AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Calculate the pressure exerted by a man weighing 85 kg standing on a piece of tile. The dimensions of his feet
are \( 30.2 \mathrm{cm} \times 15 \mathrm{cm} \)
A. \( 20,825 \mathrm{N} / \mathrm{m}^{2} \)
В. \( 2,458 N / m^{2} \)
c. \( 21,754 N / m^{2} \)
D. \( 28,456 N / m^{2} \)
Subject: Maths
\( \left|\begin{array}{cc}\mathbf{0} & \boldsymbol{a}-\boldsymbol{b} \\ -\boldsymbol{a} \mathbf{0}-\boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} \mathbf{0}\end{array}\right|=\mathbf{0} \)
Subject: Maths
Find the multiplicative inverse of \( \frac{\mathbf{5}}{\mathbf{3}} \) \( +\frac{-17}{11} \)
A \( \cdot \frac{33}{4} \)
в. \( \frac{33}{23} \)
\( c \cdot \frac{3}{4} \)
D. None of these
Subject: Chemistry
If the \( \% \) composition of \( \mathrm{Cl} \) in \( \mathrm{HCl} \) is \( 46 \% \) what is the mass of Cl in HCl?
A. \( 13.3 \mathrm{g} \)
в. 66 g
\( c \cdot 25 g \)
D. 16.76 g
Subject: Chemistry
Which of the following statement is true
for the reaction, \( \boldsymbol{H}_{2}+\boldsymbol{B} \boldsymbol{r}_{2} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \)
The rate law is \( \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}\left[\boldsymbol{H}_{2}\right]\left[\boldsymbol{B} \boldsymbol{r}_{2}\right]^{1 / 2} \)
A. order of reaction is 1.5
B. molecularity of the reaction is 2
c. by increasing the concentration of \( B r_{2} \) four times the rate of reaction is doubled
D. all the above are correct
Subject: Physics
Two pendulums differ in lengths by
\( 22 \mathrm{cm} . \) They oscillate at the same place
so that one of them makes 30
oscillations and the other makes 36
oscillations during the same time. The lengths (in \( \mathrm{cm} \) ) of the pendulums are
\( \mathbf{A} \cdot 72 \) and 50
B. 60 and 38
c. 50 and 28
D. 80 and 58
Subject: Chemistry
\( \mathbf{2} \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O C H}_{3} \stackrel{d r y H C l}{\rightarrow} \) 'X'. \( \mathbf{X} \) is
A. Mesityl oxide
B. Diacetone alcohol
c. Acetic acid
D. Mesitylene
Subject: Physics
A Wheatstone bridge consisting of four \( \operatorname{arms} \) of resistances \( P, Q, R, S \) is most
sensitive when :
A. All the resistance are equal
B. All the resistance are unequal
c. The resistances \( P \) and \( Q \) are equal but \( R>>P \) and \( S>>Q \)
D. The resistance \( P \) and \( Q \) are equal but \( R<<P \) and \( S< \) \( <Q \)
Subject: Maths
If the distance between a point \( P \) and
the point (1,1,1) on the line \( \frac{x-1}{3}= \)
\( \frac{y-1}{4}=\frac{z-1}{12} \) is \( 13, \) then the coordinates
of \( P \) are
A. (3,4,12)
В. \( \left(\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right) \)
c. (4,5,12)
D. (40, 53, 157)
Subject: Maths
\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{lll}\boldsymbol{a}_{11} & \boldsymbol{a}_{12} & \boldsymbol{a}_{13} \\ \boldsymbol{a}_{21} & \boldsymbol{a}_{22} & \boldsymbol{a}_{23} \\ \boldsymbol{a}_{31} & \boldsymbol{a}_{32} & \boldsymbol{a}_{33}\end{array}\right| \) and \( \boldsymbol{c}_{i j}= \)
\( (-1)^{i+j} \) (determinant obtained by
deleting ith row and jth column), then \( \left|\begin{array}{lll}c_{11} & c_{12} & c_{13} \\ c_{21} & c_{22} & c_{23} \\ c_{31} & c_{32} & c_{33}\end{array}\right|=\Delta^{2} \)
\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{x} & \boldsymbol{x}^{2} \\ \boldsymbol{x} & \boldsymbol{x}^{2} & \mathbf{1} \\ \boldsymbol{x}^{2} & \boldsymbol{1} & \boldsymbol{x}\end{array}\right|=\mathbf{7} \) and \( \boldsymbol{\Delta}= \)
\( \left|\begin{array}{ccc}x^{3}-1 & 0 & x-x^{4} \\ 0 & x-x^{4} & x^{3}-1 \\ x-x^{4} & x^{3}-1 & 0\end{array}\right|, \) then
A \( . \Delta=7 \)
B. \( \Delta=343 \)
c. \( \Delta=-49 \)
D. \( \Delta=49 \)
Subject: Physics
is rotated about an axis passing
through the point \( P \) as shown in figure.
