of the toroidal
solenoid described in the passage is
\( ^{A} \cdot \frac{\mu_{0} N^{2} h}{2 \pi} \)
B. \( \frac{\mu_{0} N^{2} h}{2 \pi} \log _{e} \frac{b}{a} \)
c. \( \frac{\mu_{0} N h}{2 \pi} \log _{e} \frac{b}{a} \)
D. \( \frac{\mu_{0} N^{2} h}{2 \pi} \log _{e} \frac{a}{b} \)
Subject: Maths
The equation of the tangent to the curve \( y=\sqrt{9-2 x^{2}} \) at the point where the
ordinate and abscises are equal is?
A. \( 2 x+y-3 \sqrt{3}=0 \)
В. \( 2 x+y+3 \sqrt{3}=0 \)
c. \( 2 x-y-3 \sqrt{3}=0 \)
D. \( 2 x-y+3 \sqrt{3}=0 \)
Subject: Maths
Find the area of the region bounded by
the curve \( y^{2}=x \) and the lines \( x= \)
\( 1, x=4 \) and the \( x \) -axis
\( A \cdot \frac{8}{3} \)
в. \( \frac{14}{3} \)
\( c \cdot \frac{7}{3} \)
D. \( \frac{1}{3} \)
Subject: Chemistry
If the pH of \( 0.2 M \) dibasic acid \( \left(H_{2} A\right) \)
is \( 1.699, \) than its osmotic pressure at \( T \) K temperature will be?
в. \( 0.02 R T \)
c. \( 0.4 R T \)
D. \( 0.1 R T \)
Subject: Maths
\( \operatorname{Let} A(a \cos \theta, 0), B(0, a \sin \theta) \) be any
two points then the distance between two points is
A. \( |a| \) units
B . \( a^{2} \) units
c. \( \sqrt{a} \) units
D. \( \sqrt{2} a \) units
Subject: Chemistry
Which is the correct sequence in the following properties? For the correct order mark(T) and for the incorrect
order mark (F):
(a) Lewis acidity order: \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{F}_{4}< \)
\( \boldsymbol{S} \boldsymbol{i} \boldsymbol{C l}_{4}<\boldsymbol{S} \boldsymbol{i} \boldsymbol{B} \boldsymbol{r}_{4}<\boldsymbol{S} \boldsymbol{i} \boldsymbol{I}_{4} \)
(b) Melting point: \( N H_{3}>S b H_{3}> \)
\( \boldsymbol{A} \boldsymbol{s} \boldsymbol{H}_{3}>\boldsymbol{P} \boldsymbol{H}_{3} \)
(c) Boiling point \( : N H_{3}>S b H_{3}> \)
\( \boldsymbol{A} \boldsymbol{s} \boldsymbol{H}_{3}>\boldsymbol{P} \boldsymbol{H}_{3} \)
(d) Dipole moment order : \( N H_{3}> \)
\( \boldsymbol{S b H}_{3}>\boldsymbol{A s H}_{3}>\boldsymbol{P H}_{3} \)
A. FTFT
в. TFTF
c. FFTT
D. FFTF
Subject: Physics
An electric dipole consist of two opposite charges each of magnitude \( 1 \mu C \) separated by a distance of \( 2 \mathrm{cm} \) The dipole is placed in an external field of \( 10^{5} \mathrm{N} / \) C.The maximum torque on the
dipole is:
A. \( 2 \times 10^{-4} J \)
B . \( 2 \times 10^{-3} J \)
c. \( 4 \times 10^{-3} J \)
D. \( 10^{-3} N m \)
Subject: Physics
A mercury drop of radius \( 1 \mathrm{cm} \) is
sprayed into \( 10^{6} \) drops of equal size. The
energy expended in joule is (surface tension of mercury is \( 460 x 10^{-3} \mathrm{N} / \mathrm{m} \) ):
A. 0.057
B. 5.7
c. \( 5.7 \times 10^{-4} \)
D. \( 5.7 \times 10^{-6} \)
Subject: Physics
A very long (length \( L \) ) cylindrical galaxy is made of uniformly distributed mass and has radius \( R(R<<L) . \) A star
outside the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time
period of star is \( T \) and its distance from
the galaxy s axis is \( r, \) then:
A \( \cdot T^{2} \propto r^{3} \)
B. \( T \propto r \)
c. \( T \propto r^{2} \)
D. \( T \propto \sqrt{r} \)
Subject: Chemistry
Assertion
Both o-hydroxy benzaldehyde and phydroxy benzaldehyde have same molecular weight and show H-bonding.
