AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A piece of wood collected from Cro Magnon caves gave 4 dpm. A freshly cut wood of the same weight gives \( 16 d p m \)
The cro magnon man lived about
years ago
(Half life of \( C^{14} \) is 5760 years. Assume
the activity is due to \( C^{14} \) only
A .5700
в. 2900
c. 11520
D. 1400
Subject: Physics
The focal lengths of the eyepiece and an objective lens of a compound microscope are \( 10 \mathrm{cm} \) and \( 20 \mathrm{cm} \) respectively. if the length of the tube is \( 100 \mathrm{cm}, \) what is the magnification obtained at the least distance of
distinct vision?
A . 25
в. 17.5
c. 50
D. 60
Subject: Chemistry
If \( \triangle \boldsymbol{H}_{\text {vaporisation}} \) of substance \( \boldsymbol{X}(\boldsymbol{l}) \)
(molar mass: \( 30 g / m o l \) ) is \( 300 J / g \) at
it's boiling point \( 300 K \), then molar entropy change for reversible condensation process
is
A. \( 30 J / \) mol. \( K \)
в. \( -300 \mathrm{J} / \mathrm{mol.K} \)
c. \( -30 \mathrm{J} / \mathrm{mol} . \mathrm{K} \)
D. None of these
Subject: Physics
A rubber develops a force \( \boldsymbol{F}=(-2 x+ \)
1) \( N, \) (Where \( x \) is the extension in its
natural length in \( m \) ). Work done by the force when rubber is stretched from
\( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=\mathbf{1} \boldsymbol{m} \) is :
A . \( 4 J \)
B. \( 8 J \)
c. \( Z \) ero
D. \( 10 J \)
Subject: Physics
\( \ln \) an \( A C \) circuit, the potential difference
\( \boldsymbol{V} \) and current \( \boldsymbol{I} \) are given respectively by \( \boldsymbol{V}=\mathbf{1 0 0} \sin (\mathbf{1 0 0} \boldsymbol{t}) \boldsymbol{V} \)
and \( \boldsymbol{I}=\mathbf{1 0 0} \sin \left(\mathbf{1 0 0 t}+\frac{\boldsymbol{\pi}}{\mathbf{3}}\right) \boldsymbol{m} \boldsymbol{A} \)
The power dissipated in the circuit will be
A \( \cdot 10^{4} K W \)
в. \( 10 K W \)
c. \( 2.5 K W \)
D. \( 5 K W \)
Subject: Physics
White light reflected at normal incidence from a soap film has minima
at \( 6500 A \) and maxima at \( 7500 A \) in the
visible region with not minima in between. If \( \mu \) is \( \frac{5}{3} \) for the thin film, the thickness of film is :
A \( \cdot 7.40 \times 10^{-7} \mathrm{cm} \)
B. \( 9.75 \times 10^{-5} \mathrm{mm} \)
c. \( 9.70 \times 10^{-7} \mathrm{cm} \)
D. \( 9.75 \times 10^{-4} \mathrm{mm} \)
Subject: Maths
Given \( \boldsymbol{A}=\{\mathbf{5}, \mathbf{6}, \mathbf{7}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}\} \)
Form all possible ordered pairs and write the total number of ordered pairs formed. So that the first component is from \( \mathrm{B} \) and second is from \( \mathrm{A} \)

Find the total number of such pairs.