The magnitude of angular momentum
of the rod, about the rotational axis \( y y^{\prime} \)
passing through the point \( \boldsymbol{P} \) is
A \( \cdot \frac{M L^{2}}{18} \)
B. \( \frac{M(x+y)^{2}}{9} \)
c. \( \frac{M\left(L^{2}+x^{2}\right)}{9} \)
D. \( \frac{M\left(L^{2}+2 y^{2}\right)}{18} \)
Subject: Physics
A chain couples and rotates two wheels in a bicycle. The radii of bigger and smaller wheels are \( 0.5 m \) and \( 0.1 m \)
respectively. The bigger wheel rotates at
the rate of 200 rotations per minute, then the rate of rotation of smaller
wheel will be:
A. 1000 rpm
в. \( \frac{50}{3} \) грт
c. 200 rpm
D. 40 rp
Subject: Maths
Which of the following pair of sides can form triangle? This question has multiple correct options
\( \mathbf{A} \cdot 5 \mathrm{cm}, 6 \mathrm{cm}, 4 \mathrm{cm} \)
в. 13 ст, 12 ст, 24 ст
c. \( 2 \mathrm{cm}, 7 \mathrm{cm}, 9 \mathrm{cm} \)
D. \( 5.6 \mathrm{cm}, 6.5 \mathrm{cm}, 12 \mathrm{cm} \)
Subject: Maths
A light ray emerging from the point source placed at \( \boldsymbol{P}(2,3) \) is reflected at
a point \( Q \) on the \( y \) -axis. It then passes through the point \( R(5,10) \). The
coordinates of \( Q \) are
A \( .(0,3) \)
B. (0,2)
c. (0,5)
(年. \( 0,5,5) \)
D. None of these
Subject: Chemistry
For an ideal solution with \( \boldsymbol{p}_{\boldsymbol{A}}>\boldsymbol{p}_{\boldsymbol{B}} \)
which of the following is true?
\( \mathbf{A} \cdot\left(x_{A}\right)_{l i q}=\left(x_{B}\right)_{v a p} \)
B . \( \left(x_{A}\right)_{l i q}>\left(x_{B}\right)_{v a p} \)
C . \( \left(x_{A}\right)_{l i q}<\left(x_{B}\right)_{v a p} \)
D. \( \left(x_{A}\right) \) liqand \( \left(x_{B}\right)_{v a p} \) do not bear any ralationship with each other
Subject: Chemistry
The density and eq. wt. of a metal are \( 10.5 g c m^{-3} \) and \( 100, \) respectively. The
time required for a current of 3 amp to deposit a 0.005 mm thick layer of the
same metal on an area of \( 80 \mathrm{cm}^{2} \) is
closest to:
\( \mathbf{A} \cdot 120 s \)
B. 135 s
c. \( 67.5 s \)
D. 270 \( s \)
Subject: Chemistry
\( \boldsymbol{E}^{o} \) value of \( \boldsymbol{N} \boldsymbol{i}^{2+} / \boldsymbol{N} \boldsymbol{i} \) is \( -\mathbf{0 . 2 5} \) V and
\( A g^{+} / A g \) is \( +0.80 V . \) If a cell is made by taking the two electrodes what is the feasibility of the reaction?
A. since \( E^{\circ} \) value for the cell will be positive, redox reaction is feasible
B. since \( E^{o} \) value for the cell will be negative, redox reaction is not feasible
c. Ni cannot reduce \( A g^{+} \) to Ag hence reaction is not feasible
D. Ag can reduce \( N i^{2+} \) to Ni hence reaction is feasible
Subject: Chemistry
Which of the following reactions have
same heat of reaction at constant \( \boldsymbol{P} \)
and constant volume as well?
