AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
In a school the mark distribution of 25
students in a mathematics
examination is given below. Calculate it's mode.
\( \begin{array}{cccc}30- & 40- & 50- & 6 \\ 40 & 50 & 60\end{array} \) Marks
2 No. of
students
A. 65
в. 32
c. 34
D. 31
Subject: Physics
A charged oil drop od mass \( 2.5 \times \) \( 10^{-7} k g \) is in space between the two
plates, each of area \( 2 \times 10^{-2} m^{2} \) of a
parallel plate capacitor. When the upper plate has a charge of \( 5 \times 10^{-7} C \) and the
lower plate has an equal negative
charge then the oil remains stationery. The charge of the oil drop is (take, \( g= \) \( 10 m / s^{2} \)
A \( \cdot 9 \times 10^{-1} C \)
В \( \cdot 9 \times 10^{-6} C \)
C \( .8 .85 \times 10^{-13} C \)
D. \( 1.8 \times 10^{-14} C \)
Subject: Physics
A simple harmonic motion along the \( x- \)
axis has the following properties:
amplitude \( =0.5 m, \) the time to go from
one extreme position to other is, 2 s and
\( \boldsymbol{x}=\mathbf{0 . 3} \boldsymbol{m} \) at \( \boldsymbol{t}=\mathbf{0 . 5} \boldsymbol{s} . \) The general
equation of the simple harmonic
motion is
A \( \cdot x=(0.5 m) \sin \left[\frac{\pi t}{2}+8^{\circ}\right] \)
B. \( x=(0.5 m) \sin \left[\frac{\pi t}{2}-8^{\circ}\right] \)
\( \mathbf{c} \cdot_{x}=(0.5 m) \cos \left[\frac{\pi t}{2}+8^{\circ}\right] \)
D. \( x=(0.5 m) \cos \left[\frac{\pi t}{2}-8^{\circ}\right] \)
Subject: Chemistry
Two liquids \( A \) and \( B \) form an ideal solution. At \( 300 \mathrm{K} \), the vapour pressure of a solution containing 1 mole of A and 3 mole of \( \mathrm{B} \) is \( 550 \mathrm{mm} \) of Hg. At the
same temperature, if one more mole of \( \mathrm{B} \) is added to this solution, the vapour pressure of the solution increases by 10 \( \mathrm{mm} \) of Hg. Determine the vapour pressure of \( A \) and \( B \) in their pure states.
Subject: Maths
If \( A \) and \( B \) are two mutually exclusive
events in a sample space \( S \) such that \( \boldsymbol{P}(\boldsymbol{B})=2 \boldsymbol{P}(\boldsymbol{A}) \) and \( \boldsymbol{A} \cup \boldsymbol{B}=\boldsymbol{S} \) then
\( \boldsymbol{P}(\boldsymbol{A})= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Maths
If \( \cos x \) and \( \sin x \) are solutions of the
different equation \( \boldsymbol{a}_{\mathbf{0}} \frac{\boldsymbol{d}^{\mathbf{2}} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{a}_{1} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+ \)
\( \boldsymbol{a}_{2} \boldsymbol{y}=\mathbf{0}, \) where \( \boldsymbol{a}_{0}, \boldsymbol{a}_{1}, \boldsymbol{a}_{2} \) are real
constants, then which of the following
is/are always true?