Subject: Chemistry
What is the quantity of NaOH present in \( 250 \mathrm{cc} \) of the solution, so that it gives a
\( \mathrm{pH}=13 ? \)
A \( \cdot 10^{-13} \mathrm{g} \)
B . \( 10^{-1} \mathrm{g} \)
\( c .1 .0 \mathrm{g} \)
D. \( 4.0 \mathrm{g} \)
Subject: Physics
A' block 'B' is pushed momentarily along a horizontal surface with an
initial velocity ' \( v \) '. If ' \( \mu \) ' is the coefficient of friction between 'B' and the surface,
block 'B' will come to rest after a time
A \( \cdot \frac{v}{g \mu} \)
в. \( \frac{g \mu}{v} \)
\( c \cdot \frac{g}{v} \)
D. \( \frac{v}{g} \)
Subject: Chemistry
Name the following compounds according to IUPAC system of
nomenclature:
(i) \( \boldsymbol{C H}_{3} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H O} \)
(ii)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O C H}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right) \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C l} \)
(iii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H C H O} \)
(iv) \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{2} \boldsymbol{C O C H}_{3} \)
\( (v) \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H}_{2} \boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C O C H}_{3} \)
(vi) \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C C H}_{2} \boldsymbol{C O O H} \)
\( \left(\text { vii) } \boldsymbol{O} \boldsymbol{H} \boldsymbol{C} \boldsymbol{C}_{6} \boldsymbol{H}_{4} \boldsymbol{C H} \boldsymbol{O}-\boldsymbol{p}\right. \)
Subject: Physics
In a uniform magnetic field of induction
\( B, \) a wire in the form of semicircle of
radius \( r \) rotates about the diameter of
the circle with angular velocity \( \omega . \) If the total resistance of the circuit is \( \boldsymbol{R} \)
the mean power generated per period of rotation is :
A. \( \frac{B \pi r^{2} \omega}{2 R} \)
B. \( \frac{\left(B \pi r^{2} \omega\right)^{2}}{8 R} \)
C. \( \frac{(B \pi r \omega)^{2}}{2 R} \)
D. \( \frac{\left(B \pi r \omega^{2}\right)^{2}}{8 R} \)
Subject: Physics
A particle (1) of mass m initially at A is at rest. The radius of circular path is 1
m. The particle (1), collides at bottom
with an other particle (2) of same mass
m. The distance travelled by the particle
(2) before coming at rest is
\( 4.1 .5 \mathrm{m} \)
B. 2.5
\( c .3 .5 \mathrm{m} \)
\( D \)
Subject: Biology
a) The diagram below shows the
excretory system of a human being.
Study the same and then answer the
questions that follow.
i) Name the parts labelled 1,2,3 and 4
ii) Give the main function of the parts
labelled 5,6,7 and 8
iii) Name the endocrine gland which
could be added in the diagram and
state its location/position.
Subject: Maths
\( \frac{C_{0}}{1}+\frac{C_{1}}{2}+\frac{C_{2}}{3}+\ldots \ldots+\frac{C_{10}}{11}= \)
A \( \cdot \frac{2^{11}}{11} \)
B. \( \frac{2^{11}-1}{11} \)
c. \( \frac{3^{11}}{11} \)
D. \( \frac{3^{11}-1}{11} \)
Subject: Maths
In a parallelogram \( A B C D, A B=10 \mathrm{cm} \) and
\( A D=6 \mathrm{cm} . \) The bisector of \( A \) meets DC in
E. AE and BC produced meet at F. Find the length of CF.
\( A \cdot 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 5 \mathrm{cm} \)
\( D \cdot 6 \mathrm{cm} \)
Subject: Physics
In solar cells, a silicon solar cell \( (\mu= \)
3.5) is coated with a thin film of silicon
monoxide \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}(\boldsymbol{\mu}=\mathbf{1 . 4 5}) \) to minimise
reflective losses from the surface.
Determine the minimum thickness of
SiO that produces the least reflection
at a wavelength of \( 550 n m, \) near the centre of the visible spectrum.
Subject: Physics
Potential energy of a bar magnet, of magnetic moment M is placed in a magnetic filed of induction B such that
it makes an angle \( \theta \) with the direction of B is?