This question has multiple correct options
\( \mathbf{A} \cdot 2 N O(g) \longrightarrow N_{2}(g)+O_{2}(g) \)
B \( \cdot N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}(g) \)
\( \mathbf{c} \cdot \operatorname{Co}_{3} O_{4}(s)+4 C O(g) \longrightarrow 3 \operatorname{Co}(s)+4 C O_{2}(g) \)
D. \( H_{2}(g)+C l_{2}(g) \longrightarrow 2 H C l(g) \)
Subject: Physics
Particle 1 with mass \( M \) has \( x \) position
defined by the function \( x_{1}(t)= \)
\( 2 t(t+3) \) where units are in meters
time is in seconds, and are abbreviated
in the function. Particle 2 has mass \( 2 M \)
and \( x \) position defined by \( x(t)= \)
\( (t-1)(t-2) / 2 \)
Considering the system of these two particles, what is the velocity of the
center of mass of the system at \( t=2 ? \)
A. \( 5 m / s \)
в. \( 9 m / s \)
c. \( 10 m / s \)
D. \( 10.5 m / s \)
E \( .16 \mathrm{m} / \mathrm{s} \)
Subject: Biology
Assertion: Dark periods play a more important part in flowering than light
period.

Reason: Flowering occurs in short-day plant if the dark period is interrupted by light break.
A. If both the assertion and reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reaon is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true
Subject: Maths
Let \( a_{n} \) denote the number of all \( n \) -digit
positive integers formed by the digits
0,1 or both such that no consecutive
digits in them are \( 0 . \) Let \( b_{n}= \) the
number of such \( n \) -digit integers ending
with digit 1 and \( c_{n}= \) the number of such \( n \) -digit integers ending with digit
0. The value of \( b_{6} \) is
\( A \cdot 7 \)
B. 8
\( c .9 \)
D. 11
Subject: Chemistry
A solution of calcium in liquid ammonia when evaporated to dryness gives a complex:
A. Pure \( C a \)
в. \( \left[\mathrm{Ca}\left(\mathrm{NH}_{3}\right)_{x}\right]^{2+} \)
\( c \)
\( \left[\mathrm{Ca}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2} \)
D. \( C a\left(N H_{3}\right)_{6} \)
Subject: Physics
Assertion
A body is moved from \( x=2 \) to \( x=1 \)
under a force \( \boldsymbol{F}=\mathbf{4} \boldsymbol{x} \), the work done by
this force is negative.
Reason
Force and displacement are in opposite directions.
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
Assertion
The wire of a potentiometer should be of uniform area of cross section.
Reason
It satisfies the requirement of the
principle of the potentiometer.
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: Physics
Equation of motion of a body is \( \frac{\boldsymbol{d v}}{\boldsymbol{d t}}= \) \( 6-3 v, \) where \( v \) is the velocity in \( m s^{-1} \)
and \( t \) is the time in second. Assuming
particle at rest initially. Then This question has multiple correct options
A. velocity of the body when its acceleration is zero is \( 2 m s^{-1} \)
B. initial acceleration of the body is \( 6 m / s^{2} \)
c. the velocity of the body when the acceleration is half the initial value is \( 1 \mathrm{m} / \mathrm{s} \)
D. the body has a uniform acceleration
Subject: Physics
A cracker is thrown into air with a
velocity of \( 10 \mathrm{m} / \mathrm{s} \) at an angle of \( 45^{\circ} \) with
the vertical. When it is at a height of 0.5 \( \mathrm{m} \) from the ground, it explodes into a number of pieces which follow different parabolic paths. What is the velocity of centre of mass, when it is at a height of \( 1 \mathrm{m} \) from the ground? \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A \( .4 \sqrt{5} \mathrm{m} / \mathrm{s} \)
B . \( 2 \sqrt{5} \mathrm{m} / \mathrm{s} \)
c. \( 4 \sqrt{4} m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)
Subject: Physics
For a common emitter amplifier,
current gain is \( 60 . \) If the emitter current
is \( 6.6 ~ m A \) the collector current is :
A. \( 0.108 \mathrm{mA} \)
B. 6.492 m \( A \)
c. \( 1.1 \mathrm{m} \) А
D. 3.3 \( m A \)
Subject: Physics
Assertion
Pulling a lawn roller is easier than
pushing it.
Reason
pulling decreases the apparent weight
as the vertical component of the pulling
force acts upward.