This question has multiple correct options
\( \mathbf{A} \cdot A \cos x+B \sin x \) is a solution, where \( A \) and \( B \) are real
costants
B. \( A \cos \left(x+\frac{\pi}{4}\right) \) is a solution, where \( A \) is real constant
c. \( A \cos x \sin x \) is a solution, where \( A \) is real constant
D. \( A \cos \left(x+\frac{\pi}{4}\right)+B \sin \left(x-\frac{\pi}{4}\right) \) is a solution, where \( A \)
and \( B \) are real constants
Subject: Maths
Graph the solution set
\( |x| \geq 3 \)
\( A \cdot(-3,3) \)
B \( \cdot(-\infty,-3] \cap[3, \infty) \)
\( \mathbf{c} \cdot(-\infty,-3) \cap(3, \infty) \)
D. [-3,3]
\( \langle 1,1,-7,6-5,-4 \)
Subject: Maths
f \( 25025=p_{1}^{x_{1}} \cdot p_{2}^{x_{2}} \cdot p_{3}^{x_{3}} \cdot p_{4}^{x_{4}} \) find the value
of \( p_{1}, p_{2}, p_{3}, p_{4} \) and \( x_{1}, x_{2}, x_{3}, x_{4} \)
Subject: Maths
\( \$ \$ \) lbegin \( \{\text { matrix }\} \lim || x \) \( \mathrm{~ | x r i g h t a r r o w l q u a d ~ 1 ~ l e n d \{ m a t r i x \} \$ \$ ~} \)
\( \left(\frac{1}{x-1}-\frac{2}{x^{2}-1}\right) \)
Subject: Chemistry
\( 18.4 \mathrm{g} \) mixture of \( \mathrm{CaCO}_{3} \) and \( \mathrm{MgCO}_{3} \)
on strongly heating gives \( 8.8 \mathrm{g} \) of \( \mathrm{CO}_{2} \)
gas. Calculate mole percentage of
\( M g C O_{3} \) in the mixture
Subject: Maths
If \( f(x)=\frac{x-1}{x+2}, \) then \( \frac{d f^{-1}(x)}{d x} \) is equal
to
A \( \cdot \frac{1}{(1-x)^{2}} \)
B. \( \frac{-3}{(1-x)^{2}} \)
c. \( \frac{3}{(1-x)^{2}} \)
D. \( \frac{-1}{(1-x)^{2}} \)
Subject: Maths
In the given triangle, \( A B \) is parallel to
\( \boldsymbol{P Q} \cdot \boldsymbol{A P}=\boldsymbol{c}, \boldsymbol{P C}=\boldsymbol{b}, \boldsymbol{P Q}=\boldsymbol{a}, \boldsymbol{A B}=\boldsymbol{x} \)
What is the value of \( x ? \)
A・ \( x=a-\frac{a c}{b} \)
B. \( x=b+\frac{a c}{b} \)
c. \( x=b-\frac{a c}{b} \)
D. \( x=a+\frac{a c}{b} \)
Subject: Biology
Which of the following conditions correctly describes the manner of determining the sex in the given example?
A. \( X O \) type of sex determines male sex in grasshopper
B. \( X O \) condition in humans as found in Klinefelter's syndrome determines female sex
c. Homozygous sex chromosome \( X X \) produce male in Drosophila
D. Homozygous sex chromosome \( Z Z \) determine female \( \operatorname{sex} \) in birds
Subject: Chemistry
The heat of combustion of methane is
\( -880 k J \) mol\( ^{-1} . \) The quantity of heat
liberated in the combustion of \( 3.2 g \)
methane is:
A . \( -88 k J \)
в. \( +88 k J \)
\( \mathbf{c} .+176 k J \)
D. \( -176 k J \)
Subject: Physics
An arc of radius r carries change. The linear density of charge is \( \lambda \) and the arc
subtends a angle \( \frac{\pi}{3} \) at the center. What
is electric potential at the center
\( ^{A} \cdot \frac{\lambda}{4 \varepsilon_{0}} \)
в. \( \frac{\lambda}{8 \varepsilon_{0}} \)
\( c \cdot \frac{\lambda}{12 \varepsilon_{0}} \)
D. \( \frac{\lambda}{16 \varepsilon_{0}} \)
Subject: Physics
A convex lens of power +6 dioptre is placed in contact with a concave lens of
power -4 dioptres. What will be the nature and focal length of this combination?
