AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
If the radii of two bubbles are \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \)
then the ratio of respective masses of
air in them will be:
A \( \cdot \frac{R_{1}}{R_{2}} \)
в. \( \frac{R_{2}}{R_{1}} \)
\( ^{\mathbf{c}} \cdot \frac{P_{o}+\frac{4 T}{R_{1}}}{P_{o}+\frac{4 T}{R_{2}}} \)
\( ^{\mathrm{D}} \cdot \frac{P_{o}+\frac{4 T}{R_{1}}}{P_{o}+\frac{4 T}{R_{2}}}\left(\frac{R_{1}}{R_{2}}\right)^{3} \)
Subject: Physics
Plutonium has atomic mass 210 and a
decay constant equal to \( 5.8 \times 10^{-8} s^{-1} \)
The number of \( \alpha- \) particles emitted
per second by 1 mg plutonium is
(Avogadro's constant \( \left.=\mathbf{6 . 0} \times \mathbf{1 0}^{\mathbf{2 3}}\right) \)
A \( \cdot 1.7 \times 10^{9} \)
B . \( 1.7 \times 10^{11} \)
c. \( 2.9 \times 10^{11} \)
D. \( 3.4 \times 10^{9} \)
Subject: Chemistry
Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the salt required to achieve 10 ppm of iron in 100 kg of wheat is
[Atomic weight \( : \mathrm{Fe}=\mathbf{5 5 . 8 5} \mathrm{S}=\mathbf{3 2 . 0 0} \mathrm{O} \)
\( =\mathbf{1 6 . 0 0}] \)
Subject: Maths
Assertion \( \mathbf{f}[\boldsymbol{x} \mathbf{1}]\left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ -\mathbf{2} & \mathbf{3}\end{array}\right]\left[\begin{array}{c}\boldsymbol{x} \\ -\mathbf{5}\end{array}\right]=\mathbf{0}, \) then value
of \( x \) is either- 3 or 5
Reason Two matrices \( \left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{u} & \boldsymbol{v}\end{array}\right] \) \& \( \left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right] \) are
equal if \( \& \) only if their corresponding
entries are equal
\& only if their corresponding entries are equal
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: Chemistry
Two elements 'P' and 'Q' belong to the same period of the modern periodic table and are in Group 1 and Group 2 respectively. Compare their following characteristics in tabular form.
(a) The number of electrons in their
atoms
(b) The sizes of their atoms
(c) Their metallic character
(d) Their tendencies to lose electrons
(e) The formula of their oxides
(f) The formula of their chlorides
Subject: Physics
Consider a uniform electric field \( \boldsymbol{E}= \) \( 3 \times 10^{3} \hat{i} \mathrm{N} / \mathrm{C} \)
(a) What is the flux of
this field through a square of \( 10 \mathrm{cm} \) on a side whose plane is parallel to the \( y z \) plane?
(b) What is the flux through the same square if the normal to its plane
makes a \( 60^{\circ} \) angle with the \( x \) -axis?
Subject: Physics
When electronjumps from \( n=4 \) level to \( n=1 \) level, the angular momentum
of electron changes by
\( ^{A} \cdot \frac{h}{2 \pi} \)
в. \( \frac{2 h}{2 \pi} \)
c. \( \frac{3 h}{2 \pi} \)
D. \( \frac{4 h}{2 \pi} \)
Subject: Chemistry
The mass of non-volatile, non-elctrolyte solute (molar mass \( 50 g \) mol \( ^{-1} \) ) needed
to be dissolved in \( 114 g \) octane to reduce
its vapour pressure to \( 75 \% \), is
A . \( 150 g \)
в. \( 75 g \)
c. \( 37.5 g \)
D. \( 50 g \)
Subject: Chemistry
A current of dry air was passed through a series of bulbs containing 1.25 g of a solute \( A_{2} B \) in 50 g of water and then through pure water. The loss in mass of the former series of bulbs was 0.98 g and in the later series 0.01 g. If the molar
mass of \( A_{2} B \) is \( 80, \) the degree of
dissociation of \( A_{2} B \) is (divide answer by \( 10): \)
Subject: Maths
If \( f(x)=\int_{-1}^{x}|t| d t, x \geq-1, \) then
A. \( f \) and \( f^{\prime} \) are continuous for \( x+1>0 \)
B. \( f \) is continuous but \( f^{\prime} \) is not continuous for \( x+1>0 \)
\( \mathrm{c} \cdot f \) and \( f^{\prime} \) are not continuous at \( x=0 \)
D. \( f \) is continuous at \( x=0 \) but \( f^{\prime} \) is not so
Subject: Maths
The graph of the function \( f(x)=x^{3}+1 \)
after translation 4 units to the right and 2 units up, resulted in a new graph \( l(x) \) What is the value of \( l(3.7) ? \)
A. 0.973
B. 1.784
c. 1.973
D. 2.027
E . 2.973
Subject: Chemistry
Which one of the following is a correct
set?
