AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
Under free expansion, \( \left(\frac{d U}{d V}\right)_{T} \) is \( +v e \) when
attractive forces are dominant between
gas molecules [U, V, T represent internal
energy, volume and temperature of gas respectively].
Reason
Internal energy is a state function.
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
Let \( r \) be the distance from the origin to
a point \( \boldsymbol{P} \) with coordinates \( \boldsymbol{x} \) and \( \boldsymbol{y} \) Designate the ratio \( \frac{y}{r} \) by \( s \) and the ratio \( \frac{x}{r} \) by \( c . \) Then the values of \( s^{2}-c^{2} \) are limited to the numbers:
A. less than -1 and greater than +1 , both excluded
B. less than -1 and greater than +1 , both included
c. between -1 and \( +! \), both excluded
D. between -1 and \( +1, \) both included
E. -1 and +1 only
Subject: Physics
An object is moving on a circular path of radius \( r \) with constant speed \( v \). The average acceleration of the object, after it has traveled a half rounds, is,
A \( \cdot \frac{2 v^{2}}{\pi r} \)
В. \( \frac{4 v^{2}}{3 \pi r} \)
c. \( \frac{4 v^{2}}{7 \pi r} \)
D. \( \frac{2 v^{2}}{7 \pi r} \)
Subject: Physics
toppr OGIN No
Q Type your question_
evenly at the same steady rate to both
substances.
Which table best describes the
properties of these substances?
\( A \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Quantity } & Greater for Which Substance? \\
\hline Solid Specific Heat & \( \mathrm{P} \) \\
Liquid Specific Heat & \( \mathrm{G} \) \\
Latent Heat of Vaporization & \( \mathrm{P} \) \\
\hline
\end{tabular}
\( B \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Quantity } & Greater for Which Substance? \\
\hline Solid Specific Heat & \( \mathrm{P} \) \\
Liquid Specific Heat & \( \mathrm{P} \) \\
Latent Heat of Vaporization & \( \mathrm{G} \) \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Quantity } & Greater for Which Substance? \\
\hline Solid Specific Heat & \( \mathrm{P} \) \\
Liquid Specific Heat & \( \mathrm{P} \) \\
Latent Heat of Vaporization & \( \mathrm{G} \) \\
\hline
\end{tabular}
\( D \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Quantity } & Greater for Which Substance? \\
\hline Solid Specific Heat & \( \mathrm{G} \) \\
Liquid Specific Heat & \( \mathrm{G} \) \\
Latent Heat of Vaporization & \( \mathrm{G} \) \\
\hline
\end{tabular}
\( E \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Quantity } & Greater for Which Substance? \\
\hline Solid Specific Heat & \( \mathrm{P} \) \\
Liquid Specific Heat & \( \mathrm{G} \) \\
Latent Heat of Vaporization & \( \mathrm{G} \) \\
\hline
\end{tabular}
Subject: Physics
Two balls are rolling on a flat smooth
table. One ball has velocity components \( \sqrt{3} \hat{j} \) and \( \hat{i} \) while the other has components \( 2 \hat{i} \) and \( 2 \hat{j} \). If both start moving simultaneously from the same point, the angle between their paths is:
A . 15
в. 30
c. 45
D. \( 60^{\circ} \)
Subject: Maths
The figure shows the cross section of
six identical spheres. The spheres, touching each other, are placed on a horizontal plane. The volume of each sphere is \( \frac{32 \pi}{3} c m^{3} . \) Calculate the length of \( \boldsymbol{P Q}, \) in \( \boldsymbol{c m} \)
A . 18
B. 24
c. 36
D. 58
Subject: Maths
In the figure above, \( \overline{A C} \) is a diameter of
the large circle and \( \mathrm{B} \) lies on \( \overline{\boldsymbol{A C}} \) so that
\( A B \) is a diameter of the small circle. If
\( A B=1 \) and \( B C=2, \) Calculate the
area of the shaded region.
\( A \cdot \frac{\pi}{4} \)
в.
\( c \cdot 2 \pi \)
D. \( \frac{9 \pi}{4} \)
E . \( 9 \pi \)
Subject: Maths
If \( x \) is real, then \( \frac{x^{2}+2 x+c}{x^{2}+4 x+3 c} \) can take all real values if?