\( \mathbf{A} \cdot M B \sin \theta \)
B. \( -M B \cos \theta \)
c. \( M B(1-\cos \theta) \)
D. \( M B(1+\cos \theta) \)
Subject: Chemistry
According to Bohr's theory of hydrogen atom, the product of the binding energy of the electron in \( n^{t h} \) orbit and the
radius of the \( n^{t h} \) orbit :
A . is proportional to \( n^{2} \)
B . is inversely proportional to \( n^{3} \)
c. has a constant value of \( 10.2 e V A^{0} \)
D. has a constant value of \( 7.2 e V A^{0} \)
Subject: Physics
A stone is tied to the middle of a string
and suspended from one end as shown
in the figure. Here \( \mathrm{S} \) is the stone and 0 is the pint of suspension
(ii) if we increase the pull at \( \mathrm{P} \)
gradually, the string will break
A. Below the stone
B. At the point P itself
c. Above the stone
D. Nothing can be decided
Subject: Maths
\( \mathbf{f}\left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} & \boldsymbol{0}\end{array}\right|=\mathbf{0} . \) Prove
that \( a, b, c \) are in G.P. or \( \alpha \) is a root of
\( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\mathbf{0} \)
Subject: Maths
The sum of the real roots of the
equation \( |\boldsymbol{x}-\mathbf{2}|^{2}+|\boldsymbol{x}-\mathbf{2}|-\mathbf{2}=\mathbf{0} \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.
Subject: Chemistry
For which of the following processes,
\( \Delta S \) is negative?
A \( \cdot N_{2}(g, 273 K) \rightarrow N_{2}(g, 300 K) \)
B. \( N_{2}(g, 1 \text { 1atm }) \rightarrow N_{2}(g, \text { 5atm }) \)
c. \( C(\text {diamond}) \rightarrow C(\text {graphite}) \)
D. \( H_{2}(g) \rightarrow 2 H(g) \)
Subject: Chemistry
Which of the following statements is
false?
A \( \cdot \) At temperature equal to \( \frac{a}{R b} \) (where a and b are vander Waal's constant). real gases obey ideal gas laws over an appreciable range of pressure
B. Most probable speed of a gas is always greater than its average speed
C. Dalton's law of partial pressure is not valid for reacting gases
D. A gas cannot be liquified above its critical temperature
Subject: Physics
A charge 10 esu is placed at a distance of \( 2 \mathrm{cm} \) from a charge 40 esu and \( 4 \mathrm{cm} \)
from another charge of 20 esu. The potential energy 10 esu in ergs is
A. 87.5
в. 112.5
\( c \cdot 150 \)
D. 250
Subject: Maths
If the lines \( y=m_{1} x+c \) and \( y= \)
\( \boldsymbol{m}_{2} \boldsymbol{x}+\boldsymbol{c}_{2} \) are parallel, then
A. \( m_{1}=m_{2} \)
в. \( m_{1} m_{2}=1 \)
c. \( m_{1} m_{2}=-1 \)
D. \( m_{1}=m_{2}=0 \)
Subject: Maths
Assertion
If \( \boldsymbol{x}^{2}-\boldsymbol{p} \boldsymbol{x}+\boldsymbol{q}=\mathbf{0} \) where \( \boldsymbol{p} \) is twice the
tangent of the arithmetic mean of
\( \sin ^{-1} x \) and \( \cos ^{-1} x ; \) q is the geometric
mean of \( \tan ^{-1} x \) and \( \cot ^{-1} x \) then \( x=1 \)
Reason
\( \tan \left(\sin ^{-1} x+\cos ^{-1} x\right)=1 \)
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
If \( a, b, c \) are in A.P. \( b-a, c-b \) and \( a \) in
G.P., then \( \boldsymbol{a}: \boldsymbol{b}: \boldsymbol{c} \) is
A . 1: 2: 3
B. 1: 3: 5
\( c \cdot 2: 3: 4 \)
D. None of these
Subject: Maths
Solve the following:
f \( \boldsymbol{L}=\mathbf{1 0}, \boldsymbol{f}_{1}=\mathbf{7} \mathbf{0}, \boldsymbol{f}_{0}=\mathbf{5 8}, \boldsymbol{f}_{2}= \)
\( 42, h=2, \) then find the mode by using
formula.
Subject: Maths
Construct a \( \triangle A B C \) in which \( B C= \)
\( \mathbf{7} \boldsymbol{c m} \angle \boldsymbol{B}=\mathbf{7} \mathbf{5}^{\boldsymbol{o}} \boldsymbol{\&} \boldsymbol{A} \boldsymbol{B}+\boldsymbol{A C}=\mathbf{1 3} \boldsymbol{c m} \)
Subject: Biology
Study the following figures and select
the correct statements regarding these.