A \( \cdot C l_{2} O, s p^{3}, \) Angular
B. \( B F_{3}, s p^{2}, \) T-shape
C. \( S O_{3}, s p^{3}, \) Trigonal pyramidal
D. \( N O_{2}, s p, \) Linear
E. \( S F_{4}, s p^{3} d^{2}, \) Square pyramidal
Subject: Chemistry
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}+\boldsymbol{A}+\boldsymbol{A l C l}_{3} \longrightarrow \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O N H}_{2} \)
Here A is:
A. urea
в. \( C l C O N H_{2} \)
c. \( C H_{3} C O N H_{2} \)
D. \( C l C H_{2} C O N H_{2} \)
Subject: Chemistry
Which of the following shows negative
deviation from Raoult's law?
A. \( C H C l_{3} \) and acetone
в. \( C_{6} H_{6} \) and \( C_{2} H_{5} O H \)
\( \mathbf{c} \cdot C_{6} H_{5} C H_{3} \) and \( C_{6} H_{6} \)
D. \( C_{6} H_{6} \) and \( C C l_{4} \)
Subject: Physics
What should be the angular velocity of rotation of the earth about its own axis
so that the weight of a body at the equator reduces to \( 3 / 5 \) or its present value?(Take R as the radius of the
earth)
A \( \cdot \sqrt{\frac{g}{3 R}} \)
в. \( \sqrt{\frac{2 g}{3 R}} \)
c. \( \sqrt{\frac{2 g}{5 R}} \)
D. \( \sqrt{\frac{2 g}{7 R}} \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{a}_{\boldsymbol{k}}=\boldsymbol{k}\left(^{10} \boldsymbol{C}_{\boldsymbol{k}}\right), \boldsymbol{b}_{\boldsymbol{k}}=(\mathbf{1 0}-\boldsymbol{k})\left(^{10} \boldsymbol{C}_{\boldsymbol{k}}\right) \)
and \( \boldsymbol{A}_{\boldsymbol{k}}=\left[\begin{array}{ll}\boldsymbol{a}_{\boldsymbol{k}} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{b}_{\boldsymbol{k}}\end{array}\right] \)
If \( \boldsymbol{A}=\sum_{\boldsymbol{k}=1}^{9} \boldsymbol{A}_{\boldsymbol{k}}=\left[\begin{array}{ll}\boldsymbol{a} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{b}\end{array}\right], \) find the value
of \( a+b \)
Subject: Physics
The values of current I flowing in a given resistor for the corresponding values of potential difference V across the resistor are given below -
|(amperes) 2
\( V(v \text { olts }) \) 1. 6
. 6 3.4 6.7
Plot a graph between \( \mathrm{V} \) and \( \mathrm{I} \) and
calculate the resistance of that resistor.