A. \( 0<c<2 \)
В. \( 0<c<1 \)
c. \( -1<c<1 \)
D. None of the above
Subject: Physics
rolling on a smooth horizontal surface
with velocity \( V \) and angular velocity \( \omega \)
(where \( V=\omega r) . \) The sphere collides
with a sharp edge on the wall as shown
in the figure. The coefficient of friction
between the sphere and the edge \( \mu= \)
1/5. Just after the collision the angular
velocity of the sphere becomes equal to
zero. The linear velocity of the sphere
just after the collision is equal to:
\( \mathbf{A} \cdot V \)
B. \( \underline{V} \) \( \overline{5} \)
c. \( \frac{3 V}{5} \)
D. \( \frac{V}{6} \)
Subject: Maths
The following table shows the age distribution of cases of a certain
disease reported during a year in a particular city.
\( \begin{array}{lllll}\text { Age } & 5- & 15- & 25- & 35- \\ \text { in } & 14 & 24 & 34 & 44 \\ \text { years } & & & \end{array} \)
No. of 6
11
Obtain the mean, median and mode of
the above data.
Subject: Physics
In a Zener diode regulated power supply, unregulated DC input of \( 10 V \) is
applied. If the resistance \( \left(R_{s}\right) \) connected
in series with a Zener diode is \( 200 \Omega \)
and the Zener voltage \( V_{z}=5 V \), the
current across the resistance \( \boldsymbol{R}_{s} \) is:
\( \mathbf{A} \cdot 15 m A \)
B. \( 10 \mathrm{mA} \)
c. \( 20 m A \)
D. \( 5 m A \)
E . \( 25 m A \)
Subject: Chemistry
Wavelength of the de-Broglie wave of an electron revolving in the sixth orbit of
the hydrogen atom is: \( \left(r_{0} \) is the Bohr's \right. radius \( =0.529 A \)
A \( \cdot \pi r_{0} \)
В. \( 12 \pi r_{0} \)
\( c \cdot 6 \pi r_{0} \)
D. \( 4 \pi r_{0} \)
Subject: Maths
\( f(\alpha, \beta, \gamma \) are the zeros of the polynomial
\( \boldsymbol{x}^{3}+\boldsymbol{p} \boldsymbol{x}^{2}+\boldsymbol{q} \boldsymbol{x}+\boldsymbol{2} \) such that \( \boldsymbol{\alpha} \boldsymbol{\beta}+\mathbf{1}= \)
\( 0, \) find the value of \( 2 p+q+5 \)
Subject: Physics
Three tuning fork of frequency \( 400 \mathrm{Hz} \)
\( 401 \mathrm{Hz} \) and \( 402 \mathrm{Hz} \) are sounded
simultaneously.the number of beats heard per second are :
\( A \cdot 1 \)
B. 2
\( c \cdot 3 \)
D. none of these
Subject: Physics
The period of small oscillations is
A \( \cdot \pi a \sqrt{\frac{m}{C}} \)
В. \( \pi a \sqrt{\frac{2 m a}{c}} \)
C \( \cdot 2 \pi \sqrt{\frac{2 m a^{3}}{C}} \)
D. \( 2 \pi a \sqrt{\frac{m a}{C}} \)
Subject: Maths
If the mean deviation of the numbers
\( \mathbf{1}, \mathbf{1}+\boldsymbol{d}, \dots, \mathbf{1}+\mathbf{1 0 0} \boldsymbol{d} \) from their mean
is \( 255, \) then a value of \( d \) is:
A . 10.1
B. 20
c. 10
D. 20.2
Subject: Maths
Verify Rolle's theoremlquad for the
function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{-\boldsymbol{x}} \sin \boldsymbol{x}, \boldsymbol{x} \boldsymbol{\epsilon}[\mathbf{0}, \boldsymbol{\pi}] \)
Subject: Chemistry
If octane number of gasoline sample is
70, then this sample will be similar to:
A. 70\% n-heptane + 30\% n-octane
B. 70\% n-octane + 30\% n-heptane
c. 70\% isooctane + 30\% n-heptane
D. 70\% n-heptane + 30\% isooctane
Subject: Physics
The amount of heat energy required to
convert 1 kg of ice \( a t-10^{\circ} C \) to water at
\( 100^{\circ} \mathrm{C} \) is \( 7,77,000 \mathrm{J} \). Calculate the specific latent heat of ice. Specific heat capacity of ice \( 2100 J k g^{-1} K^{-1} \), specific heat capacity of water = \( 4200 J k g^{-1} K^{-1} \)
A. \( 3,360 J k g^{-1} \)
B. \( 33,600 J k g^{-1} \)
c. \( 33,60,000 J k g^{-1} \)
D. \( 3,36,000 J k g^{-1} \)
Subject: Physics