(i) A shows mode of asexual
reproduction in sponges through internal buds.
(ii) B shows sexual reproduction
through zoospores in Chlamydomonas.
(iii) \( \mathrm{C} \) shows asexual reproduction through conidiospores in Penicillium.
(iv) D shows external budding in Sycon.
A. (i) and (ii)
B. (i) and (iii)
c. (ii), (iii), and (iv)
D. (i), (iii) and (iv)
Subject: Physics
Out of the following equations which is
WRONG?
A \( \cdot \vec{\tau}=\vec{r} \times \vec{F} \)
B . \( \vec{a} r=\vec{\omega} \times \vec{v} \)
c. \( \vec{a} t=\vec{\alpha} \times \vec{r} \)
\( \mathbf{D} \cdot \vec{v}=\vec{r} \times \vec{\omega} \)
Subject: Chemistry
The specific conductance of a
\( N / 10 K C I \) at \( 25^{0} C \) is
0.0112 oh \( m^{-1} c m^{-1} . \) The resistance of
cell containing solution at the same temperature was found to be 55ohms.
The cell constant will be:
A \( \cdot 6.16 \mathrm{cm}^{-1} \)
B. \( 0.616 c m^{-1} \)
c. \( 0.0616 \mathrm{cm}^{-1} \)
D. \( 616 \mathrm{cm}^{-1} \)
Subject: Physics
\( \ln C H_{4} \) molecule, there are four \( C-H \)
bonds. If two adjacent bonds are in \( \hat{\mathbf{i}}+ \) \( \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) direction, then find
the angle between these bonds.
A \( \cdot \sin ^{-1}\left(\frac{-1}{3}\right) \)
B. \( \cos ^{-1}\left(\frac{1}{3}\right) \)
\( ^{c} \cdot \sin ^{-1}\left(\frac{1}{3}\right) \)
D. \( \cos ^{-1}\left(\frac{-1}{3}\right) \)
Subject: Maths
Find the value of the determinant
\( \left|\begin{array}{cc}\mathbf{2} \boldsymbol{i} & -\mathbf{3} \boldsymbol{i} \\ \boldsymbol{i}^{3} & -\mathbf{2} \boldsymbol{i}\end{array}\right| \) where \( \boldsymbol{i}=\sqrt{-\boldsymbol{i}} \)
Subject: Chemistry
Which of the following statement is
true?
A. Diethyl ether is almost as soluble in water as n-butyl alcohol
B. Diethyl ether is more soluble in water than n-butyl alcohol.
C. Diethyl ether is less soluble in water than n-butyl alcohol.
D. Diethyl ether is sparingly soluble in water whereas \( n \) butyl alcohol is highly soluble in water.
Subject: Physics
When a small mass \( m \) is suspended at
lower end of the elastic wire having upper end fixed with ceiling. There is loss in gravitational potential energy.
let it be \( x, \) due to extension of wire,
mark correct option,
A. The lost energy can be recovered
B. The lost energy can be irrecoverable
C . only \( \frac{x}{2} \) amount of energy recoverable
D. only \( \frac{x}{3} \) amount of energy recoverable
Subject: Chemistry
Hydrogenation of vegetable ghee at
\( 25^{\circ} C \) reduces the pressure of \( H_{2} \) from 2 atm to 1.2 atm in 50 minutes.

The rate of reaction in terms of change of molarity per second is:
A. \( 1.6 \times 10^{-2} \) at \( m \) min \( ^{-1} \)
В. \( 3.3 \times 10^{-2} \) atm \( \min ^{-1} \)
c. \( 2.6 \times 10^{-3} \)atm \( \min ^{-1} \)
D. None of these
Subject: Maths
The area bounded by the parabola \( y^{2}= \)
\( 4 x \) and its latusrectum is:
A \( \cdot \frac{8}{3} \) sq. units
B. \( \frac{3}{8} \) sq. units
c. 12 sq. units
D. \( \frac{1}{3} \) sq. units
Subject: Physics
An LC circuit has \( L=5 \mathrm{mH} \) and \( \mathrm{C}=20 \mu \boldsymbol{F} \)
\( \boldsymbol{V}=\mathbf{5} \times \mathbf{1 0}^{-3} \) coswt is supplied. \( \boldsymbol{\omega} \) is
twice the resonant frequency. Find the maximum charge stored in the capacitor.