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 acids/ bases are used for the
following?
(i) To neutralize sting of wasps
(ii) In alkaline batteries
(iii) Manufacturing of soap
A \( \cdot \) (i) \( C H_{3} C H O \) (ii) \( C s O H \) (iii) \( C a(O H)_{2} \)
B . (i) \( C H_{3} C O O H \) (ii) \( C u S O_{4} \) (iii) \( B a(O H)_{2} \)
c. \( \left(\text { i) } C H_{3} \text { COOH (ii) } K O H \text { (iii) } N a O H\right. \)
D. None of these
Subject: Physics
A body of mass \( 5 k g \) is cut into two
parts of masses
(a) \( \frac{m}{4} ; \frac{3 m}{4} \)
(b) \( \frac{m}{7} ; \frac{5 m}{7} \)
(c) \( \frac{\boldsymbol{m}}{2} ; \frac{\boldsymbol{m}}{\boldsymbol{2}} \)
(d) \( \frac{\boldsymbol{m}}{\mathbf{5}} ; \frac{\boldsymbol{4} \boldsymbol{m}}{\mathbf{5}} . \) When these two
pieces are kept apart by certain distance; In which case the gravitational force acting is maximum?
A. In case a
B. In case \( c \)
c. In case d
D. In case b
Subject: Physics
An electron experiences a magnetic force of magnitude \( 4.60 \times 10^{-15} N \)
when moving at an angle of \( 60.0^{\circ} \) with respect to a magnetic field of magnitude \( 3.50 \times 10^{-3} T . \) If \( v \) is the
speed of the electron, find \( x, \) such that \( \boldsymbol{x}=\boldsymbol{v} / \mathbf{1 0}^{4} \)
Subject: Chemistry
5 moles of oxygen are heated at constant
volume from \( 10^{0} C \) to \( 20^{0} C . \) The change in
internal energy of the gas is:
\( C_{p}=7.03 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{K}^{-1} \) and \( R= \)
\( 8.31 J \mathrm{mol}^{-1} \mathrm{K}^{-1} \)
A . 125 call \( l \)
B. 252 call
c. 50 call
D. 500 call
Subject: Maths
A particle moves in a line with velocity given by \( \frac{d s}{d t}=s+1 . \) The time taken by the particle to cover a distance of 9 meter is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \log 10 \)
\( c \cdot 2 \log , 10 \)
D. 10
Subject: Chemistry
A mixture of an organic liquid \( A \) and water distilled under one atmospheric
pressure at \( 99.2^{\circ} \mathrm{C} \). How many grams of steam will be condensed to obtained
1.0 \( g \) of liquid \( A \) in the distillate?
(Vapour pressure of water at \( 99.2^{\circ} \mathrm{C} \) is
739 mm Hg. Molecular weight of \( A= \)
\( \mathbf{1 2 3}) \)
Subject: Physics
A rod of mass \( ^{\prime} M^{\prime} \) is subjected to force
\( t^{\prime} \) and \( ^{\prime} 2 f^{\prime} \) at both the ends as shown in
the figure. If young modulus of
its material is ' \( y^{\prime} \) and its length is \( L \)
find total elongation of rod.
A \( \cdot \frac{f l}{2 A y} \)
в. \( \frac{f l}{A y} \)
c. \( \frac{3 f l}{2 A v} \)
D. \( \frac{4 f l}{2 A y} \)
Subject: Maths
Three years ago, a High School started charging an admission fee for volleyball
games to raise money for new sports. The initial price was \( \$ 2 \) per person, now school raised this price of admission to \( \$ 2.50 \) this year. Assuming this trend continues, which of the following equations can be used to described the \( \operatorname{cost} \) of admission \( (c), y \) years after the school began charging for admission to games?