Reason

Melting point of p-hydroxy benzaldehyde is more than o-hydroxy benzaldehyde.
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
As shown in the figure, \( P \) and \( Q \) are two coaxial conducting loops separated by
some distance. When the switch \( S \) is
closed, a clockwise current \( l_{p} \) flows in \( P \)
(as seen by \( E \) ) and an induced current
\( l_{Q 1} \) flows in \( Q . \) The switch remains
closed for a long time. When \( S \) is
opened, a current \( l_{Q 2} \) flows in \( Q \). Then
the direction \( l_{Q 1} \) and \( l_{Q 2}(\text { as seen by } E) \)
are
A. respectively clockwise and anti-clockwise
B. both clockwise
\( c . \) both anti-clockwise
D. respectively anti-clockwise and clockwise
Subject: Maths
\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) where \( \boldsymbol{a} \neq \mathbf{0} . \) Then
\( \boldsymbol{A}^{n}=? \)
\( A^{n}=\left[\begin{array}{cc}a^{n} & \frac{b\left(a^{n}-1\right)}{(a-1)} \\ 0 & 1\end{array}\right] \)
\( A^{n}=\left[\begin{array}{cc}\frac{a\left(b^{n}-1\right)}{(b-1)} & \frac{b\left(a^{n}-1\right)}{(a-1)} \\ 0 & 1\end{array}\right] \)
\( ^{\mathbf{C}}, \quad A^{n}=\left[\begin{array}{cc}a^{n} & b^{n} \\ 0 & 1\end{array}\right] \)
D. none of these
Subject: Chemistry
Dry air was drawn through bulbs containing a solution of 40 grams of
urea in 300 grams of water, then through bulbs containing pure water at the same temperature and finally through a tube in which pumice
moistened with strong \( H_{2} S O_{4} \) was kept. The water bulbs lost
\( 0.0870 g r a m s \) and the sulphuric acid
tube gained 2.036 grams. Calculate the
molecular weight of urea.
A. \( \quad M=26.9 \)
В. \( \quad M=46.8 \)
c. \( \quad M=53.8 \)
D. \( M=93.6 \)
Subject: Physics
A ball is thrown vertically upwards from the ground. It crosses a point at the height of \( 25 m \) twice at an interval of
4 secs. The ball was thrown with the
velocity of
A. \( 20 \mathrm{m} / \mathrm{sec} \)
B. \( 25 \mathrm{m} / \mathrm{sec} \)
c. \( 30 m / \)sec.
D. \( 35 \mathrm{m} / \mathrm{sec} \)
Subject: Maths
Let the observations \( x_{i}(1 \leq i \leq 10) \) satisfy the equations, \( \sum_{i=1}^{10}\left(x_{i}-5\right)=10 \) and \( \sum_{i=1}^{10}\left(x_{i}-5\right)^{2}=40 . \) If \( \mu \) and \( \lambda \) are the mean and the variance of the
observations, \( x_{1}-3, x_{2}-3, \dots ., x_{10} \)
3, then the ordered pair \( (\mu, \lambda) \) is equal
to?