A. 66.6 nc
B. 11.3 nC
c. 23.2 nc
D. 33.3 nc
Subject: Chemistry
The hybridizations of atomic orbitals of
nitrogen in \( N O_{2}^{+}, N O_{3}^{-} \) and \( N H_{4}^{+} \)
respectively are:
A \( \cdot s p, s p^{2} \) and \( s p^{3} \)
B \( \cdot s p^{2}, s p \) and \( s p^{3} \)
\( \mathbf{c} \cdot s p, s p^{3} \) and \( s p^{2} \)
D. \( s p^{2}, s p^{3} \) and \( s p \)
Subject: Physics
The photograph of a house occupies an
area of \( 1.75 \mathrm{cm}^{2} \) on a \( 35 \mathrm{mm} \) slide. The
slide is projected on to a screen, and the area of the house on the screen is
\( 1.55 m^{2} . \) What is the linear
magnification of the projector-screen
arrangement.
Subject: Physics
A stone thrown vertically upwards with
a speed of \( 5 m / s \) attains a height \( H_{1} \)
Another stone thrown upwards from the same point with a speed of \( 10 m / s \)
attains a height \( \boldsymbol{H}_{2} \). The correct relation
between \( H_{1} \) and \( H_{2} \) is
A \( . H_{2}=4 H_{1} \)
В. \( H_{2}=3 H_{1} \)
\( \mathbf{c} \cdot H_{1}=2 H_{2} \)
D. \( H_{1}=H_{2} \)
Subject: Biology
Assertion
During anaphase, centromere of each chromosome splits to the chromatids
separate.
Reason
During anaphase, chromatids move to opposite poles.
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 steriochemistry change in
following \( \boldsymbol{S}_{N} \boldsymbol{2} \) is:
A. \( S, S \) changes to \( S, S \)
B. \( R, R \) changes to \( S, R \)
c. \( R, R \) changes to \( R, S \)
D. \( S, S \) changes to \( S, R \)
Subject: Biology
Assertion
Radial vascular bundle is the
characteristic of majority of the roots including dicots and monocots.
Reason
Monocot stem is characterized by collatral open vascular bundle.
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
Consider the statements
(i)Two plus three is five.
(ii) Every square is a rectangle.
(iii) Sun rises in the east.
(iv) The earth is not a star.
Which of the above statements have
truth value (T) ?
A. (i) and (ii)
B. (ii) and (iii)
c. (iii) and (iv)
D. All of these
Subject: Maths
Generate a polynomial equation if \( \boldsymbol{A} \) is
singular. \( \boldsymbol{A}=\left[\begin{array}{ccc}\boldsymbol{x}-\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \boldsymbol{x}-\mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \boldsymbol{x}-\mathbf{1}\end{array}\right] \)
Subject: Maths
In a hostel, \( 60 \% \) of the students read
Hindi newspaper, \( 40 \% \) read English
newspaper and \( 20 \% \) read both Hindi and English newspapers. A student is selected at random. Find the probability that she reads neither Hindi nor English
newspapers.
A \( \cdot \frac{1}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{4}{5} \)
Subject: Physics
Assertion
The excess pressure above atmospheric
pressure is usually called as gauge
pressure.