A ball is dropped off a high building and strikes the ground with an impact velocity of \( 30 \mathrm{m} / \mathrm{s} \). Calculate the height of building:
\( A \cdot 15 \mathrm{m} \)
B. 20 \( \mathrm{m} \)
c. 30 \( m \)
D. 45 \( m \)
E. \( 60 \mathrm{m} \)
Subject: Maths
Let the function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined
by \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}+\cos \boldsymbol{x} \) then \( \boldsymbol{f} \)
A. Has maximum at \( x=0 \)
B. Has minimum at \( x=\pi \)
c. Is an increasing function
D. Is a decreasing
Subject: Chemistry
Which one of the following has largest number of isomers? \( (\mathbf{R}= \) alkyl group,
en \( = \) ethylenediamine
\( \mathbf{A} \cdot\left[\operatorname{Ru}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{C} 1_{2}\right]^{+} \)
B \( \cdot\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{C} 1\right]^{2+} \)
\( \mathbf{c} \cdot\left[\operatorname{Ir}\left(\mathrm{PR}_{3}\right)_{2} \mathrm{H}(\mathrm{CO})\right]^{2+} \)
D. \( \left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{C} 1_{2}\right] \)
Subject: Physics
Consider a film of thickness \( L \) as shown
in four different cases below. Notice the
observation of film with perpendicularly falling light. Mark the correct statement(s). (Take \( L=1.5 \lambda) \)
This question has multiple correct options
A. For (1) and (2), the reflection at film interfaces causes zero phase difference for two reflected rays
B. For 92 ) and (3), the reflection at film interfaces causes phase difference of \( \pi \) for two reflected rays
C. For (1) , the film will appear dark, if it is observed through reflected rays from film interfaces
D. For
(3), the film will appear dark, if it is observed through reflected rays from film interfaces
Subject: Maths
The conjugates of
a) \( -2+3 i \)
b) \( 1-i \)
c) 4
d) \( 4 i \)
in order are:
A . \( 2-3 i, 1+i, 4,-4 i \)
B. \( +2-3 i, 1+i, 4,-4 i \)
c. \( 2-3 i, 1+i, 4,4 i \)
D. \( -2-3 i, 1+i, 4,-4 i \)
Subject: Chemistry
\( \mathbf{1} P a=1 N m^{-2} \)
If mass of air at sea level is 1034 g
\( c m^{-2}, \) calculate the pressure in pascal
A \( \cdot 101 \times 10^{5} P a \)
C. \( 1.0133 \times 10^{5} P a \)
D. \( 10133 \times 10^{5} P a \)
Subject: Physics
The wavelength \( \lambda_{e} \) of an electron and \( \lambda_{p} \) of a photon of same energy \( \boldsymbol{E} \) are
related by
\( A \cdot \lambda_{p} \propto \lambda_{e}^{2} \)
B . \( \lambda_{p} \propto \lambda_{e} \)
\( \mathbf{c} \cdot \lambda_{p} \propto \sqrt{\lambda_{e}} \)
D. \( \lambda_{p} \propto \frac{1}{\sqrt{\lambda_{e}}} \)
Subject: Physics
The refractive index of a certain flint
glass is \( 1.65 . \) Incident angle is the light reflected from the surface of the glass
completely polarized if the glass is immersed in (a) air and (b) water is
\( \left(\tan 58.8^{\circ}=1.65\right)\left(\tan 51.1^{\circ}=1.24\right) \)
A. \( 60^{\circ}, 50^{\circ} \)
B. 58.8', 51.1 \( ^{\circ} \)
\( c \cdot 65^{\circ}, 52^{\circ} \)
D. \( 61^{\circ}, 54^{\circ} \)
Subject: Maths
A quadratic polynomial is exactly divisible by \( (x+1) \&(x+2) \) and leaves the remainder 4 after division by \( (x+3) \) then that polynomial is
A \( \cdot x^{2}+6 x+4 \)
B. \( 2 x^{2}+6 x+4 \)
c. \( 2 x^{2}+6 x-4 \)
D. \( x^{2}+6 x-4 \)
Subject: Maths
If a line makes an angle \( \theta_{1}, \theta_{2}, \theta_{3} \) which
the axis respectively, then \( \cos 2 \theta_{1}+ \)
\( \cos 2 \theta_{2}+\cos 2 \theta_{3}=? \)
A . -4
B . 2
\( c .3 \)
D. -
Subject: Chemistry
Select the correct option.