Subject: Maths
Solution of the differential equation
\( \tan y \cdot \sec ^{2} x d x+\tan x \cdot \sec ^{2} y d y=0 \) is
A. \( \tan x+\tan y=k \)
B. \( \tan x-\tan y=k \)
c. \( \frac{\tan x}{\tan y}=k \)
D. \( \tan x \cdot \tan y=k \)
Subject: Maths
If \( a, b, c \) are non-coplanar vectors and \( \lambda \) is a real number, then \( \left[\lambda(\vec{a}+\vec{b}) \lambda^{2} \vec{b} \lambda \vec{c}\right]=[\vec{a} \quad \vec{b}+\vec{c} \quad \vec{b}] \) for
A. exactly two values of \( \lambda \)
B. exactly three values of \( \lambda \)
c. no value of \( \lambda \)
D. exactly one value of \( \lambda \)
Subject: Physics
\( A \) and \( B \) are two points on the axis and the perpendicular bisector respectively of an electric dipole. A and B are far away from the dipole and at equal distances from it. The potentials at \( A \)
and \( \mathrm{B} \) are \( V_{A} \) and \( V_{B} \) respectively. Then
A. \( V_{A}=V_{B}=0 \)
в. \( V_{A}=2 V_{B} \)
\( \mathbf{c} \cdot V_{A} \neq 0, V_{B}=0 \)
D. \( V_{A} \neq 0, V_{B} \neq 0 \)
Subject: Maths
Function \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+\mathbf{2}) \boldsymbol{e}^{-\boldsymbol{x}} \) is
A. decreasing
B. decreasing in \( (-\infty,-1) \) and increasing in \( (-1, \infty) \)
c. increasing
D. decreasing in \( (-1, \infty) \) and increasing in \( (-\infty,-1) \)
Subject: Chemistry
Given the numbers: \( 161 \mathrm{cm} ; 0.161 \mathrm{cm} \)
\( 0.0161 \mathrm{cm} . \) The number of significant figure for three numbers is:
\( \mathbf{A} \cdot 3,4,5 \)
в. 3,3,3
c. 3,3,4
D. 3,4,4
Subject: Physics
Assertion
A galvanometer can be used as a voltmeter to measure the voltage
across a given section of the circuit.
Reason
For this it must be connected in parallel
with that section of the circuit.
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 domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( (\sqrt{1-\sqrt{1-\sqrt{1-x^{2}}}}) \) is
A . [0,1]
в. [-1,1]
\( c \cdot(-\infty, \infty) \)
D. (-1,1)
Subject: Chemistry
A sudden large jump between the values of second and third ionization
energies of an element would be associated with the
electronic configuration of:
A \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{1} \)
B . \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{1} \)
C \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{2} \)
D. \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2} \)
Subject: Physics
A vessel has \( 6 g \) of hydrogen at pressure \( P \) and temperature \( 500 K . A \) small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is \( \boldsymbol{P} / 2 \) and temperature falls to \( 300 \mathrm{K} ? \)
\( A \cdot 28 \)
B. 3g
\( c \cdot 4 g \)
D. 18
Subject: Chemistry
when compound \( \mathbf{C} \) is treated with
\( \boldsymbol{B} \boldsymbol{r}_{2} / \boldsymbol{C} \boldsymbol{C l}_{4} \)
A. a meso dibromide is formed.
B. four stereo-isomers of dibromides are fromed.
C . racemic mixture of dibromides are formed.
D. a pair of enantiomers of dibromides in unequal amount is formed.
Subject: Physics
Calculate the wavelength of \( k_{\alpha} \) line for \( Z=31 \) when \( \alpha=5 \times 10^{7} H z^{1 / 2} \) for a
characteristic X-ray spectrum.