A. \( c=6 y+2 \)
B \( \cdot c=\frac{y}{6}+2.5 \)
\( \mathbf{c} \cdot c=\frac{y}{6}+2 \)
D. \( c=\frac{y}{2}+6 \)
Subject: Chemistry
The number of molecules in 89.6 litre of
a gas at NTP are:
A \( \cdot 6.02 \times 10^{23} \)
В. \( 2 \times 6.02 \times 10^{23} \)
c. \( 4 \times 6.02 \times 10^{23} \)
D. \( 3 \times 6.02 \times 10^{23} \)
Subject: Physics
Uniform speed of \( 2 c m \) diameter ball is \( 20 \mathrm{cm} / \mathrm{s} \) in a viscous liquid. Then, the
speed of \( 1 \mathrm{cm} \) diameter ball in the same liquid is:
A \( .5 \mathrm{cms}^{-1} \)
B. \( 10 \mathrm{cms}^{-1} \)
c. \( 40 \mathrm{cms}^{-1} \)
D. \( 80 \mathrm{cms}^{-1} \)
Subject: Physics
If the average kinetic energy of a molecule of a hydrogen gas at \( 300 \mathrm{K} \) is \( \mathrm{E} \) then the average kinetic energy of a molecule of a nitrogen gas at the same temperature is:
A . \( 7 \mathrm{E} \)
в. \( E / 14 \)
\( c .14 E \)
D. \( E / 7 \)
\( E . \)
Subject: Maths
The distance (in \( \mathrm{km} \) ) of 40 engineers from their residence to their place of
work were found as follows:
\[
\begin{array}{ccccccccc}
5 & 3 & 10 & 20 & 25 & 11 & 13 & 7 & 12 \\
19 & 10 & 12 & 17 & 18 & 11 & 32 & 17 & 16 \\
7 & 9 & 7 & 8 & 3 & 5 & 12 & 15 & 18
\end{array}
\]
\( \begin{array}{llllll}\mathbf{1 2} & \mathbf{1 4} & \mathbf{2} & \mathbf{9} & \mathbf{6} & \mathbf{1 5}\end{array} \) 15
\[
7
\]
What is the empirical probability that an engineer lives:
(i) less than \( 7 k m \) from her place of
work?
(ii) more than or equal to \( 7 k m \) from her
place of work?
(iii) within \( \frac{1}{2} k m \) from her place of work?
Subject: Chemistry
The general electronic configuration of the transition elements is:
\( \mathbf{A} \cdot(n-1) d^{10},(n+1) s^{2} \)
B \cdot \( (n-1) d^{1-10},(n+1) s^{1-2} \)
c. \( (n-1) d^{1-10}, n p^{6}, n s^{2} \)
D \cdot \( (n-1) d^{1-10}, n s^{1-2} \)
Subject: Physics
The \( \frac{B . E}{A} \) ratio for deuteron and \( \alpha \)
particle are \( X_{1} \) and \( X_{2} \) respectively. The energy released in the fusion of
deuteron into \( \alpha \) -particle is
\( \mathbf{A} \cdot 4\left(X_{2}-X_{1}\right) \)
B \( \cdot 2\left(X_{2}-X_{1}\right) \)
\( \mathbf{c} \cdot 4\left(X_{2}+X_{1}\right) \)
D. \( \frac{X_{2}-X 1}{4} \)
Subject: Physics
Assertion
If the velocity time graph of a body moving in a straight line is as shown in the figure, the acceleration of the body
must be constant.
Reason
The rate of change of quantity which is
constant is always zero.
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 coordinates of the foot of the
perpendicular drawn from the point \( A(1,0,3) \) to the join of the points
\( B(4,7,1) \) and \( C(3,5,3) \) are
A \( \cdot(5,7,17) \)
B \( \cdot\left(\frac{-5}{7}, \frac{7}{3}, \frac{-17}{3}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{5}{7}, \frac{-7}{3}, \frac{17}{3}\right) \)
D. \( \left(\frac{5}{7}, \frac{7}{3}, \frac{17}{3}\right) \)
Subject: Physics
Three particles, each of mass \( m \) are
situated at the vertices of an
equilateral triangle \( A B C \) of side \( C \mathrm{cm} \)
(as shown in the figure). The moment of
inertia of the system about a line \( A x \)
perpendicular to \( A B \) and in the plane of
\( A B C, \) in \( g r a m c m^{2} \) units will be :-
\( \mathbf{A} \cdot 2 \mathrm{m} \ell^{2} \)
\( \mathbf{B} \cdot \frac{5}{4} m \ell^{2} \)
\( \mathbf{c} \cdot \frac{3}{2} m t^{2} \)
D \( \cdot \frac{3}{4} m^{2} \)
Subject: Physics
A square loop of side \( a \) and a straight
long wire are placed in the same plane as shown in figure. The loop has a
resistance \( \boldsymbol{R} \) and inductance \( \boldsymbol{L} \). The
frame is turned through \( 18^{\circ} \) about the
axis \( O O^{\prime} . \) What is the electric charge
that flows through the loop?