Reason
Gauge pressure \( =(\text { Total pressure }) \) (atmospheric pressure)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Maths
Find order and degree (if defined) of the differential equation \( \frac{\boldsymbol{d}^{4} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{4}}+ \)
\( \sin \left(\frac{\boldsymbol{d}^{3} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{3}}\right)=\mathbf{0} \)
Subject: Physics
A road is \( 8 \mathrm{m} \) wide. Its average radius of curvature is \( 40 \mathrm{m} . \) The outer edge is above the lower edge by a distance of \( 1.28 \mathrm{m} . \) Find the velocity of vehicle for
which the road is most suited? \( (\boldsymbol{g}= \)
\( 10 m / s^{2} \)
Subject: Maths
A bird moves from point \( (1 m,-2 m, 3 m) \) to \( (4 m, 2 m, 3 m) . \) If
the speed of the bird is \( 10 m / s \), then the
velocity vector of the bird in \( \boldsymbol{m} / \boldsymbol{s} \) is:
\( \mathbf{A} \cdot 5(\hat{i}-2 \hat{j}+3 \hat{k}) \)
B . \( 5(4 \hat{i}+2 \hat{j}+3 \hat{k}) \)
c. \( 0.6 \hat{i}+0.8 \hat{j} \)
D. \( 6 \hat{i}+8 \hat{j} \)
Subject: Physics
The energy equivalent of \( 1 \mathrm{mg} \) of mass in joule is
\( A \cdot 3 \times 10^{2} \)
B. 3 \times10 \( ^{10} \)
\( c \cdot 9 \times 10^{10} \)
D. \( 9 \times 10^{2} \)
Subject: Physics
When the temperature of a gas is \( 20^{0} C \)
and pressure is changed from \( \boldsymbol{P}_{1}= \) \( \mathbf{1 . 0 1} \times \mathbf{1 0}^{\mathbf{5}} \boldsymbol{P a} \) to \( \boldsymbol{P}_{\mathbf{2}}=\mathbf{1 . 1 6 5} \times \mathbf{1 0}^{\mathbf{5}} \boldsymbol{P a} \)
then the volume changes by \( 10 \% . \) The bulk modulus is
A \( .1 .55 \times 10^{5} \mathrm{Pa} \)
в. \( 1.05 \times 10^{5} P a \)
c. \( 1.4 \times 10^{5} P a \)
D. \( 0.115 \times 10^{5} P a \)
Subject: Maths
If \( A \) and \( B \) are square matrices of order
3 such that \( |\boldsymbol{A}|=-\mathbf{1},|\boldsymbol{B}|=\mathbf{3}, \) then
\( |\mathbf{3} \boldsymbol{A} \boldsymbol{B}|= \)
A . -9
B. -81
c. -27
D. 81
Subject: Maths
If \( \boldsymbol{x}=\mathbf{1}+\boldsymbol{i} \tan \boldsymbol{\alpha}, \) where \( \boldsymbol{\pi}<\boldsymbol{\alpha}<\frac{\mathbf{3} \boldsymbol{\pi}}{\mathbf{2}} \)
then \( |z| \) is equal to?
Subject: Chemistry
The correct electronic configurationfor
the ground state of silicon (atomic
number 11 ) is
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 p^{4} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{4} 3 s^{2} 3 p^{4} \)
D. \( 1 s^{2} s^{2} 2 p^{5} 3 s^{1} 3 p^{3} \)
Subject: Maths
Equation of a straight line passing through the origin and making an acute
angle with \( x- \) axis twice the size of the
angle made by the line \( y=(0.2) x \) with
the \( x- \) axis, is:
A \( . y=(0.4) x \)
В. \( y=(5 / 12) x \)
c. \( 6 y-5 x=0 \)
D. \( 6 y+5 x=0 \)
Subject: Maths
Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as
stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{2} \boldsymbol{x}^{2}-\boldsymbol{x}+\boldsymbol{3} \) on \( [\mathbf{0}, \mathbf{1}] \)
Subject: Physics
The electric field in a region is given by \( \overrightarrow{\boldsymbol{E}}=\frac{\mathbf{3}}{\mathbf{5}} \boldsymbol{E}_{\boldsymbol{o}} \hat{\boldsymbol{i}}+\frac{\boldsymbol{4}}{\mathbf{5}} \boldsymbol{E}_{\boldsymbol{o}} \widehat{\boldsymbol{j}} \) with \( \boldsymbol{E}_{\boldsymbol{o}}=\boldsymbol{2} \boldsymbol{0} \times \mathbf{1 0}^{\boldsymbol{3}} \)
N/C. Find the flux of this field (in
\( \left.N m^{2} C^{-1}\right) \) through a rectangular
surface of area \( 0.2 \mathrm{m}^{2} \) parallel to the \( \mathrm{Y}-\mathrm{Z} \)
plane.