A . (6,6)
в. (3,6)
\( c .(3,3) \)
D. (6,3)
Subject: Chemistry
The degree of dissociation of \( \boldsymbol{P C l}_{5}(\boldsymbol{\alpha}) \)
obeying the equilibrium \( \boldsymbol{P} \boldsymbol{C l}_{5} \rightleftharpoons \)
\( P C l_{3}+C l_{2} \) is related to the
equilibrium pressure by
A \( \cdot \alpha \propto \frac{1}{P^{4}} \)
B. \( \quad \alpha \propto \frac{1}{\sqrt{P}} \)
c. \( \quad \alpha \propto \frac{1}{P^{2}} \)
D. \( \alpha \propto P \)
Subject: Physics
A particle of mass \( m \) and negative
charge \( q \) is thrown in a gravity free
space with speed \( u \) from the point \( A \) in the large nonconducting charged sheet with surface charge density \( \sigma, \) as
shown in figure. The maximum
distance from \( A \) on sheet where the
particle can strike is \( \frac{\boldsymbol{x} \epsilon_{0} \boldsymbol{u}^{2} \boldsymbol{m}}{\boldsymbol{q} \boldsymbol{\sigma}} . \) Find \( \boldsymbol{x} \)
Subject: Maths
If \( \boldsymbol{x y}=\boldsymbol{e}^{\boldsymbol{x}-\boldsymbol{y}} \) then
This question has multiple correct options
A \( \cdot \frac{d y}{d x} \) doesn't exist at \( x=0 \)
B. \( \frac{d y}{d x}=0 \) when \( x=1 \)
C. \( \frac{d y}{d x}=\frac{1}{2} \) when \( x=0 \)
D. none of these
Subject: Maths
The standard deviation of variate \( \boldsymbol{x}_{\boldsymbol{i}} \) is \( \boldsymbol{\sigma} \)
Then standard deviation of the variate \( \frac{a x_{i}+b}{c}, \) where \( a, b, c \) are constants is
A \( \cdot\left(\frac{a}{c}\right)^{\sigma} \)
в. \( \left|\frac{a}{c}\right| \sigma \)
\( ^{\mathrm{c}} \cdot\left(\frac{a^{2}}{c^{2}}\right) \sigma \)
D. none of these
Subject: Physics
If \( u \) denotes 1 atomic mass unit. One
atom of an element has mass exactly equal to \( A u, \) where \( A \) is mass number
of element.
\( \mathbf{A} \cdot A=1 \)
B. \( A=12 \)
c. \( A=16 \)
D. \( A \) can take up any integral value from 1 to 110
Subject: Physics
A capacitor of capacity \( 10 \mu F \) is
charged to a potential of \( 10000 \mathrm{V} \) and a
wire is stretched by \( 0.2 m \) by a force of
\( \mathbf{5 0 0 0} N . \) The ration of the potential energies stored in them will be
A . 1
в. 500
c. 0.002
D. 0.0001
Subject: Maths
Find the value of \( m \) for which
(i) \( 5^{m} \div 5^{-3}=5^{5} \)
(ii) \( 4^{m}=64 \)
(iii) \( 8^{m-3}=1 \)
(iv) \( \left(a^{3}\right)^{m}=a^{9} \)
(v) \( \left(5^{m}\right)^{2} \times(25)^{3} \times 125^{2}=1 \)
\( (\mathrm{vi}) 2^{m}=(8)^{\frac{1}{3}} \div\left(2^{3}\right)^{2 / 3} \)
Subject: Chemistry
The orbital angular momentum and
angular momentum (classical
analogue) for the electron of \( 4 s \) -orbita
are respectively, equal to:
A \( \cdot \sqrt{12} \frac{h}{2 \pi} \) and \( \frac{h}{2 \pi} \)
B. zero and \( \frac{2 h}{\pi} \)
c. \( \sqrt{6} h \) and \( \frac{2 h}{\pi} \)
D. \( \sqrt{2} \frac{h}{2 \pi} \) and \( \frac{3 h}{2 \pi} \)
Subject: Physics
The quantityjerk, \( j, \) is defined as the
time derivative of an objects acceleration, \( \boldsymbol{J}=\frac{\boldsymbol{d} \boldsymbol{a}}{\boldsymbol{d} \boldsymbol{t}}=\frac{\boldsymbol{d}^{\boldsymbol{3}} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{t}^{3}} \)
What is the physical meaning of the area under a graph of jerk versus time?
A. The area represents the object's change in acceleration.
B. The area represents the object's acceleration.
c. The area represents the object's change in velocity.
D. The area represents the object's velocity.
Subject: Maths
Assertion
If trace of the matrix
\( \left[\begin{array}{cccc}\boldsymbol{x}-\mathbf{5} & \boldsymbol{0} & \boldsymbol{2} & \boldsymbol{4} \\ \boldsymbol{3} & \boldsymbol{x}^{\boldsymbol{2}}-\boldsymbol{1 0} & \boldsymbol{6} & \boldsymbol{1} \\ -\boldsymbol{2} & \boldsymbol{3} & \boldsymbol{x}-\boldsymbol{7} & \boldsymbol{1} \\ \boldsymbol{1} & \boldsymbol{2} & \boldsymbol{0} & \boldsymbol{-} \boldsymbol{2}\end{array}\right] \)
zero,then value of \( x \) is -6 or 4
Reason
Distinct roots of a quadratic equation
\( a x^{2}+b x+c=0 \) are possible if
discriminant of the equation is positive
i.e, \( b^{2}-4 a c>0 \)
A. Both (A) \& (R) are individually true \& (R) is correct explanation of \( (A) \)
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of \( (A) \)
