AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \int\left\{\frac{(\log x-1)}{1+(\log x)^{2}}\right\}^{2} d x \) is equal to
A \( \cdot \frac{x}{(\log x)^{2}+1}+c \)
B. \( \frac{x e^{x}}{1+x^{2}}+c \)
c. \( \frac{x}{x^{2}+1}+c \)
D. \( \frac{\log x}{(\log x)^{2}+1}+c \)
Subject: Maths
If tangents \( \boldsymbol{P} \boldsymbol{A} \) and \( \boldsymbol{P} \boldsymbol{B} \) from a point \( \boldsymbol{P} \)
to a circle with centre \( O \) are inclined to
each other at angle of \( 80^{\circ}, \) then \( \angle P O A \) is equal to.
A \( .50^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 70^{\circ} \)
D. \( 80^{\circ} \)
Subject: Physics
A magnet of moment \( 1.2 A m^{2} \) is kept
suspended in a magnetic field of
induction \( 2 \times 10^{-6} \). The work done in
rotating it through \( 120^{\circ} \) is:
A \( \cdot 2.4 \times 10^{-6} J \)
B . \( 4.8 \times 10^{-6} J \)
c. \( 1.2 \times 10^{-6} J \)
D. \( 3.6 \times 10^{-6} J \)
Subject: Physics
A long cylindrical tank of cross-
sectional area \( 0.5 m^{2} \) is filled with
water. It has a small hole at a height
\( 50 \mathrm{cm} \) from the bottom. A movable
piston of cross-sectional area almost
equal to \( 0.5 m^{2} \) is fitted on the top of the
tank such that it can slide in the tank
freely. A load of \( 20 k g \) is applied on the
top of the water by piston, as shown in
the figure. Calculate the speed of the
water jet with which it hits the surface
when piston is \( 1 m \) above the bottom.
(Ignore the mass of the piston).
Subject: Physics
If elements of quantum number greater
than ' \( n^{\prime} \) were not allowed, the number of possible elements in nature would have
been
A \( \cdot \frac{1}{2} n(n+1) \)
\( ^{\mathbf{B}}\left\{\frac{n(n+1)}{2}\right\}^{2} \)
c. \( \frac{1}{6} n(n+1)(2 n+1) \)
D. \( \frac{1}{3} n(n+1)(2 n+1) \)
Subject: Physics
If \( I_{1} \) and \( I_{2} \) are the magnitudes if
inclined current in the cases I and II
respectively, then.
\( \mathbf{A} \cdot I_{1}=I_{2} \)
\( \mathbf{B} \cdot I_{1}>I_{2} \)
\( \mathbf{C} \cdot I_{1}<I_{2} \)
D. Nothing can be said
Subject: Physics
Assertion
A solid sphere placed in the fluid under high pressure is compressed uniformly on all sides.
Reason
The volume of solid sphere will decrease
with change of its geometrical shape.
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
A \( 40 \mathrm{N} \) block is supported by two ropes. One rope is horizontal and the other
makes an angle of \( 30^{\circ} \) with the ceiling.
The tension in the rope attached to the ceiling is approximately:
A. 80 N
B. 40 N
c. \( 34.6 \mathrm{N} \)
D. 46.2 N
Subject: Chemistry
In a saturated of the sparingly soluble
strong electrolyte \( A g l O_{3} \) (Molecular mass \( =283 \) ), the equilibrium which
sets in is
\( \boldsymbol{A} \boldsymbol{g} \boldsymbol{I} \boldsymbol{O}_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{I} \boldsymbol{O}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
If the solubility product constant \( \boldsymbol{K}_{s p} \) of
\( A g l O_{3} \) at a given temperature is \( 1.0 \times \)
\( 10^{-8}, \) what is the mass of \( A g l O_{3} \)
contained in \( 100 m L \) of its saturated
solution?