A \( \cdot 1.33 \) a
B. 1.33 nm
c. \( 133 \times 10^{-10} \mathrm{m} \)
D. 133 пт
Subject: Physics
Two numbers are given as i) 20.96 and
ii) \( 0.0003125 . \) Rounding off above numbers to 3 significant figures will lead to :
A \( . \) i) \( 21.0, \) ii) 312
B . i) 21.0, ii) 3.12 \( \times 10^{-4} \)
\( c \cdot \) i) \( 2.10, \) ii) \( 3.12 \times 10^{-4} \)
4
4
Subject: Physics
The velocity of a sound wave in \( v \) and
the wave energy density is \( E, \) then the
amount of energy transferred per unit area per second by the wave in a direction normal to the wave
propagation is
A. \( E \)
в. \( E v \)
\( \mathrm{c} \cdot E^{2} v^{2} \)
D. \( \sqrt{E v} \)
Subject: Chemistry
The number of lone pair(s) of electrons
on the central atom in \( \left[\boldsymbol{B} \boldsymbol{r} \boldsymbol{F}_{4}\right]^{-}, \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \)
and \( \left[\boldsymbol{S b C l}_{\mathbf{6}}\right]^{3-} \) are respectively:
\( \mathbf{A} \cdot 2,1 \) and 1
B. 2,1 and 0
c. 2,0 and 1
D. 1,0 and 0
Subject: Physics
Five conducting plates are placed parallel to each other Separation
between them is \( d \) and area of each
plate is \( A \). Plate number 1,2 and 3 are
connected with each other and at the
same time through a cell of emf \( \boldsymbol{E} \). The
charge on plate number 1 is
\( \mathbf{A} \cdot E \varepsilon_{0} A / d \)
B . \( E \varepsilon_{0} A / 2 d \)
\( \mathbf{c} \cdot 2 E \varepsilon_{0} A / d \)
D. zero
Subject: Physics
The power radiated by a black body is \( P \)
and it radiates maximum energy around
the wavelength \( \lambda_{0} . \) If the temperature of
the black body is now changed so that it radiates maximum energy around wavelength \( \frac{3}{4} \lambda_{0}, \) power radiated by it will increase by a factor of
\( A \cdot \frac{4}{3} \)
В. \( \frac{16}{9} \)
c. \( \frac{64}{27} \)
D. \( \frac{256}{81} \)
Subject: Biology
Assertion
In humans the gamete contributed by the male determines whether the child
produced will be male or female.
Reason

Sex in humans is polygenic trait
dependent upon the cumulative effect
of some genes on X-chromosome and
some on Y-chromosome.
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
Which of the following statement is/are true for \( _{1} \boldsymbol{H}^{1},_{1} \boldsymbol{H}^{2} \) and \( _{1} \boldsymbol{H}^{3} \)
respectively? This question has multiple correct options
A. They are isotopes of each other
B. They have similar electronic configuration
c. They exist in the nature in the ratio 1: 2: 3
D. Their atomic masses are in the ratio 1: 2: 3
Subject: Maths
Give examples of two one-one functions
\( f_{1} \) and \( f_{2} \) from \( R \) to \( R \) such that \( f_{1}+ \)
\( \boldsymbol{f}_{2}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \) defined by \( \left(\boldsymbol{f}_{1}+\boldsymbol{f}_{2}\right)(\boldsymbol{x})= \)
\( f_{1}(x)+f_{2}(x) \) is not one-one.
Subject: Physics
When temperature of \( \operatorname{gas} \) is \( 20^{\circ} \mathrm{C} \) and pressure is changed from \( P_{1}=1.01 \times 10^{5} \)
Pa to \( P_{2}=1.165 \times 10^{5} \) Pa then the volume
changed by \( 10 \% \). the bulk modulus is:
A \( .1 .55 \times 10^{5} P a \)
В. \( 0.155 \times 10^{5} P a \)
c. \( 15.5 \times 10^{5} P a \)
D. \( 155 \times 10^{5} P a \)
Subject: Chemistry
Assertion
Boiling point of pentane is higher than 2,2-dimethylpropane.
Reason
There is steady increase in boiling point with increase in molecular mass.
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
Answer the following question in one word or one sentence or as per exact requirement of the question.