Subject: Chemistry
Which of the following equations are
correctly represented for \( 0.10 \mathrm{M} \) solution of acetic acid in water?
\( \mathbf{A} \cdot[H O A c]=[H O A c c]_{e q .}+\left[O A c^{-}\right]_{e q .}=0.10 \mathrm{M} \)
B . \( \left[H^{+}\right]_{e q .}=\left[O A c^{-}\right]_{e q .}+\left[O H^{-}\right]_{e q} \)
\( \mathbf{c} \cdot\left[H^{+}\right]>\left[O H^{-}\right] \)
D. All of the above
Subject: Maths
The rate of change of the volume of a cone with respect to the radius of its
base is-
\( \mathbf{A} \cdot \pi^{2} h \)
в. \( \frac{4}{3} \pi r h \)
c. \( \frac{4}{3} \pi r^{2} h \)
D. \( \frac{2}{3} \pi r h \)
Subject: Maths
Find the value of
\( a \) for which the function \( f \) defined by
\( f(x)=\left\{\begin{array}{ll}a \sin \frac{\pi}{2}(x+1) & , x \leq 0 \\ \frac{\tan x-\sin x}{x^{3}} & , x>0\end{array}\right. \)
continuous at \( x=0 \)
Subject: Maths
A graph and the system of inequalities are shown above. Which region of the
graph could represent the solution for
the system of in equations?
\( \boldsymbol{y}>\boldsymbol{x} \)
\( \mathbf{3} \boldsymbol{y} \leq-\mathbf{4} \boldsymbol{x}+\mathbf{6} \)
\( A \cdot A \)
в. \( B \)
\( c . c \)
D. \( D \)
Subject: Chemistry
For the equilibrium in a closed vessel
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
\( K_{p} \) is found to be double of \( K_{c \cdot} \) This is
attained when:
A. \( T=2 K \)
в. \( T=12.18 K \)
c. \( T=24.36 K \)
D. \( T=27.3 K \)
Subject: Physics
Two particles \( A \) and \( B \) are moving as shown in the figure. Their total angular
momentum about the point 0 is.
A. \( 9.8 k g m^{2} / s \)
B. Zero
c. \( 52.7 k g m^{2} / s \)
D. \( 37.9 k g m^{2} / s \)
Subject: Maths
Evaluate:
\( 8\left(x^{3} y^{2} z^{2}+x^{2} y^{3} z^{2}+x^{2} y^{2} z^{3}+x^{2} y^{2} z^{2}\right) \)
\( 4 x^{2} y^{2} z^{2} \)
Subject: Physics
Which of the following is/are example(s) of isobars?
A. \( 11 . N a^{23} \) and \( 12 \mathrm{Mg}^{24} \)
\( ^{4} \)
B . \( _{19} K^{39} \) and \( _{20} A r^{40} \)
\( \mathbf{c} \cdot_{18} A r^{40} \) and \( _{20} C a^{40} \)
D・ \( _{17} C l^{35} \) and \( _{17} C l^{37} \)
Subject: Chemistry
Name the type of solution formed in the following cases:
i) \( 20 g \) of \( N a C l \) in \( 100 g \) of water.
ii) \( 36 g \) of \( N a C l \) in \( 100 g \) of water.
iii) \( 45 g \) of \( N a C l \) in \( 100 g \) of water at
\( 80^{\circ} \mathrm{C} \)
iv) Sulphur dissolved in \( C S_{2} \)
v) Nitrogen in soil
Subject: Chemistry
The velocity of an electron in the first
Bohr orbit of a hydrogen atom is:
A . \( 3.08 \times 10^{6} \mathrm{m} / \mathrm{s} \)
B. \( 2.18 \times 10^{6} \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 2.78 \times 10^{6} m / s \)
D. none of these