A \( \cdot 1.0 \times 10^{-7} \)
В. \( 1.0 \times 10^{-4} \)
c. \( 28.3 \times 10^{-2} \)
D. \( 2.83 \times 10^{-3} \)
Subject: Physics
The length, breadth and thickness of a block are measured with the help of a
meter scale. given \( \ell=(5.12+0.01) \mathrm{cm}, \mathrm{b} \)
\( =(10.15+0.01) \mathrm{cm}, \mathrm{t}=(5.28+0.01) \mathrm{cm} . \) The
percentage error in volume is:
A . 0.64\%
B. 0.28\%
c. 0.37\%
D. 0.48\%
Subject: Physics
In a biprism experiment, the distance of 20 th bright bandfrom the center of the
interference pattern is \( 8 \mathrm{mm} . \) The distance of 30 th bright band from the center is
A . \( 11.8 \mathrm{mm} \)
B. 12mm
c. \( 14 \mathrm{mm} \)
D. \( 16 \mathrm{mm} \)
Subject: Maths
The area bounded by \( y=\cos x, y= \)
\( x+1 \) and \( y=0 \) in the second quadrant
is
A \( \cdot \frac{3}{2} \) sq. units
B. 2 sq. units
c. 1 sq. unit
D. \( \frac{1}{2} \) sq, units
Subject: Maths
Show that \( f(x)= \) \( \left\{\begin{array}{ll}\frac{\cos a x-\cos b x}{x^{2}}, & \text { if } x \neq 0 \\ \frac{1}{2}\left(b^{2}-a^{2}\right), & \text { if } x=0\end{array}\right. \)
where \( a \) and \( b \) are real constants, is
continuous at \( \boldsymbol{x}=\mathbf{0} \)
Subject: Physics
A pressure meter attached to a closed
water tap reads \( 1.5 \times 10^{5} \) Pa. When the
\( \operatorname{tap} \) is opened, the velocity of flow of
water is \( 10 \mathrm{ms}^{-1} \) and the reading of the
pressure meter is
A . \( 1.5 \times 10^{5} \mathrm{Pa} \)
B. \( 3 \times 10^{5} \mathrm{Pa} \)
c. \( 0.5 \times 10^{5} \mathrm{Pa} \)
D. \( 10^{5} \mathrm{Pa} \)
Subject: Physics
A boy standing on an open car throws a ball vertically upwards with a velocity of
\( 9.8 m / s, \) while moving horizontally with
uniform acceleration of \( 1 \mathrm{m} / \mathrm{s}^{2} \) starting from rest. The ball will fall behind the
boy on the car at a distance of
\( \mathbf{A} \cdot 1 m \)
B. \( 2 m \)
\( c .3 m \)
D. \( 4 m \)
Subject: Chemistry
\( \boldsymbol{Z} \boldsymbol{n}_{(s)}\left|\boldsymbol{Z} \boldsymbol{n}_{(\boldsymbol{a q})}^{\boldsymbol{2}+}(\boldsymbol{1} \boldsymbol{M}) \| \boldsymbol{N} \boldsymbol{i}_{(\boldsymbol{a q})}^{2+}(\boldsymbol{1} \boldsymbol{M})\right| \boldsymbol{N} \boldsymbol{i}_{(s)} \)
Which is incorrect for the above given
cell?
A. Electrochemical cell
B. Voltaic cell
c. Galvanic cell
D. Daniel cell
Subject: Chemistry
Which is the correct increasing order of boiling points of the following compounds?
1 - lodobutane,
1 - Bromobutane, 1 -
Chlorobutane, Butane
A. Butane <1 - Chlorobutane <1- Bromobutane <1 lodobutane
B. 1 - lodobutane <1 - Bromobutane <1 - Chlorobutane Butane
c. Butane \( <1 \) - lodobutane \( <1 \) - Bromobutane \( <1- \) Chlorobutane
D. Butane <1 - Chlorobutane <1 - lodobutane <1 Bromobutane
Subject: Physics
The number of turns in th coil of an \( a c \)
generator is 5000 and the area of the
coil is \( 0.25 m^{2} . \) The coil is rotated at the
rate of 100 cycles/s in a magnetic field
of \( 0.2 T . \) The peak value of emf
generated is nearly:
A. \( 786 k V \)
\( V \)
в. \( 440 \mathrm{kV} \)
c. \( 220 k V \)
D. \( 157.1 k V \)
Subject: Chemistry
The correct statement(s) pertaining to
the adsorption of a gas on a solid surface is/are:

This question has multiple correct options
A. Adsorption is always exothermic
B. Physisorption may transform into chemisorption at high temperature
C. Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature
D. Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation
Subject: Biology
\( \mathrm{C} 6 \mathrm{H} 1206+602 \rightarrow 6 \mathrm{CO} 2+6 \mathrm{H} 2 \mathrm{O}+\mathrm{ATP} \)
The given equation indicates which of the following activities in plants?