A. Concave, \( 25 \mathrm{cm} \)
B. Convex, \( 50 \mathrm{cm} \)
c. concave, \( 20 \mathrm{cm} \)
D. Convex, \( 100 \mathrm{cm} \)
Subject: Chemistry
lonisation constant of \( N H_{4}^{+} \) in water is \( 5.6 \times 10^{-10} \) at \( 25^{\circ} C . \) The rate constant
for reaction of \( N H_{4}^{+} \) and \( O H^{-} \) to form
\( N H_{3} \) and \( H_{2} O \) at \( 25^{\circ} C \) is \( 3.4 \times \) \( 10^{10} \) litre.mol\( ^{-1} . \)sec\( ^{-1} \). Calculate rate
constant for proton transfer from water to \( \boldsymbol{N} \boldsymbol{H}_{3} \)
Subject: Physics
The area of rectangle of size \( 1.23 \mathrm{cm} \times \)
\( 2.345 \mathrm{cm} \) is ?
A. \( 2.88 c m^{2} \)
2
B . \( 2.884 c m^{2} \)
\( \mathrm{c} \cdot 2.9 \mathrm{cm}^{2} \)
D . \( 2.88435 \mathrm{cm}^{2} \)
Subject: Physics
Assertion
Magnetic field lines are continuous and closed.
Reason Magnification of a convex mirror is
always positive, but that of a concave
mirror may be both positive or negative.
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 \( a \sin ^{-1} x-b \cos ^{-1} x=c, \) then the
value of \( a \sin ^{-1} x+b c o s^{-1} x \) (whenever
exists) is equal to
A . 0
B. \( \frac{\pi a b+c(b-a)}{a+b} \)
\( c \cdot \frac{\pi}{2} \)
D. \( \frac{\pi a b+c(a-b)}{a+b} \)
Subject: Chemistry
The correct arrangement of following
acids of phosphorus in the increasing
order of oxidation state of phosphorous
¡S:
A. hypophosphorous acid < orthophosphorous acid pyrophosphoric acid
B. hypophoshporous acid < pyrophosphoric acid \( < \) orthophosphorous acid
C. pyrophosphoric acid < hypophosphrous acid orthophosphorous acid
D. pyrophosphoric aicd < orthophosphorous acid hypophosphorous acid
Subject: Maths
If the sum of \( n \) terms of an A.P. is \( n A+ \)
\( n^{2} B, \) where \( A, B \) are constants, then its
common difference will be
A. \( A-B \)
в. \( A+B \)
\( c .2 A \)
D. 2 \( B \)
Subject: Biology
Match the columns and find the correct
answer
\( \begin{array}{lllll} & \text { Column I } & & \text { Column II } \\ \text { (a) } & \text { Streptomyces } & \text { (p) } & \begin{array}{l}\text { Food } \\ \text { poisoning }\end{array} \\ \text { (b) } & \text { Rhizobium } & \text { (q) } & \begin{array}{l}\text { Source of } \\ \text { antibiotic }\end{array} \\ \text { (c) } & \text { Nitrosomonas } & \text { (r) } & \begin{array}{l}\text { Nitrogen } \\ \text { fixation }\end{array} \\ \text { (d) } & \text { Acetobacter } & \text { (s) } & \text { Nitrification } \\ & \text { (t) } & \begin{array}{l}\text { Vinegar } \\ \text { synthesis }\end{array}\end{array} \)
\( \mathbf{A} \)
\( a-s, b-t, c-p, d-r \)
B. a-t, b-p, c-r, d-s
\( c \cdot a-q, b-r, c-p, d-t \)
D. \( a-q, b-r, c-s, d-t \)
Subject: Maths
\( \ln \Delta O A B, \) if \( O A=\vec{a}, \overrightarrow{O B}=\vec{b} . L \) is mid