If \( \boldsymbol{x}<\mathbf{2}, \) then write the value of \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}(\sqrt{\boldsymbol{x}^{2}-\boldsymbol{4} \boldsymbol{x}+\boldsymbol{4}}) \)
Subject: Chemistry
Compound (D) is:
\( \mathbf{A} \cdot C H_{3}-\underset{C H_{3}}{C H}-C_{D H_{3}}-C H_{2} O H \)
\( \mathbf{B} \)
\[
C H_{3}-\underset{_{C H_{3}}^{\mathrm{I}}}{C}-C H_{2} C H_{2} O H
\]
\( \mathbf{c} . C H_{3}-C H-C H_{2}-C H O H \)
\( _{C H_{3}} \)
Subject: Physics
For measuring time in sports events
like sprinting, milisecond\( (\boldsymbol{m s}) \) is a commonly used unit of time. 1 ms \( =? \)
\( \mathbf{A} \cdot 10^{-12} s \)
B. \( 10^{-9} s \)
\( \mathbf{c} \cdot 10^{-3} s \)
D. None of these
Subject: Maths
Differentiate the following function with
respect to \( x \)
\( x^{2} e^{x} \) log \( x \)
A \( \cdot x e^{x}(x \log x+2 \log x) \)
B. \( x e^{x}(1+2 \log x) \)
C \( \cdot x e^{x}(1+x \log x) \)
D. \( x e^{x}(1+x \log x+2 \log x) \)
Subject: Physics
Assertion: Stress is the internal force
per unit area of a body Reason: Rubber is more elastic than
stee
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false.
E. If reason is true but assertion is false
Subject: Physics
A (trolley+child) of total mass \( 200 k g \) is moving at a uniform speed of \( 36 k m / h \) on a frictionless track. The child of
mass \( 20 k g \) starts running on the trolley from one end to the other \( (10 m \) away)
with a speed of \( 10 m s^{-1} \) relative to the
trolley in the direction of the trolley's motion and jumps out of the trolley with the same relative velocity. What is the final speed of the trolley? How much has the trolley moved from the time the
child begins to run and just before
jump?
Subject: Maths
\( \lim _{n \rightarrow \infty}\left[\frac{1}{3 n+1}+\frac{1}{3 n+2}+\dots+\right. \)
\( \left.\frac{1}{3 n+n}\right] \)
A \( \cdot \log (2 / 3) \)
and 5
B. \( \log (3 / 2) \)
\( c \cdot \log (4 / 3) \)
\( \mathbf{D} \cdot \log (3 / 4) \)
Subject: Physics
\( 0.1 m^{3} \) of water at \( 80^{\circ} C \) is mixed with
\( 0.3 m^{3} \) of water at \( 60^{\circ} \mathrm{C} \). The final
temperature of the mixture is
\( A \cdot 65^{\circ} C \)
B . \( 70^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 60^{\circ} \mathrm{C} \)
D. \( 75^{\circ} \mathrm{C} \)
Subject: Physics
The ratio of nuclear magneton and Bohr
magneton is
\( \mathbf{A} \cdot m_{e} / m_{p} \)
в. \( m_{p} / m_{e} \)
\( \mathbf{c} \cdot m_{e} m_{p} \)
\( \mathbf{D} \cdot 2 m_{p} / m_{e z} \)
Subject: Maths
Which of the following is not the reciprocal of \( \left(\frac{2}{3}\right)^{4} ? \)
\( ^{A} \cdot\left(\frac{3}{2}\right)^{4} \)
\( ^{\text {B }}\left(\frac{2}{3}\right)^{-4} \)
\( ^{c}\left(\frac{3}{2}\right)^{-4} \)
D. \( \frac{3^{4}}{4^{2}} \)
Subject: Physics
A light spring balance hangs from the hook of the other light spring balance and a block of mass \( M \) kg hangs from the former one. Then the true statement
about scale reading is
A. both the scales read \( M \) kg each
B. the scale of the lower one reads \( M \) kg and of upper on zero
c. the reading of the two scales can be anything but summ of the reading will be \( M \) kg
D. both the scales read \( M / 2 \mathrm{kg} \)
Subject: Chemistry
\( I_{2} \) has less solubility in water, but its
solubility increases on adding \( K I \) in
the solution. When \( K I \) and \( I_{2} \) react,
then a species \( X \) is formed and
solubility of \( I_{2} \) solution increases.