A. Digestion
B. Respiration
c. Transpiration
D. None of the above
Subject: Physics
A truck of mass \( 5 \times 10^{3} k g \) starting
from rest travels a distance of \( 0.5 \mathrm{km} \) in
\( 10 s \) when a force is applied on ¡t. Calculate the acceleration acquired by the truck
A \( \cdot 25 m s^{-2} \)
B. \( 1 m s^{-2} \)
c. \( 10 \mathrm{cms}^{-2} \)
D. \( 10 m s^{-2} \)
Subject: Maths
The cross section of a canal is in the
shape of trapezium. The canal is \( 15 m \)
wide at the top and \( 9 m \) wide at the
bottom. If the area of the cross section
is \( 720 m^{2}, \) then the depth of the canal is
\( \mathbf{A} \cdot 58.4 m \)
B. \( 58.6 m \)
c. \( 58.8 m \)
D. \( 60 m \)
Subject: Chemistry
The rate law of the reaction
\( \boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{3} \boldsymbol{l}^{-} \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{4}+\boldsymbol{2} \boldsymbol{B} \boldsymbol{r}^{-}+ \)
\( \boldsymbol{I}_{3}^{-} \) is rate \( =\boldsymbol{k}\left[\boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{B} \boldsymbol{r}_{2}\right]\left[\boldsymbol{I}^{-}\right] . \) The rate of
reaction is found to be \( 1.1 \times 10^{-4} M / s \)
when the concentrations of \( C_{2} H_{4} B r_{2} \)
and \( I^{-} \) are \( 0.12 \mathrm{M} \) and \( 0.18 \mathrm{M} \)
respectively. Calculate the rate constant of the reaction.
\( \mathbf{A} \cdot 4.27 \times 10^{-3} M^{-1} s^{-1} \)
B . \( 1.65 \times 10^{-3} M^{-1} s^{-1} \)
C \( .5 .1 \times 10^{-3} M^{-1} s^{-1} \)
D. None of these
Subject: Chemistry
A radioactive element X decays to give two inert gases. X is :
\( A \cdot \frac{238}{92} \mathrm{U} \)
B \( \cdot \frac{286}{88} \) Rа
\( \mathbf{C} \cdot_{84}^{20 \mathrm{p}} \mathrm{o} \)
D. \( \frac{223}{87} \) Fr
Subject: Physics
A beam of the plane polarized light
having flux \( 10^{-3} \) watt falls normally on a polarizer of a cross sectional area \( 3 \times \) \( 10^{-4} m^{2} . \) The polarizer rotates with an
angular frequency of 31.4 rad/s. The energy of the light passes through the polarizer per resolution will be
A \( \cdot 10^{-4} \) Joule
B. \( 10^{-3} \) Joule
c. \( 10^{-2} \) Joule
D. \( 10^{-1} \) Joule
Subject: Chemistry
The true statement for the acids of
phosphorus, \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) is :
\( \mathbf{A} \cdot \) the order of their acidity is \( H_{3} P O_{2}>H_{3} P O_{3}> \)
\( H_{3} P O_{4} \)
B. all of them are reducing in nature
C. all of them are tribasic acids
D. the geometry of phosphorus is tetrahedral in all the three
Subject: Maths
An equation of a plane containing the
lines \( r=a_{1}+t b_{1} \) and \( r=a_{2}+t b_{2} \)
where \( \left[\boldsymbol{a}_{2}-\boldsymbol{a}_{1}, \boldsymbol{b}_{1}, \boldsymbol{b}_{2}\right]=\boldsymbol{0} \) is
A \( \cdot\left[r-a_{1}, b_{1}, b_{2}\right]=0 \)
B . \( \left[r-a_{2}, b_{1}, b_{2}\right]=0 \)
c. \( \left[r-a_{2}, a_{1}, b_{2}\right]=0 \)
D . \( \left[r-a, a_{2}, b_{2}\right]=0 \)
Subject: Physics
Choose the correct statement from the
following:
This question has multiple correct options
\( \mathbf{A} \cdot 50^{\circ} \mathrm{C} \) is equal to \( 122^{\circ} \mathrm{F} \)