point of \( \boldsymbol{O A} \) and \( \boldsymbol{M} \) is point on \( \boldsymbol{O B} \) such that \( \boldsymbol{O} \boldsymbol{M}: \overrightarrow{\boldsymbol{M}} \boldsymbol{B}=\boldsymbol{2}: 1 . \) If \( \boldsymbol{P} \) is mid
point of \( L M \) then \( \overrightarrow{A P}= \)
A \( \cdot \frac{1}{3} \vec{b}-\frac{3}{4} \vec{a} \)
B \( \cdot \frac{1}{3} \vec{b}+\frac{3}{4} \vec{a} \)
c. \( \frac{1}{3} \vec{a}-\frac{3}{4} \vec{b} \)
D. \( \frac{1}{3} \vec{a}+\frac{3}{4} \vec{b} \)
Subject: Maths
The coordinates of points on the line joining the points \( \boldsymbol{P}(\boldsymbol{3},-\boldsymbol{4}) \) and \( Q(-2,5) \) that is twice as far from \( P \) as from \( Q \) is
A \( \cdot\left(\frac{-1}{3}, 2\right) \)
в. \( \left(\frac{2}{3}, 2\right) \)
c. \( \left(\frac{1}{3}, 4\right) \)
D. \( \left(\frac{4}{3}, 2\right) \)
Subject: Chemistry
\( I_{2} \) produced, when ozone reacts with
moist \( K I \), is used to convert \( C_{2} H_{5} O H \)
to \( C I_{3} C H O . \) The number of moles of
ozone required to convert 1 mol of
\( C_{2} H_{5} O H \) into \( C I_{3} C H O \) is :
A . 1
B . 2
\( c \cdot 4 \)
D. 3
Subject: Chemistry
At \( 1127 \mathrm{K} \) and 1 atm pressure,
gaseous mixture of \( C O \) and \( C O_{2} \) in
equilibrium with solid carbon has \( 90.55 \% C O \) by mass;
\( \boldsymbol{C}_{(s)}+\boldsymbol{C O}_{2(g)} \rightleftharpoons \mathbf{2} \boldsymbol{C O}_{(\boldsymbol{g})} \)
Calculate \( K_{c} \) for the reaction at the
above temperature
Subject: Physics
Find the value of following on the basis of significant figure rule:
The height of a man is \( 5.87532 \mathrm{ft} \). But measurement is correct upto three significant figures. The correct height is?
A \( .5 .86 \mathrm{ft} \)
B. \( 5.87 \mathrm{ft} \)
c. \( 5.88 \mathrm{ft} \)
D. \( 5.80 \mathrm{ft} \)
Subject: Physics
A positively charged particle of \( 2.0 C \)
moves upward into an area where both a magnetic field and an electric field
are acting. The magnetic field has a
magnitude of \( 4.0 \times 10^{4} T \) and the
electric field has a magnitude of
\( 0.1 N / C . \) At what velocity must the particle be moving if it is not deflected when it enters this area?
A \( \cdot 4.0 \times 10^{-3} \mathrm{m} / \mathrm{s} \)
в. \( 125 \mathrm{m} / \mathrm{s} \)
\( c \cdot 250 m / s \)
D. \( 500 \mathrm{m} / \mathrm{s} \)
E. The particle will be deflected to the left regardless its velocity
Subject: Maths
\( \int \tan ^{-1} x d x=-1 \)
A. \( x \tan ^{-1} x+\frac{1}{2} \log \left|\frac{\tan ^{-1} x}{x^{2}+1}\right| \)
S. \( x \tan ^{-1} x-\frac{1}{2} \log \left|x^{2}+1\right| \)
C. \( x \tan ^{-1} x+\frac{1}{2} \log \left|x^{2}+1\right| \)
Subject: Maths
Let ' \( n^{\prime} \) be the number of elements in
the domain set of the function \( f(x)= \) \( \left|\ln \sqrt{x^{2}+4 x} C_{2 x^{2}+3}\right| \)
and ' \( Y^{\prime} \) be the global maximum value
of \( \boldsymbol{f}(\boldsymbol{x}), \text { then }[\boldsymbol{n}+[\boldsymbol{Y}]] \text { is .... (where }]= \)
Greatest Integer Function).