(a) Energy of ground state of \( \boldsymbol{H} e^{+} \)
\[
(i)+6.04 e v
\]
(b) Potential energy of I orbit of \( \boldsymbol{H}- \)
atom
(ii) -27.2 eV
(c) Kinetic energy of II excited state of
\( \boldsymbol{H} e^{+} \)
(iii) +54.4 ev
(d) Ionisation potential of \( \boldsymbol{H} \boldsymbol{e}^{+} \)
(iv) \( -54.4 \mathrm{eV} \)
\( A \cdot a(i), b \) (ii) \( , c \) (iii), d (iv)
B. a (iv), b (iii), c (ii), d(i)
\( c \cdot a(i v), b(i i), c(i), d \) (iii)
D. a (ii), b (iii), c (i), d (iv)
Subject: Chemistry
Given there are 3 isotopes of hydrogen \( \left(^{1} \boldsymbol{H},^{2} \boldsymbol{H} \text { and }^{3} \boldsymbol{H}\right) \) and \( \boldsymbol{2} \) isotopes of
oxygen \( \left(^{15} \boldsymbol{O} \text { and }^{16} \boldsymbol{O}\right), \) how many peaks
would be expected on a mass spectrum
for the hydronium ion, \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \) ?
\( \mathbf{A} \cdot \mathbf{6} \)
B. 7
c. 8
D.
Subject: Physics
Two parallel plane mirrors placed facing each other forms \( \infty \) images of an
object. Does this hold good, if they are placed at an angle \( \boldsymbol{\theta} \neq \mathbf{0} ? \)
A. Yes
B. No
c. only if angle is of the form \( \theta=\pi / n, n=1,2,3 \dots \)
D. only if angle is of the form \( \theta \neq \pi / n, n=1,2,3 \dots \)
Subject: Chemistry
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) of \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O H} \) is \( \boldsymbol{4} . \boldsymbol{7} 4 . \) If the ratio of
the buffer mixture \( \left[\boldsymbol{N} \boldsymbol{H}_{\boldsymbol{4}} \boldsymbol{C l}\right]: \)
\( \left[N H_{4} O H\right] \) is \( 1: 10, \) then the \( p H \) of that
buffer is:
A .4 .74
B. 10.26
c. 9.26
D. 3.74
Subject: Chemistry
A solution prepared by dissolving 2.8 \( \mathrm{gm} \) of lime. \( \mathrm{CaO} \) in enough water to make 100 L of lime water
\( \left(\operatorname{Ca}(O H)_{2}(a q .)\right) . \) If solubility of
\( \boldsymbol{C a}(\boldsymbol{O} \boldsymbol{H})_{2} \) in water is 148 gm. The \( \boldsymbol{p} \boldsymbol{H} \)
of the solution obtained will be:
\( [\log 2=0.3, \text { Atomic masses are } C a= \) \( \mathbf{4 0}, \boldsymbol{O}=\mathbf{1 6}, \boldsymbol{H}=\mathbf{1 1}] \)
A . 12.3
B. 1.3
c. 12.6
D. 13
Subject: Physics
Two rings have their \( M . I \) in the ratio 2
1, If their diameters are in ratio of 2: 1
then the ratio of their masses will be:
\( \mathbf{A} \cdot 2: 1 \)
B. 1: 1
c. 1: 2
\( \mathbf{D} \cdot 1: 4 \)
Subject: Maths
There are three coins. One is a two-
headed coin (having head on both faces), another is a biased coin that
comes up heads \( 75 \% \) of the times and
third is also a biased coin that comes
up tails \( 40 \% \) of the times. One of the three coins is chosen at random and
tossed, and it shows heads. What is the probability that it was the two-headed
\( \operatorname{coin} ? \)
Subject: Physics
A solid body starts rotating about a stationary axis with an angular acceleration \( \boldsymbol{\alpha}=\left(\mathbf{2 . 0} \times \mathbf{1 0}^{-\mathbf{2}}\right) \boldsymbol{t} \boldsymbol{r a d} / \boldsymbol{s}^{2} \)
where \( t \) is in seconds. How soon(in
seconds) after the beginning of rotation will the total acceleration vector of an
arbitrary point of the body form an angle
\( \boldsymbol{\theta}=\mathbf{6 0}^{\circ} \) with its velocity vector?