B. A clinical thermometer cannot be sterilized using boiling water.
C. Unequal expansion causes cracks in the walls of the buildings.
D. Graphite is a bad conductor of heat.
Subject: Chemistry
Find the number of ligand(s) which is/are non-classical ligand.
\( \boldsymbol{C O}, \boldsymbol{N O}, \boldsymbol{C}_{2} \boldsymbol{H}_{4}, \boldsymbol{C}_{3} \mathrm{H}_{5}^{-}, \boldsymbol{H}^{-} \)
Subject: Physics
Calculate the wavelength of a wave if its frequency is \( 256 \mathrm{Hz} \) and and speed of the wave is \( 350 \mathrm{m} / \mathrm{s} \)
\( A \cdot 89,600 m \)
B. 350 \( m \)
\( c \cdot 94 m \)
D. \( 1.4 \mathrm{m} \)
E. \( 0.73 \mathrm{m} \)
Subject: Physics
\( \ln \) a parallel \( L-C-R \) circuit as
shown in figure if \( I_{R}, I_{L}, I_{C} \) and \( I \)
represents the rms values of current
flowing through resistor, inductor, capacitor and the source, then choose the appropriate correct answer
\( \mathbf{A} \cdot I=I_{R}+I_{L}+I_{C} \)
В . \( I=I_{R}+I_{L}-I_{C} \)
c. \( I_{L} \) or \( I_{C} \) may be greater than \( I \)
D. None of the above
Subject: Chemistry
The standard reduction potential of a \( A g C l / A g \) electrode is \( 0.2 V \) and that of
a silver electrode \( \left(\boldsymbol{A} \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}\right) \) is \( \mathbf{0 . 7 9} \boldsymbol{V} \)
The maximum amount of \( A g C l \) that
can dissolve in \( 10^{6} \) L of a \( 0.1 M A g N O_{3} \)
solution is:
A. \( 0.5 \mathrm{mmol} \)
в. \( 1.0 \mathrm{mmol} \)
c. \( 2.0 \mathrm{mmol} \)
D. \( 2.5 \mathrm{mmol} \)
Subject: Physics
Which of the following is the right
derivation for Ampere-Maxwell law?
A \( \cdot \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} i_{c}+4 \pi \mu_{0} \varepsilon_{0} \frac{d \phi_{E}}{d t} \)
B \( \cdot \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} i_{c}+3 \mu_{0} \varepsilon_{0} \frac{d \phi_{E}}{i d t} \)
\( ^{\mathbf{C}} \cdot \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} i_{c}+\mu_{0} \varepsilon_{0} \frac{d \phi_{E}}{d t} \)
D \( \cdot \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} i_{c}+\frac{\mu_{0}}{\varepsilon_{0}} \frac{d \phi_{E}}{d t} \)
Subject: Chemistry
toppr
Q Type your ques
to the processes that occur in living organisms. This primarily because the functioning of enzymes-catalysts for these processes - is sharply pH dependent. The normal pH value of blood plasma is \( 7.4 . \) Severe illness or death
can result from sustained variations of
a few tenths of pH unit.
Among the factors that lead to a condition of acidosis, in which there is a
decrease in the pH of blood are heart failure, kidney failure diabetes mellitus
persistent diarrhoea or a long term high protein diet.A temporary condition of acidosis may result from prolonged, intensive exercise. Alkalosis, which
causes increase in pH of blood may occur as a result of severe vomiting over breathing or exposure to high altitudes.