The geometry of the anionic part of \( \boldsymbol{X} \)
is:
A. Linear
B. T-shape
c. Pyramidal
D. See-saw
Subject: Physics
Two identical uniform discs roll without
slipping on two different surfaces \( A B \) and \( C D \) starting at \( A \) and \( C \) with linear
speed \( v_{1} \) and \( v_{2}, \) respectively, and always remain in contact with the
surfaces. If they reach \( \mathrm{B} \) and \( \mathrm{D} \) with the
same linear speed and \( \boldsymbol{v}_{1}=\mathbf{3} \boldsymbol{m} / \boldsymbol{s} \) then
\( v_{2} \) in \( m / s \) is \( \left(g=10 m / s^{2}\right) \)
Subject: Physics
Two coherent monochromatic light
beams of intensities \( I \) and \( 4 I \) are
superposed. The maximum and minimum possible intensities in the resulting beam are:
A. \( 5 I \) and \( I \)
B. \( 5 I \) and \( 3 I \)
c. \( 9 I \) and \( I \)
D. \( 9 I \) and \( 3 I \)
Subject: Maths
What is the modal class for the
following distributions?
\( \begin{array}{llll}\text { Class } & \mathbf{2 2}- & \mathbf{3 3}- & \mathbf{4 4}- \\ \text { interval } & \mathbf{3 3} & \mathbf{4 4} & \mathbf{5 5}\end{array} \)
Frequency 23 45 67
A \( .55-66 \)
в. \( 66-77 \)
c. \( 77-88 \)
D. \( 88-99 \)
Subject: Maths
Determine for what values of \( x, \) the
function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\frac{\mathbf{1}}{\boldsymbol{x}^{3}}(\boldsymbol{x} \neq \mathbf{0}) \) is
strictly increasing or strictly decreasing.
Subject: Physics
Match the following:
Table - 1
(a) Minimum current will flow through
(b) Maximum current will flow through
(c) Maximum power will be generated across
(d) Minimum power will be generated across
\( \mathbf{A} \cdot a-p ; b-p ; c-q ; d-r \)
B \( . a-r ; b-r ; c-p ; d-s \)
\( \mathbf{c} \cdot a-q ; b-p ; c-r ; d-q \)
D. \( a-s ; b-s ; c-r ; d-q \)
Subject: Physics
Two bodies start falling freely from the rest from the same height at an interval of 1 s. How long after the first body begins to fall will the two bodies be \( 10 \mathrm{m} \)
apart? \( \left(g=10 m / s^{2}\right) \)
A . \( 0.5 \mathrm{s} \)
B. \( 1.0 \mathrm{s} \)
\( c \cdot 1.5 s \)
D. 2.0 s
Subject: Physics
Rms value of current \( \boldsymbol{i}=\mathbf{3}+ \)
\( 4 \sin \left(\omega t+\frac{\pi}{3}\right) \) is:
A . \( 5 A \)
в. \( \sqrt{17} A \)
\( c \cdot \frac{5}{\sqrt{2}} A \)
D. \( \frac{7}{\sqrt{2}} A \)
Subject: Physics
Two different adiabatic parts for the
same gas intersect two isothermals at
\( T_{1} \) and \( T_{2} \) as shown in P-V diagram
Then the ratio of \( \frac{V_{a}}{V_{b}} \) will be:
A \( \cdot \frac{V_{c}}{\longrightarrow} \)
\( \overline{V_{d}} \)
B. \( \underline{V}_{d} \)
\( V_{c} \)
\( c \cdot \gamma \frac{V_{d}}{V} \)
D. \( \frac{1}{\sim} \frac{V_{d}}{V} \)
Subject: Chemistry
The osmotic pressure of a solution in atm obtained on mixing each 50 mL of \( 1.2 \% \) mass/volume urea solution and
\( 2.4 \% \) mass/volume glucose solution at \( \mathbf{3 0 0} \mathrm{K} \) is: \( (\boldsymbol{R}=\mathbf{0 . 0 8} \) litre atm
\( \left.\boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right) \)
Subject: Chemistry
The symbols \( F . H . S . V_{m} \) and \( E^{o} \) denote
Helmholtz free energy, enthalpy, entropy, molar volume and standard
electrode potential, respectively. The correct classification of the properties
is:
A. \( F . H . S \) are intensive; \( V_{m} \) and \( E^{o} \) are extensive
B. F.H.S are extensive; \( V_{m} \) and \( E^{\circ} \) are intensive
c. \( F . H . S \) and \( V_{m} \) are intensive; \( E^{o} \) are extensive
D. \( F . H . S \) and \( E^{o} \) are extensive; \( V_{m} \) are intensive
Subject: Chemistry
Assertion
According to de Broglie, the wavelengths associtated with electrons and other subatomic particles can be
detected experimentally.