\( ^{\mathbf{A}} \cdot \frac{\mu_{0} I a}{2 \pi R} \ln \left(\frac{2 a+b}{b}\right) \)
в. \( \frac{\mu_{0} I a}{2 \pi R} \ln \left(\frac{b}{b^{2}-a^{2}}\right) \)
c. \( \frac{\mu_{0} I a}{2 \pi R} \ln \left(\frac{a+2 b}{b}\right) \)
D. None of these
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{a} e^{-k t} \cos (\boldsymbol{p} \boldsymbol{t}+\boldsymbol{c}), \) then prove
that \( \frac{d^{2} y}{d t^{2}}+2 k \frac{d y}{d t}+n^{2} y=0, \) where \( n^{2}= \)
\( \boldsymbol{p}^{2}+\boldsymbol{k}^{2} \)
Subject: Chemistry
Which series shows molecules in order
of increasing bond angle?
A \( \cdot C H_{4}<B F_{3}<N H_{3} \)
в. \( H_{2} O<C O_{2}<B F_{3} \)
\( \mathrm{c} . N H_{3}<C H_{4}<\mathrm{CO}_{2} \)
D. \( N H_{3}<C H_{4}<H_{2} O \)
Subject: Physics
A body dropped freely from a height hon to a horizontal plane, bounces up and
down and finally comes to rest.The coefficient of restitution is e. The ratio
of velocities at the beginning and after two rebounds is
A \( \cdot 1: e \)
B. e:
\( c \cdot 1: e^{3} \)
D. \( e^{2}: 1 \)
Subject: Chemistry
A catalyst decrease \( E_{a} \) from \( 100 \mathrm{kJ} \)
\( m o l^{-1} \) to \( 80 \mathrm{kJ} \) mol\( ^{-1} . \) At what
temperature the rate of reaction in the absence of the catalyst at \( 500 \mathrm{K} \) will be equal to rate reaction in the presence of the catalyst:
\( A \cdot 400 K \)
B. 200 K
c. \( 625 \mathrm{k} \)
D. None of these
Subject: Maths
Workout the following divisions
\( \mathbf{3 6}(\boldsymbol{x}+\mathbf{4})\left(\boldsymbol{x}^{2}+\mathbf{7} \boldsymbol{x}+\mathbf{1 0}\right) \div \mathbf{9}(\boldsymbol{x}+\mathbf{4}) \)
\( \mathbf{A} \cdot\left(x^{2}+7 x+10\right) \)
B. \( 4\left(x^{2}+7 x+6\right) \)
c. \( 4\left(x^{2}+7 x+10\right) \)
D. None
Subject: Physics
The displacement of an object attached to a spring and executing simple harmonic motion is given by \( \boldsymbol{x}=\mathbf{2} \times \)
\( 10^{-2} \) cos \( \pi t \) meters. The time at which
the maximum speed first occurs is :
A . \( 0.5 \mathrm{s} \)
B. 0.75 s
c. 0.125 s
D. \( 0.25 \mathrm{s} \)
Subject: Physics
The radioactive material A and B have
decay constant \( 5 \lambda \) and \( \lambda \)
respectively.Initially both A and B have
the same number of nuclei.The ratio of
the number of nuclei of \( A \) and \( B \) will be \( \frac{1}{e}, \) after the time is \( \frac{x}{8 \lambda} \) then \( x \) is
Subject: Chemistry
A certain compound when burnt gave three oxides. The first turned lime water
milky, the second turned cobalt chloride
paper pink and the third formed an
aqueous solution of pH 3 nearly. The elements present in the compound are:
\( \mathbf{A} \cdot C, S, O \)
B. \( C, H, N a \)
c. \( C, H, S \)
D. \( C, H, C a \)
Subject: Maths
If the \( 6^{t h} \) term in the expansion of
\( \left[\frac{1}{x^{8 / 3}}+x^{2} \log _{10} x\right]^{8} \) is \( 5600, \) then \( x= \)
A . 10
B. 8
\( c \cdot 11 \)
\( D \)
Subject: Maths
The shortest distance of \( (a, b, c) \) from \( x \) axis is
A \( \cdot \sqrt{a^{2}+b^{2}} \)
B. \( \sqrt{b^{2}+\mathrm{c}^{2}} \)
c. \( \sqrt{c^{2}+a^{2}} \)
D. \( \sqrt{a^{2}+b^{2}+c^{2}} \)
Subject: Physics
A perpendicular force is applied to a
certain area and produces a pressure \( \boldsymbol{P} \) If the same force is applied to a twice bigger area, the new pressure on the surface is:
A \( \cdot \frac{P}{2} \)
в. \( \frac{P}{3} \)
c. \( \frac{P}{4} \)
D. none
Subject: Chemistry
If the molar concentration of \( \boldsymbol{P b I}_{2} \) is
\( 1.5 \times 10^{-3} \) mol \( L^{-1}, \) then the
concentration of iodide ions of \( g \) ion \( L^{-1} \)
is ?