Subject: Maths
For what value of \( a \), the function
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}
\frac{1-\cos 4 x}{\boldsymbol{x}^{2}}, & \boldsymbol{i f} \quad \boldsymbol{x}<0 \\
\boldsymbol{a}, \quad \boldsymbol{i f x}=\mathbf{0} & \\
\frac{\sqrt{\boldsymbol{x}}}{\sqrt{\mathbf{1 6 + \sqrt { \boldsymbol { x } }}-\boldsymbol{4}}}, & \boldsymbol{i f} \boldsymbol{x}>0
\end{array}\right.
\]
continuous at \( \boldsymbol{x}=\mathbf{0} \)
Subject: Chemistry
The total pressure in a mixture of 8 g of dioxygen and 4 g of dihydrogen confined in a vessel of \( 1 d m^{3} \) at \( 27^{\circ} C \) is :
\( \left(R=0.083 \text { bar } d m^{3} K^{-1} m o l^{-1}\right) \)
A . 44.02 bar
B . 35.35 bar
c. 56.025 bar
D. 42.39 bar
Subject: Physics
Assertion
Sound waves do not travel through
vacuum
Reason
Sound waves are mechanical waves
which require a medium for their
propogation
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 line represented by the equation \( y= \) \( x \) is the perpendicular bisector of line segment AB. If A has the coordinates
\( (-3,3), \) what are the coordinates of \( \mathrm{B} \) ?
A \( \cdot(6,-3) \)
в. (3,-6)
c. (3,-3)
D. (6,3)
Subject: Maths
If \( z_{1} \) and \( z_{2} \) two complex numbers satisfying the equation \( \left|\frac{z_{1}+i z_{2}}{z_{1} i z_{2}}\right|=1 \) then \( \frac{z_{1}}{z_{2}} \) is a
A . purely real
B. of unit modulus
c. purely imaginary
D. none of these
Subject: Physics
A ball is dropped from the top of a building. The ball takes 0.5 s to fall past the length of a window, the top of the window being at a distance of \( 3 \mathrm{m} \) from the top of the building. If the speed of the ball at the top and the bottom of the
window are \( V_{T} \) and \( V_{B} \) respectively,
then \( \left(\boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s e c}^{2}\right) \)
A \( \cdot V_{T}+V_{B}=12 m s^{-1} \)
в. \( V_{T}-V_{B}=4.9 \mathrm{ms}^{-1} \)
c. \( V_{B} V_{T}=1 \mathrm{ms}^{-1} \)
D. \( \frac{V_{B}}{V_{T}}=1 \mathrm{ms}^{-1} \)
Subject: Chemistry
Given that the equilibrium constant for the reaction \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons \)
\( 2 S O_{3}(g) \)
has a value of 278 at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature? \( \boldsymbol{S O}_{3(g)} \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{2(g)}+\frac{\mathbf{1}}{2} \boldsymbol{O}_{2(g)} \)
B . \( 1.3 \times 10^{-5} \)
c. \( 1.8 \times 10^{-3} \)
D. \( 3.6 \times 10^{-5} \)
Subject: Physics
An electric dipole is along a uniform
electric field. If it is deflected by \( 60^{\circ} \)
work done by the agent is \( 2 \times 10^{-19} J \)
Then the work done by an agent if it is
deflected by \( 30^{\circ} \) further is:
A \( \cdot 2.5 \times 10^{-19} \mathrm{J} \)
В. \( 2 \times 10^{-19} J \)
c. \( 4 \times 10^{-19} \mathrm{J} \)
D. \( 2 \times 10^{-16} J \)
Subject: Maths
\( \left(x^{2}+y^{2}-z^{2}\right)^{2}-\left(x^{2}-y^{2}+z^{2}\right)^{2}= \)
\( A \cdot O \)
B \( \cdot 4 x^{2} z^{2} y^{2} \)
C \( .-4 x^{2} z^{2}+4 x^{2} y^{2} \)
D・ \( x^{4}+y^{4}+z^{4} \)
Subject: Maths
If the roots of \( a x^{3}+b x^{2}+c x+d=0 \)
are in A.P., then the roots of \( a(x+ \)
\( k)^{3}+b(x+k)^{2}+c(x+k)+d=0 \) are
in
A. A.P
в. G.