Reason
The wavelength associated with any material particle is directly proportional
to its mass.
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
\( \mathbf{2} N \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{O} \boldsymbol{C l}(\boldsymbol{g}) \)
The following data were collected. All the
measuremnets were taken at \( 263 \mathrm{K} \)
Initial rate
disappear:
\( \begin{array}{llll}\begin{array}{l}\text { Experiment } \\ \text { No. }\end{array} & \begin{array}{l}\text { Initial } \\ \text { [NO] } \\ \text { (M) }\end{array} & \begin{array}{l}\text { Initial } \\ {\left[C_{2}\right]} \\ \text { (M) }\end{array} & \begin{array}{l}\text { In } \\ \text { di }\end{array} \\ & & \text { of }\end{array} \) \( C l_{2} \) or \( C l_{2} \)
\( (M / m i n) \)
0.15 0.15 0.60
0.15 \( \quad 0.30 \) 1.20
3 \( \begin{array}{ll}\text { 0.30 } & \text { 0.15 }\end{array} \) 2.40
0.25 0.25
(a) Write the expression for rate law.
(b) Calculate the value of rate constant
and specify its units.
(c) What is the initial rate of
disappearance of \( C l_{2} \) in exp. \( 4 ? \)
Subject: Maths
Find the value of \( x^{3}+7 x^{2}-x+16 \)
when \( \boldsymbol{x}=\mathbf{1}+\mathbf{2} \boldsymbol{i} \)
\( \mathbf{A} \cdot-11+24 i \)
B . \( -17+24 i \)
c. \( -17-24 i \)
D. \( -1+24 i \)
Subject: Maths
If \( x^{2}+y^{2}=a^{2} \) and \( k=1 / a, \) then \( k \) is
equal to?
A \( \cdot \frac{y \prime}{\sqrt{1+y^{\prime}}} \)
B. \( \frac{|y \prime \prime|}{\sqrt{\left(1+y^{\prime 2}\right)^{3}}} \)
c. \( \frac{2 y \prime}{\sqrt{1+y \prime}} \)
D. \( \frac{y \prime}{2 \sqrt{\left(1+y^{\prime 2}\right)^{3}}} \)
Subject: Biology
Which one of the following is a possibility for most of us with regards to breathing, by making a conscious effort?
A. One can consciously breathe in and breathe out by moving the diaphragm alone, without moving the ribs at all
B. The lungs can be made fully empty by forcefully breathing out all air from them.
c. One can breathe out air totally without oxygen
D. One can breathe out air through eustachian tubes by closing both the nose and the mouth.
Subject: Maths
\( \int x^{2} e^{x^{3}} d x \) equals
A \( \cdot \frac{1}{3} e^{x^{3}}+C \)
B \( \cdot \frac{1}{3} e^{x^{2}}+C \)
c. \( \frac{1}{2} e^{x^{3}}+C \)
D. \( \frac{1}{2} e^{x^{2}}+C \)
Subject: Maths
If \( \sin (\theta+\alpha)=a \) and \( \sin (\theta+\beta)= \)
\( \boldsymbol{b},((\mathbf{0}<\boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\theta}<\boldsymbol{\pi} / 2)) \) then
\( 2 \cos ^{2}(\alpha-\beta)-1-4 a b \cos (\alpha-\beta) \) is
A \( \cdot 1-a^{2}-b^{2} \)
B . \( 1-2 a^{2}-2 b^{2} \)
c. \( 2+a^{2}+b^{2} \)
D . \( 2=a^{2}-b^{2} \)