Several factors are involved in the
control of the pH of blood. A particularly important one is the ratio of dissolved \( H C O_{3}^{-} \) to \( H_{2} C O_{3} . C O_{2}(g) \) is
moderately soluble in water and in aqueous solution reacts only to a
limited extent to produce \( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3} \)
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}(\boldsymbol{a} \boldsymbol{q}) \)
\( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{1}}=\mathbf{6 . 1 1} \)
\( \boldsymbol{H} \boldsymbol{C O}_{3}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{3}^{2-}+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{2}}=\mathbf{1 0 . 2 5} \)
In the \( H_{2} C O_{3}, H C O_{3}^{-} \) buffer system, we deal only with the first ionization
\( \operatorname{step}\left(\boldsymbol{K}_{a_{1}}\right): \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3} \) is a weak acid and
\( H C O_{3}^{-} \) is the conjugate base (salt)
\( C O_{2} \) enters the blood from tissues as
the by -product of a metabolic reaction.
In the lungs, \( C O_{2}(g) \) is exchanged for \( O_{2}(g), \) which is transported throughout the body by the blood.Important diagnostic analysis in the blood is :
A \( \cdot\left[H_{2} P O_{4}^{-}\right] /\left[H P O_{4}^{-}\right. \)
в \( \cdot\left[H C O_{3}^{-}\right] /\left[C O_{2}\right] \)
c. \( \left[C O_{3}^{2-}\right] /\left[H C O_{3}^{2-}\right] \)
D \cdot \( \left[P O_{4}^{3-}\right] /\left[H P O_{4}^{2-}\right] \)
Subject: Physics
Heat energy is supplied at a constant
rate to \( 100 \mathrm{g} \) of ice at \( 0^{\circ} \mathrm{C} \). The ice is
converted into water at \( 0^{\circ} \mathrm{C} \) in 2
minutes. How much time will be
required to raised the temperature of water from \( 0^{\circ} \mathrm{C} \) to \( 20^{\circ} \mathrm{C} \) ? [Given:
specific heat capacity of water \( = \)
\( 4.2 J g^{-1 \circ} C^{-1}, \) specific latent heat of
ice \( =\mathbf{3 3 6} \boldsymbol{J} \boldsymbol{g}^{-\mathbf{1}} \)
Subject: Physics
The breakdown field for air is about \( 2 x \)
\( \mathbf{1 0}^{6} \) volt/m. Therefore, the maximum
charge that can be placed on a sphere of diameter \( 10 \mathrm{cm} \) is
A \( .2 .0 \times 10^{-4} \mathrm{c} \)
В. \( 5.6 \times 10^{-7} \mathrm{c} \)
c. \( 5.6 \times 10^{-2} \mathrm{c} \)
D . \( 2.0 \times 10^{2} \mathrm{c} \)
Subject: Physics
Man A is sitting in a car moving with a speed of \( 54 \mathrm{km} / \mathrm{hr} \) observes a man \( \mathrm{B} \) in
front of the car crossing perpendicularly a road of width \( 15 \mathrm{m} \) in three seconds. Then the velocity of man
\( \mathrm{B}(\text { in } \mathrm{m} / \mathrm{s}) \) will be
A \( .5 \sqrt{10} \) towards the car at some angle
B. \( 5 \sqrt{10} \) away from the car at some angle
c. 5 perpendicular to the road
D. 15 along the road
Subject: Physics
A square plate lies in the xy plane with its centre at the origin and its edges parallel to the \( x \) and \( y \) axes. Its moments of inertia about the \( x, y \) and \( z \) axes are
\( I_{x}, I_{y}, \) and \( I_{z} \) respectively, and about a
diagonal it is \( \boldsymbol{I}_{D} \)
A \( \cdot I_{x}=I_{y}=\frac{1}{2} I_{z} \)
В . \( I_{x}=I_{y}=2 I_{z} \)
c. \( I_{D}=I_{x} \)
D \( \cdot I_{D}=I_{z} \)
Subject: Physics
The torque of force \( \overrightarrow{\boldsymbol{F}}=\mathbf{2} \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}}+\mathbf{4} \hat{\boldsymbol{k}} \)