Subject: Chemistry
Calculate the number of
revolutions/sec around the nucleus of
an electron placed in III orbit of \( \boldsymbol{H} \) -atom
A \( \cdot 1.44 \times 10^{12} \)
B . \( 7.29 \times 10^{7} \)
c. \( 15.33 \times 10^{14} \)
D. \( 2.44 \times 10^{14} \)
Subject: Maths
If \( \sum_{r=1}^{n} t_{r}=\frac{n(n+1)(n+2)(n+3)}{8} \)
then \( \sum_{r=1}^{n} \frac{1}{t_{r}} \) equals
A. \( -\left(\frac{1}{(n+1)(n+2)}-\frac{1}{2}\right) \)
B. \( \left(\frac{1}{(n+1)(n+2)}-\frac{1}{2}\right) \)
c. \( \left(\frac{1}{(n+1)(n+2)}+\frac{1}{2}\right) \)
D. \( \left(\frac{1}{(n-1)(n-2)}+\frac{1}{2}\right) \)
Subject: Maths
If \( f(x) \) and \( g(x) \) are differentiable
functions for \( 0 \leq x \leq 1 \) such that
\( \boldsymbol{f}(\mathbf{0})=\mathbf{2}, \boldsymbol{g}(\mathbf{0})=\mathbf{0}, \boldsymbol{f}(\mathbf{1})=\mathbf{6}, \boldsymbol{g}(\mathbf{1})=\mathbf{2} \)
then in the interval \( (\mathbf{0}, \mathbf{1}) \)
\( \mathbf{A} \cdot f^{\prime}(x)=0 \) for all \( x \)
B . \( f^{\prime}(x)=2 g^{\prime}(x) \) for at least one \( x \)
\( \mathbf{C} \cdot f^{\prime}(x)=2 g^{\prime}(x) \) for at most one \( x \)
D. None of these
Subject: Maths
The inverse of the propositions \( (p \wedge \sim \)
\( \boldsymbol{q}) \rightarrow \boldsymbol{r} \) is
\( \mathbf{A} \cdot(\sim r) \rightarrow(\sim p) \vee q \)
в. \( (\sim p) \vee q \rightarrow(\sim p) \)
c. \( r \rightarrow p \vee(\sim q) \)
D. \( (\sim p) \wedge(\sim q) \rightarrow r \)
Subject: Physics
Two concentric spheres of radii \( R \) and \( r \)
have positive charges \( q_{1} \) and \( q_{2} \) with equal surface charge densities. What is the electric potential at their common centre?
A \( \cdot \frac{\sigma}{\epsilon_{0}}(R+r) \)
в. \( \frac{\sigma}{\epsilon_{0}}(R-r) \)
c. \( \frac{\sigma}{\epsilon_{0}}\left(\frac{1}{R}+\frac{1}{r}\right) \)
D. \( \frac{\sigma}{\epsilon_{0}}\left(\frac{R}{r}\right) \)
Subject: Physics
A body of 0.5 kg moves along the positive x-axis under the influence of a
varying force \( F \) (in Newtons) as shown
below.