c. н.
D. A.G.P.
Subject: Maths
The displacement of a particle is given by \( \boldsymbol{y}=\left(6 t^{2}+3 t+4\right) m, \) where \( t \) is in
seconds. Calculate the instantaneous
speed of the particle.
A . 12
B. \( 12 t+3 \)
c. \( 12 t+4 \)
D. \( 3 t+3 \)
Subject: Chemistry
The complete balanced equation is:
\( \boldsymbol{C l}_{2}+\boldsymbol{I O}_{3}^{-}+\boldsymbol{O H}^{-} \rightarrow \boldsymbol{I} \boldsymbol{O}_{4}^{-}+\boldsymbol{C l}^{-}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
A \( \cdot C l_{2}+I O_{3}^{-}+2 O H^{-} \rightarrow I O_{4}^{-}+2 C l^{-}+H_{2} O \)
в. \( 4 C l_{2}+I O_{3}^{-}+4 O H^{-} \rightarrow I O_{4}^{-}+C l^{-}+H_{2} O \)
c. \( C l_{2}+I O_{3}^{-}+3 O H^{-} \rightarrow I O_{4}^{-}+2 C l^{-}+H_{2} O \)
D. none of these
Subject: Physics
(i) If specific heat of ice is 0.5 cal \( g^{-1} C^{-1}, \) then the amount of heat required to convert 10 g of ice from \( -5^{\circ} C \) to \( 0^{\circ} C \)
\( \mathbf{A} \cdot 15 \mathrm{cal} \)
B . \( 25 \mathrm{cal} \)
\( \mathbf{c} .50 \mathrm{cal} \)
D. 100 cal
Subject: Physics
The block is moved from A to C along
three different paths. Find the Work done by friction when the block is
displaced from \( A \) to \( B \) and then from \( B \) to
\( \mathrm{C} \)
A. \( W=-\mu m g(a+b) \)
в. \( W=-\mu m g \)
C. \( W=-\mu m g(a+b) / 2 \)
D. None of the above
Subject: Chemistry
Assertion
Statement \( -1: H_{2} S O_{4} \) is more viscous
than water.
Reason
Statement \( -2: \ln H_{2} S O_{4}, \) sulphur has
highest oxidation state.
A. Statement - 1 is true, Statement - 2 is true and Statement - 2 is correct explanation for Statement -
1
B. Statement - 1 is true, Statement - 2 is true and Statement - 2 is NOT the correct explanation for Statement - 1.
c. statement -1 is true, statement - 2 is false
D. statement -1 is false, Statement - 2 is true
Subject: Chemistry
Statement I : An exothermic reaction
has a positive \( \Delta \boldsymbol{H} \) value
Because
Statement II : Heat must be added to
the reaction for the reaction to occur
A. Statement 1 and Statement 2 are correct and
Statement 2 is the correct explanation of Statement 1.
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.