newton acting at a point \( \vec{r}=3 \hat{i}+2 \hat{j}+ \) \( 3 \hat{k} \) metre about is:
A. \( 6 \hat{i}-6 \hat{j}+12 \hat{k} N-m \)
B . \( -6 \hat{i}+6 \hat{j}-12 \hat{k} N-m \)
c. \( 17 \hat{i}-6 \hat{j}-13 \hat{k} N-m \)
D. \( -17 \hat{i}+6 \hat{j}+13 \hat{k} N-m \)
Subject: Maths
A letter is known to have come either
from \( L O N D O N \) or \( C L I F T O N ; \) on the
postmark only the two consecutive letters \( \boldsymbol{O} \boldsymbol{N} \) are ellegible. The probability that it came from \( L O N D O N \) is
A \( \cdot \frac{5}{17} \)
в. \( \frac{12}{17} \)
c. \( \frac{17}{30} \)
D. \( \frac{3}{5} \)
Subject: Maths
Three numbers are chosen at random
without replacement from \( 1,2,3, \dots . ., 10 \) The probability that the minimum of
the chosen numbers is 3 or their
maximum is 7 is
A \( \cdot 1 / 2 \)
в. \( 1 / 3 \)
c. \( 1 / 4 \)
D. \( 11 / 40 \)
Subject: Physics
Two particles \( X \) and \( Y \) having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field
and describe circular paths or radii \( \boldsymbol{R}_{1} \)
and \( R_{2} \) respectively. The ratio of mass
of \( X \) to that of \( Y \) is equal to:
\( ^{\mathbf{A}} \cdot\left(\frac{R_{1}}{R_{2}}\right)^{2} \)
B. \( \left(\frac{R_{1}}{R_{2}}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{R_{1}}{R_{2}}\right)^{1 / 2} \)
D. \( \frac{R_{2}}{R_{1}} \)
Subject: Physics
Q Type your question.
surrounded by an incompressible liquid in a cylindrical container. A massless
piston of area \( A \) floats on the surface of
the liquid. The magnitude of fractional change in the radius of the sphere \( \left(\frac{d R}{R}\right) \) when a mass \( M \) is placed slowly on the
piston to compress the liquid is:
\( ^{\mathrm{A}} \cdot \frac{M g}{3 A B} \)
в. \( \frac{M g}{A B} \)
c. \( \frac{3 M g}{A B} \)
D. none of thes
Subject: Physics
When a rod of length I is rotated with angular velocity of \( \omega \) in a perpendicular field of induction \( \mathrm{B} \), about one end, the
emf across its ends is
\( \mathbf{A} \cdot B l^{2} \omega \)
в. \( \frac{B l^{2} \omega}{2} \)
\( c . B l \omega \)
D. \( \frac{B l \omega}{2} \)
Subject: Chemistry
\( L n^{3+}( \) trivalent lanthanides ions) have
\( E C \)
A \( \cdot[X e] 4 f^{1} \) to \( [X e] 4 F^{14} \)
B . \( [X e] 4 d^{1} 4 f^{1} \) to \( [X e] 4 d^{1} 4 F^{14} \)
\( \mathbf{c} \cdot[X e] 4 d^{2} 4 f^{0} \) to \( [X e] 4 d^{1} 4 F^{1} \)
D \( \cdot[X e] 4 f^{0} \) to \( [X e] 4 F^{1} \)
Subject: Maths
Find the sum of \( 7+10 \frac{1}{2}+14+\ldots+84 \)
A \( \cdot \frac{2093}{2} \)
в. \( \frac{1093}{2} \)
c. \( \frac{2193}{2} \)
D. \( \frac{3093}{2} \)
Subject: Biology
Assertion
Most of the premature babies suffer
from Respiratory distress syndrome
Reason
Lecithin (surfactant) is secreted on the
inner side of the alveoli and prevent
collapsing of aveolar wall
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 equation is not a balanced chemical reaction?
A \( \cdot P_{4}+20 H N O_{3} \rightarrow 4 H_{3} P O_{4}+20 N O_{2}+4 H_{2} O \)
B . \( I_{2}+10 H N O_{3} \rightarrow 2 H I O_{3}+10 N O_{2}+4 H_{2} O \)
c. \( S+6 H N O_{3} \rightarrow H_{2} S O_{4}+6 N O_{2}+2 H_{2} O \)
D. None of these
Subject: Physics
Choose the correct statements from the
following
This question has multiple correct options
A. Evaporation takes place from the surface of a liquid at all temperatures.
B. The rate of evaporation depends upon the area of the exposed surface of the liquid, nature of the liquid and its temperature.