f the speed of the object at \( x=4 \) m is
\( 3.16 \mathrm{m} . \mathrm{s}^{-1} \) then its speed at \( \mathrm{x}=8 \mathrm{m} \) is
A. \( 3.16 m \cdot s^{-1} \)
B. \( 9.3 m \cdot s^{-1} \)
\( c \cdot 8 m \cdot s^{-1} \)
D. \( 6.8 m \cdot s^{-1} \)
Subject: Biology
Put the following parts of a reflex arc in the correct order beginning with the
sensory receptor:
(A) Motor neuron
(B) Interneuron
(C) Effector
(D) Sensory neuron
(E) Sensory receptor
A \( \cdot(E)(D)(B)(A)(C) \)
B. \( (E)(D)(A)(B)(C) \)
c. \( (A)(B)(C)(D)(E) \)
D. \( (A)(E)(D)(B)(C) \)
Subject: Chemistry
A compound \( X \) is obtained by the
reaction of alkaline \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \) with
another compound \( Y \) followed by
acidification. Compound \( X \) also reacts with compound \( Y \) in presence of few
drops of \( H_{2} S O_{4} \) to form a sweet
smelling compound \( Z \). The compound
\( X, Y \) and \( Z \) are respectively:
A. ethanol, ethene, ethanoic acid
B. ethanoic acid, ethanol, ethylethanoate
c. ethanoic acid, ethanal, ethene
D. ethanol, ethanoic acid, sodium ethanoate
Subject: Maths
A plot of land has a shape of a
parallelogram. It is to be covered by mud. Find the cost of speeding mud at the rate of \( R s 100 \) per square meter
while the adjacent sides of the plot are
\( \mathbf{3 9} \boldsymbol{m} \) and \( \mathbf{2 5} \boldsymbol{m} \) and the diagonal is
\( \mathbf{5 6} \boldsymbol{m} \)
Subject: Chemistry
Compound (X) containing chlorine on treatment with strong ammonia gives a solid Y which is free from chlorine. (Y) analysed as: \( (C)=49.31 \%, H=9.59 \%, \) and
\( \mathrm{N}=19.18 \% \) and reacts with \( \mathrm{Br}_{2} \) and caustic soda to give a basic compound
(Z). \( (z) \) reacts with \( H N O_{2} \) to give ethanol. Suggest structures for \( (X),(Y) \) and \( (z) \)
Subject: Physics
A disc of mass \( M k g \) and radius \( R \)
metre is rotating at an angular speed of
\( \boldsymbol{\omega} \) rad/s when the motor is switched
off. Neglecting the friction at the axle, the force that must be applied
tangentially to the wheel to bring it to
rest in time \( t \) is
A \( \cdot \frac{M R \omega}{2 t} \)
B. \( \frac{M R \omega}{t} \)
c. \( \frac{2 M R \omega}{t} \)
D. \( \frac{M R^{2} \omega}{2 t} \)
Subject: Chemistry
The given reaction is called:
\[
\mathbf{R}-\mathbf{C}^{-} \mathbf{R} \frac{\mathbf{N}_{3} \mathbf{H}}{\mathbf{U}}-\mathbf{R} \mathbf{C O N H R}+\mathbf{N}_{\mathbf{2} \mathbf{S O}_{\mathbf{4}}}^{\mathbf{J}}
\]
A. Claisen-Schmidt reaction
B. Kolbe-Schmidt reaction
C. Schmidt reaction
D. Kolbe's reaction
Subject: Physics
Assertion
A heavy object always falls faster than a light object when dropped from a height
Reason

Gravitational force is proportional to the
mass of an object.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Biology
Assertion
When the ambient temperature is high and soil contains excess of water, the plants tend to lose water in the form of
droplets from lenticels.
Reason
Root pressure regulates the rate of loss of water form lenticels.
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
\( N_{2} O_{4} \rightleftharpoons 2 N O_{3}, K_{C}=4 . \) This reversible
reaction is studied graphically as shown in figure. Select the correct statements out of I, II and III
I: Reaction quotient has maximum
value at point \( \boldsymbol{A} \)

II: Reaction proceeds left to right at a
point when \( \left[\boldsymbol{N}_{2} \boldsymbol{O}_{4}\right]=\left[\boldsymbol{N} \boldsymbol{O}_{2}\right]=\mathbf{0 . 1} \boldsymbol{M} \)
Ill: \( K_{c}=Q \) when a point \( D \) or \( F \) is
reached.