A. \( 3.0 \times 10^{-3} \)
В. \( 6.0 \times 10^{-3} \)
c. \( 0.3 \times 10^{-3} \)
D. \( 0.6 \times 10^{-6} \)
Subject: Chemistry
Calculate the ratio of \( H C O O^{-} \) and \( F^{-} \)
in a mixture of \( 0.2 M \) HCOOH \( \left(K_{a}=\right. \)
\( \left.2 \times 10^{-4}\right) \) and \( 0.1 M H F\left(K_{a}=6.6 \times\right. \)
\( \left.10^{-4}\right) \)
A .1: 6.6
B. 1: 3.3
c. 2: 3.3
D. 3.3 : 2
Subject: Maths
If \( \boldsymbol{A}=\{1,2,3, \ldots, 9\} \) and \( \boldsymbol{R} \) be the
relation in \( A \times A \) defined by
\( (a, b) R(c, d) . \) If \( a+d=b+c \) for
\( (a, b),(c, d) \) in \( A \times A . \) Prove that \( R \) is an
equivalence relation. Also, obtain the
equivalence class [(2,5)]
Subject: Physics
Set the angles made by following vectors with \( x \) -axis in increasing order:
a) \( 3 \hat{i}+4 \hat{j} \)
b) \( 4 \hat{i}+3 \hat{j} \)
c) \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}} \)
\( A \cdot a, b, c \)
B. \( c, b, a \)
\( c \cdot b, c, a \)
D. a, c, b
Subject: Maths
Ordered pair \( (x, y) \) satisfying the
system of simultaneous equation \( \sin ^{-1} x+\sin ^{-1} 2 y=\pi \) and \( \cos ^{-1} x+ \)
\( \cos ^{-1} x^{2}=0 \) is
\( ^{\mathrm{A}} \cdot\left(-1,-\frac{1}{2}\right) \)
B \( \cdot\left(1,-\frac{1}{2}\right) \)
\( ^{c} \cdot\left(-1, \frac{1}{2}\right) \)
D. \( \left(1, \frac{1}{2}\right) \)
Subject: Physics
The differential equation of a wave is :
A \( \cdot \frac{d^{2} y}{d t^{2}}=v^{2} \frac{d^{2} y}{d x^{2}} \)
B. \( \frac{d^{2} y}{d x^{2}}=v^{2} \frac{d^{2} y}{d t^{2}} \)
c. \( \frac{d^{2} y}{d x^{2}}=\frac{1}{v} \frac{d^{2} y}{d t^{2} y} \)
D. \( \frac{d^{2} y}{d x^{2}}=-v \frac{d^{2} y}{d t^{2}} \)
Subject: Maths
Let \( \vec{a}, \vec{b} \) and \( \vec{c} \) br non-coplanar unit vectors equally inclined to one another at an acute angle \( \theta . \) Then \( [\vec{a} \vec{b} \vec{c}] \) in terms
of \( \theta \) is equal to
A \( \cdot(1+\cos \theta) \sqrt{\cos 2 \theta} \)
B. \( (1+\cos \theta) \sqrt{1-2 \cos 2 \theta} \)
c. \( (1-\cos \theta) \sqrt{1+2 \cos 2 \theta} \)
D. none of these
Subject: Biology
Match the above lists and choose the
correct option.
\( A \cdot A-2, B-3, C-4, D-1 \)
B. \( A-3, B-2, C-4, D-1 \)
\( C \cdot A-2, B-4, C-3, D-1 \)
D. \( A-2, B-3, C-1, D-4 \)