C. (A)is true but (R) is false,
D. (A)is false but (R) is true.
Subject: Maths
\( \int\left(\frac{4 e^{x}-25}{2 e^{x}-5}\right) d x=A x+ \)
\( \boldsymbol{B} \log \left|\mathbf{2} e^{x}-\mathbf{5}\right|+\boldsymbol{c}, \) then
A. \( A=5, B=3 \)
В. \( A=5, B=-3 \)
\( \mathbf{c} \cdot A=-5, B=3 \)
D. \( A=-5, B=-3 \)
Subject: Physics
The force on a particle of mass 10 g is \( (10 \hat{i}+5 \hat{j}) N . \) if it starts from rest, what would be its position at time \( t=5 s ? \)
A . \( 12500 \hat{i}+6250 \hat{j} \mathrm{m} \)
B. 6250\hat \( +12500 \hat{j} \mathrm{m} \)
c. \( 12500 \hat{i}+12500 \hat{j} \mathrm{m} \)
D. 6250\hat + 6250\hat m
Subject: Maths
A 15 liter of a mixture contains \( 20 \% \)
alcohol and rest water. if 3 liter of water
is added in it, find the \( \% \) of alcohol in
the new mixture.
A . \( 16.66 \% \)
B. 26.66\%
c. \( 15 \% \)
D. \( 20 \% \)
Subject: Physics
The potential energy of an object of a mass m moving in xy plane in a conservative field is given by U=ax+by, where \( x \) and \( y \) are position coordinates of the object. Find magnitude of acceleration :-
A \( \cdot \frac{\sqrt{a^{2}+b^{2}}}{2 m} \)
\( ^{\text {В } \cdot \frac{a^{2}+b^{2}}{m}} \)
c. \( \sqrt{a^{2}+b^{2}} \)
D. None
Subject: Maths
Prove that \( \triangle= \)
\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} & \boldsymbol{0}\end{array}\right|=\boldsymbol{0} \) if \( \mathbf{a}, \mathbf{b}, \mathbf{c} \)
\( \operatorname{arcin} \mathrm{G} . \mathrm{P} \)
Subject: Maths
Find the equation of the line parallel to \( 2 \bar{i}-\bar{j}+2 \bar{k} \) and which passes through
point \( ^{\prime} A^{\prime}(3 \bar{i}+\bar{j}-\bar{k}) . \) if \( P \) is a point on
the line such that \( A P=15 . \) Find the
position vectors of \( \boldsymbol{P} \)
Subject: Physics
A bus travelling the first one third distance at a speed of \( 10 k m / h \), the next one third at20km/ \( h \) and the last
one third at \( 60 k m / h . \) The average speed of the bus is
\( \mathbf{A} \cdot 9 k m / h \)
в. \( 16 k m / h \)
c. \( 18 k m / h \)
D. \( 48 k m / h \)
Subject: Chemistry
Hydrated sulphate of a divalent metal of atomic weight 65.4 loses \( 43.85 \% \) of its weight on dehydration. Find the number of molecules of water of crystallisation in the formula of hydrated salt.
A. \( M S O_{4} \cdot 16 H_{2} O \)
в. \( M S O_{4} \cdot 5 H_{2} O \)
\( \mathrm{c} \cdot M S O_{4} \cdot 10 H_{2} O \)
D. \( M S O_{4} \cdot 12 H_{2} O \)
Subject: Physics
A ray of light in a liquid of refractive
index 1.4 approaches the boundary surface between the liquid and air at an
angle of incidence whose sine is 0.8 Which of the following statement is correct about the behaviour of the light?