\( A \cdot 1,1 \)
в. ॥, III
\( c \cdot \) ।, ॥
D. I. II. II
Subject: Maths
\( \int_{0}^{\pi / 2} \frac{\sin x d x}{(\sin x+\cos x)^{2}}= \)
A \( \cdot \sqrt{2} \log (\sqrt{2}+1) \)
B \( \cdot \frac{1}{\sqrt{2}} \log (\sqrt{2}+1) \)
\( \mathbf{c} \cdot 2 \log (\sqrt{2}+1) \)
D \( \frac{1}{2 \sqrt{2}} \log (\sqrt{2}+1) \)
Subject: Chemistry
A certain current liberated 0.504 g of
hydrogen in 2 hours. How many grams of copper can be liberated by the same current flowing for the same time in copper sulphate solution?
A. \( 31.8 \mathrm{g} \)
B. \( 16.0 \mathrm{g} \)
c. \( 12.7 \mathrm{g} \)
D. \( 63.5 \mathrm{g} \)
Subject: Physics
The distance travelled by particle from
\( \boldsymbol{t}=\mathbf{0} \) to \( \boldsymbol{t}=\mathbf{2} \) seconds is:
\( \mathbf{A} \cdot 2 m \)
B. \( 3 m \)
c. \( 4 m \)
D. \( 6 m \)
Subject: Physics
At what height from the surface of earth
will the value of \( g \) be reduced by \( 36 \% \)
from the value at the surface? \( \boldsymbol{R}= \)
\( 6400 k m \)
A . \( 400 k m \)
B. \( 800 k m \)
\( c .1600 k m \)
D. 3200km
Subject: Maths
The value of \( \cos \left[\frac{1}{2} \cos ^{-1}\left(\cos \left(\frac{-14 \pi}{5}\right)\right)\right] \) is/are:
\( ^{\mathbf{A}} \cdot \cos \left(\frac{-7 \pi}{5}\right) \)
B・ \( \sin \left(\frac{\pi}{10}\right) \)
c. \( \cos \left(\frac{2 \pi}{5}\right) \)
D. \( -\cos \left(\frac{3 \pi}{5}\right) \)
Subject: Physics
A body has a charge of one coulomb. The
number of excess (or lesser) electrons
on it from its normal state will be :
\( A \cdot \infty \)
B . \( 1.6 \times 10^{-19} \)
\( \mathbf{c} \cdot 1.6 \times 10^{19} \)
D. \( 6.25 \times 10^{18} \)
Subject: Physics
The moment of inertia of a sphere of
mass \( M \) and radius \( R \) about an axis passing through its centre is \( \frac{2}{5} M R^{2} \) The radius of gyration of the
sphere about a parallel axis tangent to
the sphere is:
A \( \cdot \frac{7}{5} R \)
B. \( \frac{3}{5} R \)
\( ^{C} \cdot \frac{\sqrt{7}}{\sqrt{5}} R \)
D. \( \frac{\sqrt{3}}{\sqrt{5}} R \)
Subject: Maths
\( \boldsymbol{x}+\mathbf{1} \leq \mathbf{7}, \) where \( \boldsymbol{x} \in \boldsymbol{N} \)
A \( \cdot\{1,2,3,4,5,6,7\} \)
в. \{1,2,3,4,5,6\}
c. Data insufficient
D. None of these
Subject: Physics
Total energy of an electron in the ground state of hydrogen atom is \( -13.6 e V \). Its
total energy, when hydrogen atom is in the first excited state, is:
\( \mathbf{A} \cdot+13.6 \mathrm{eV} \)
B. \( +3.4 e V \)
c. \( -3.4 e V \)
D. \( -54.4 e V \)
Subject: Physics
A particle moves along the \( x \) -axis with a
position given by the equation \( \boldsymbol{x}=\mathbf{5}+ \)
\( 3 t, \) where \( x \) is in meters, and \( t \) is in
seconds. The positive direction is east Which of the following statements about the particle is false?
A. The particle is east of the origin at \( t=0 \)
B. The particle is at rest at \( t=0 \)
c. The particle's velocity is constant
D. The particle's acceleration is constant
Subject: Chemistry
A constant current(0.5 amp) is passed
for 1 hour through (i) aqueous \( A g N O_{3} \)
(ii) aqueous \( C u S O_{4} \) and (iii) molten
\( A l F_{3}, \) separately. The ratio of the mass of the metals deposited on the cathode
is? \( \left[M_{A g}, M_{C u}, M_{A l} \) are molar masses \right. of the respective metals].