Subject: Maths
\( \boldsymbol{i}^{2}=-\mathbf{1}, \) then \( \boldsymbol{i}^{2}+\boldsymbol{i}^{4}+\boldsymbol{i}^{\boldsymbol{6}}+\boldsymbol{i}^{\boldsymbol{8}}+\ldots+ \)
\( (2 n) \) terms is:
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c \cdot i \)
D. \( -i \)
Subject: Maths
Find the inverse of the matrix
\( \mathbf{A}=\left[\begin{array}{ccc}\mathbf{0} & \mathbf{1} & \mathbf{2} \\ {[\mathbf{0 . 3 e m}] \mathbf{1}} & \mathbf{2} & \mathbf{3} \\ {[\mathbf{0 . 3 e m}] \mathbf{3}} & \mathbf{1} & \mathbf{1}\end{array}\right] \)
Subject: Physics
An electron moves at right angle to a magnetic field of \( 15 \times 10^{-2} T \) with a
speed of \( 6 \times 10^{7} m / s . \) If the specific
charge of the electron is \( 1.7 \times \) \( 10^{11} C / k g . \) The radius of the circular
path will be
\( \mathbf{A} \cdot 2.9 \mathrm{cm} \)
в. \( 3.9 \mathrm{cm} \)
\( c .2 .35 \mathrm{cm} \)
D. \( 2 c m \)
Subject: Physics
An ideal battery of emf \( 2 V \) and a series
resistance \( R \) are connected in the
primary circuit of a potentiometer of length \( 1 \mathrm{m} \) and resistance \( \Omega \). The value of \( \boldsymbol{R} \) to give a potential difference of \( \mathbf{5} \) \( m V \) across the \( 10 \mathrm{cm} \) of potentiometer wire is:
\( \mathbf{A} \cdot 180 \Omega \)
в. \( 190 \Omega \)
c. \( 195 \Omega \)
D. 200\Omega
Subject: Physics
Six resistors of each 2 ohm are
connected as shown in the figure. The
resultant resistance between \( A \) and \( B \)
is.
\( \mathbf{A} \cdot 4 \Omega \)
B. \( 2 \Omega \)
\( c \cdot 1 \Omega \)
D. \( 10 \Omega \)
Subject: Physics
The distance between two particle is decreasing at the rate of \( 6 \mathrm{m} / \mathrm{sec} \). If these particles travel with same speeds and in the same direction, then the separation increase at the rate of 4 m/sec. The particle have speed as
A. \( 5 \mathrm{m} / \mathrm{sec} ; 1 \mathrm{m} / \mathrm{sec} \)
B. \( 4 \mathrm{m} / \mathrm{sec} ; 1 \mathrm{m} / \mathrm{sec} \)
c. \( 4 \mathrm{m} / \mathrm{sec} ; 2 \mathrm{m} / \mathrm{sec} \)
D. \( 5 \mathrm{m} / \mathrm{sec} ; 2 \mathrm{m} / \mathrm{sec} \)
Subject: Physics
Two exactly similar wires of steel \( (\mathrm{y}=20 \) \( x 10^{11} \) dyne \( / \mathrm{cm}^{2} \) ) and copper \( (\mathrm{y}=12 \times 10 \)
11 dyne /cm \( ^{2} \) )are stretched by equal forces. If the total elongation is \( 1 \mathrm{cm} \) elongation of copper wire is
\( \mathbf{A} \cdot 3 / 5 \mathrm{cm} \)
в. \( 5 / 3 c m \)
\( \mathbf{c} \cdot 3 / 8 c m \)
D. \( 5 / 8 c m \)
Subject: Physics
Sound waves are passing through two
routes-one in straight path and the other along a semicircular path of
radius \( r \) and are again combined into
one pipe and superposed as shown in
the figure. If the velocity of sound waves
in the pipe is \( v, \) then frequencies of
resultant waves of maximum
amplitude will be integral multiples of:
\( A \)
в. \( \frac{v}{r(\pi-1)} \)
c. \( \frac{2 v}{r(\pi-1)} \)
D. \( \frac{v}{r(\pi+1)} \)
Subject: Physics
A mixture of polarised and unpolarised
light is incident on a polariser. As the
polariser is rotated through \( 360^{\circ}, \) it is
found that the minimum and the
maximum of the transmitted intensity
is in the ratio \( 1: q . \) The ratio of
intensities of polarised to unpolarised light in the incident beam is
A \( \cdot \frac{1}{2}(q-1): 1 \)
в. \( _{1: \frac{1}{2}(q-1)} \)
c. \( \frac{1}{2} q: 1 \)
D. \( _{1}: \frac{1}{2} q \)