C. The rate of evaporation depends on the pressure to which the liquid is subjected.
D. The cooling produced in evaporation is a consequence of the fact that a liquid has latent heat.
Subject: Biology
Which of the following is not relevant to
the structure of double helical DNA?
A. The helix makes one complete spiral turn every \( 34 A^{\circ} \)
B. The diameter of the helix is \( 20 A^{\circ} \)
C. The distance between adjacent nucleotide is \( 3.4 \mathrm{A}^{\circ} \)
D. Each strand of helix has a backbone made up of alternating ribose sugar and phosphate
E. The two adjacent sugar molecules joined with phosphate by phosphodiester bond.
Subject: Physics
Velocity versus time graph of a ball of mass \( 50 \mathrm{g} \) rolling on a concrete floor is shown in the figure. Calculate the acceleration
A . \( -10 m s^{-2} \)
B . \( -20 m s^{-2} \)
c. \( -30 m s^{-2} \)
D. \( -40 m s^{-2} \)
Subject: Physics
Statement \( (A): \) The reactance offered by an inductance in A.C. circuit decreases with the increase of \( A C \)
frequency. Statement \( (\mathrm{B}): \) The reactance offered
by a capacitor in AC circuit increases with the increase of AC frequency.
A. A is true but B is false
B. Both A and B are true
c. A is false but B is true
D. Both A and B are false
Subject: Physics
Figure shows the position time graph of
a particle moving on the \( x \) -axis.
A. The particle is continuously going in positive \( x \) direction
B. Area under x - t curve shows the displacement of particle
C. The velocity increases up to a time \( t_{0} \), and then becomes constant
D. The particle moves at a constant velocity up to a time
\( t_{0}, \) and then stops
Subject: Chemistry
A metal 'M' which is one of the best
conductor of heat and electricity is used in making electric wires is found
in nature as sulphide ore \( M_{2} S ? \)
(i) Name the metal 'M'.
(ii) Which process will be suitable for extraction of this metal M from its ore
\( M_{2} S ? \) Write the balanced chemical
reactions involving in the process of extraction. With the help of a labelled diagram, explain the process of electrolytic refining of the metal.
Subject: Chemistry
When a gas is bubbled through water at \( 298 K, \) a very dilute solution of gas is
obtained. Henry's law constant for the
gas is \( 100 k \) bar. If gas exerts a pressure
of 1 bar, number of moles of gas
dissolved in 1 litre of water is :
A. 0.555
В. \( 55.55 \times 10^{-5} \)
c. \( 55.55 \times 10^{-3} \)
D. \( 5.55 \times 10^{-5} \)
Subject: Physics
The coefficient of friction between two
surfaces is 0.2. The angle of friction is
\( A \cdot \sin ^{-1}(0.2) \)
\( B \cdot \cos ^{-1}(0.2) \)
\( c \cdot \tan ^{-1}(0.1) \)
D. \( \cot ^{-1}(5) \)
Subject: Maths
The coefficient of the term independent of \( x \) in the expansion of \( \left(\frac{x+1}{x^{\frac{2}{3}}-x^{\frac{1}{3}}+1}-\frac{x-1}{x-x^{\frac{1}{2}}}\right)^{10} \)
A . 210
в. 105
c. 70
D. 112
Subject: Maths
If \( A, B, C \) are three independent events
of an experiment such that, \( \boldsymbol{P}(\boldsymbol{A} \cap \) \( \left.\boldsymbol{B}^{C} \cap \boldsymbol{C}^{C}\right)=\frac{1}{4}, \boldsymbol{P}\left(\boldsymbol{A}^{C} \cap \boldsymbol{B} \cap \boldsymbol{C}^{C}\right)= \)
\( \frac{1}{8}, P\left(A^{C} \cap B^{C} \cap C^{C}\right)=\frac{1}{4}, \) then find
\( \boldsymbol{P}(\boldsymbol{A}), \boldsymbol{P}(\boldsymbol{B}), \boldsymbol{P}(\boldsymbol{C}) \)