A \( \cdot M_{A g}: 2 M_{C u}: 3 M_{A l} \)
B. \( M_{A g}: M_{C u}: M_{A l} \)
\( \mathbf{c} \cdot 6 M_{A g}: 3 M_{C u}: 2 M_{A l} \)
D. \( 3 M_{A g}: 2 M_{C u}: M_{A} \)
Subject: Physics
A non-conducting hollow sphere of
mass \( m \) and radius \( R \) having total charge 'q' is rotating with constant
angular velocity ' \( \omega^{\prime} \) about a vertical
axis as shown in the figure. The sphere is then gently placed on the horizontal
surface having a magnetic field applied in the horizontal direction as shown. If
there is sufficient friction to prevent
any slipping, then the friction force acting on the sphere at \( t=0 \) is \( \frac{q \omega R B}{n} \)
Find the value of \( n \)
Subject: Physics
A black body (heat capacity \( =\mathrm{C} \) ) at absolute temperature \( T \) is kept in a surrounding of absolute temperature
T/2. Its rate of cooling is :
\( (\sigma \) is stefan's constant)
\( ^{\mathrm{A}} \cdot \frac{\sigma A}{C}\left(\frac{T}{2}\right)^{4} \)
в. \( \frac{\sigma A T^{4}}{C^{2}} \)
\( ^{\mathrm{c}} \cdot \frac{_{15 \sigma A T^{4}}}{C^{2}} \)
\( ^{\mathrm{D}} \frac{15 \sigma A}{C}\left(\frac{T}{2}\right)^{4} \)
Subject: Maths
ff \( \left[\begin{array}{cc}\boldsymbol{\alpha} & \boldsymbol{\beta} \\ \boldsymbol{\gamma} & -\boldsymbol{\alpha}\end{array}\right] \) is square root of \( \boldsymbol{I}_{2}, \) then \( \boldsymbol{\alpha} \)
\( \beta \) and \( \gamma \) will satisfy the relation
A. \( 1+\alpha^{2}+\beta \gamma=0 \)
В. \( 1-\alpha^{2}+\beta \gamma=0 \)
C \( \cdot 1+\alpha^{2}-\beta \gamma=0 \)
D. \( -1+\alpha^{2}+\beta \gamma=0 \)
Subject: Maths
Consider three vectors \( \overrightarrow{\boldsymbol{p}}=\boldsymbol{i}+\boldsymbol{j}+ \)
\( \boldsymbol{k}, \overrightarrow{\boldsymbol{q}}=2 \boldsymbol{i}+\boldsymbol{4} \boldsymbol{j}-\boldsymbol{k} \) and \( \overrightarrow{\boldsymbol{r}}=\boldsymbol{i}+\boldsymbol{j}+\boldsymbol{3} \boldsymbol{k} . \)
\( p, q \) and \( r \) denotes the position vector of three non-collinear points, then the equation of the plane containing these points is
A. \( 2 x-3 y+1=0 \)
B. \( x-3 y+2 z=0 \)
c. \( 3 x-y+z-3=0 \)
D. \( 3 x-y-2=0 \)
Subject: Biology
Statement I: EEG is of immense
diagnostic value in the cardiac disease Statement II: Defects in cardiac
functions can be reflected in changes in the pattern of electrical potentials recorded in the EEG
A. Statement - - lis True, Statement - -II is True, Statement I is correct
B. Statement-lis True, Statement- -II is True; Statement I is NOT a correct explanation for the statement - -
c. Statement- - I is True, Statement- - II is false
D. Both the statements are false
Subject: Biology
Assertion
A mangrove tree growing in marshy
place has pneumatophores.
Reason
Pneumatophores helps in better
anchorage to marshy soil.
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.