A. It is impossible to predict the behaviour of the light ray on the basis of the information supplied
B. The sine of the angle of refraction of the emergent ray will be less than 0.8
C. The ray will be internally reflected
D. The sine of the angle of refraction of the emergent ray will be greater than 0.8
Subject: Physics
A \( 2 m m^{2} \) cross-sectional area wire is
stretched by \( 4 \mathrm{mm} \) by a certain weight.If
the same material wire of cross-
sectional area \( 8 m m^{2} \) is stretched by
the same weight, the stretched length
is
\( A \cdot 2 m m \)
B. \( 0.5 \mathrm{mm} \)
\( \mathrm{c} \cdot 1 \mathrm{mm} \)
D. \( 1.5 \mathrm{mm} \)
Subject: Physics
The value of acceleration due to gravity at height \( h \) from earth surface will
become half its value on the surface if
\( (R=\text { radius of earth }) \)
\( \mathbf{A} \cdot h=R \)
в. \( h=2 R \)
c. \( h=(\sqrt{2}-1) R \)
D. \( h=(\sqrt{2}+1) R \)
Subject: Chemistry
The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}}(\text { in atm }) \) for the reaction is 9 at 7 atm and \( 300 \mathrm{K} \)
\( \boldsymbol{A}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{B}_{2}(\boldsymbol{g})+\boldsymbol{C}_{2}(\boldsymbol{g}) \cdot \) Calculate the
average molar mass (in gm/mol)of an equilibrium mixture. Given: Molar mass
of \( A_{2}, B_{2} \) and \( C_{2} \) are \( 70,49 \& 21 \mathrm{gm} / \mathrm{mol} \)
respectively.
\( \mathbf{A} \cdot 50 \)
B . 45
c. 40
D. 37.5
Subject: Biology
Assertion
Systematics is the branch of biology
that deals with classification of living organisms.
Reason
The aim of classification is to group the
organisms.
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
ABCD is a square frame of side \( l \). The
force at B if charges as shown in figure
are placed at the corners of the square
will be:
A \( \cdot \frac{q^{2}(2 \sqrt{2}-1)}{4 \pi \varepsilon_{0} 2 l^{2}} \)
B. \( \frac{q^{2}(2 \sqrt{2}+1)}{4 \pi \varepsilon_{0} l^{2}} \)
c. \( \frac{q^{2}(2 \sqrt{2}-1)}{4 \pi \varepsilon_{0} l^{2}} \)
D. \( \frac{q^{2}(2 \sqrt{2}+1)}{4 \pi \varepsilon_{0} 2 l^{2}} \)
Subject: Physics
A step down transformer changes the
high input voltage used in our houses \( (120 V) \) into the low voltage used to charge an electric razor \( (24 V) . \) What must be the ratio of the turns of wire
from the primary side of the transformer to the secondary side?
A . 1: 5
в. 2: 7
\( c \cdot 1: 8 \)
D. 2: 9
E .1: 10
Subject: Chemistry
Calculate the degree of ionization of
\( 0.05 \mathrm{M} \) acetic acid of its \( _{p} \boldsymbol{K}_{a} \) value is 4.74. How is the degree of dissociation affected when its solution is also (a)
\( 0.01 \mathrm{M} \) and
(b) \( 0.1 \mathrm{M} \) in hydrochloric acid?
Subject: Physics
A machine gun fires bullets of \( 50 \mathrm{gm} \) at the speed of \( 1000 \mathrm{m} / \mathrm{sec} . \) If an average force of \( 200 \mathrm{N} \) is exerted on the gun, the maximum number of bullets fired per
minutes is:
A . 240
B. 180
\( c \cdot 60 \)
D. 30
Subject: Maths
Using properties of determinants, find
the following:
\( \left|\begin{array}{ccc}\boldsymbol{\alpha} & \boldsymbol{\beta} & \boldsymbol{\gamma} \\ \boldsymbol{\alpha}^{2} & \boldsymbol{\beta}^{2} & \boldsymbol{\gamma}^{2} \\ \boldsymbol{\beta}+\boldsymbol{\gamma} & \boldsymbol{\gamma}+\boldsymbol{\alpha} & \boldsymbol{\alpha}+\boldsymbol{\beta}\end{array}\right| \)
A \( \cdot(\alpha+\beta)(\beta+\gamma)(\gamma-\alpha)(\alpha+\beta+\gamma) \)
B . \( (\alpha-\beta)(\beta-\gamma)(\gamma-\alpha)(\alpha+\beta+\gamma) \)
c.
D. None of these