AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \int \frac{e^{x}}{\left(2 e^{x}-3\right)^{2}} d x= \)
A \( \cdot \frac{-1}{2\left(2 e^{x}-3\right)}+c \)
в. \( \frac{1}{2 e^{x}-3}+c \)
c. \( \frac{1}{2\left(2 e^{x}-3\right)^{2}}+c \)
D. \( \frac{1}{\left(2 e^{x}-3\right)^{2}}+c \)
Subject: Chemistry
The \( \triangle S \) for the reaction
\( \mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(l) \) at \( \boldsymbol{3 0 0} \boldsymbol{K} \)
when
\( \boldsymbol{S}_{\boldsymbol{H}_{2}}^{\boldsymbol{o}}(\boldsymbol{g})=\mathbf{1 2 6 . 6}, \boldsymbol{S}_{\boldsymbol{O}_{2}}^{o}(\boldsymbol{g})=\mathbf{2 0 1 . 2 0} \)
\( S_{H_{2}} o(l)=68.0 J K^{-1} m o l-1 \)
respectively is:
A. \( -318.4 J K^{-1} \) mol \( ^{-1} \)
B. \( 318.4 J K^{-1} \) mol \( ^{-1} \)
c. \( 31.84 J K^{-1} \) mol \( ^{-} \)
D. 3.184 J K \( ^{-1} \) mol \( ^{-1} \)
Subject: Maths
Let \( f(x) \) be a real -valued function such that \( f(0)=\frac{1}{2} \) and \( f(x+y)= \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{a}-\boldsymbol{y})+\boldsymbol{f}(\boldsymbol{y}) \boldsymbol{f}(\boldsymbol{a}-\boldsymbol{x}) \forall \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \)
then for some real \( a \)
This question has multiple correct options
A. \( f(x) \) is a periodic function
B. \( f(x) \) is a constant function
c. \( f(x)=\frac{1}{2} \)
D. \( f(x)=\frac{\cos x}{2} \)
Subject: Chemistry
How many grams of \( N a O H \) should be
added to water to prepare \( 250 \mathrm{ml} \) solution of 2 M NaOH ?
A \( \cdot 9.6 \times 10^{3} \)
В. \( 2.4 \times 10^{3} \)
c. 20
D . 24
Subject: Chemistry
Centigrade or Celsius scale can be
converted into Kelvin scale by which of
the following formula?
\( \mathbf{A} \cdot^{o} C= \) Temperature in \( \mathrm{Kelvin}+273.15 \)
B \( \cdot^{\circ} C= \) Temperature in Kelvin -273.15
C \( \cdot^{\circ} C= \) Temperature in Fahrenheit +273
D. \( ^{o} C= \) Temperature in Fahrenheit -273
Subject: Maths
A soft drink can has a circular base
with diameter \( 7 \mathrm{cm} \) and height \( 12 \mathrm{cm} . \) A powder tin has a square base with side
\( 7 c m \) and height \( 12 c m . \) What is the difference in their capacities?
A \( \cdot 126 c m^{3} \)
В. \( 132 c m^{3} \)
\( \mathrm{c} \cdot 146 \mathrm{cm}^{3} \)
D. \( 150 \mathrm{cm}^{3} \)
Subject: Maths
\( \underset{n \rightarrow \infty}{L t}\left[\frac{n^{1 / 2}}{(n+3)^{3 / 2}}+\frac{n^{1 / 2}}{(n+6)^{3 / 2}}+\frac{n^{1 / 2}}{(n+9)}\right. \)
is equal to :
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{3} \)
D. None of these
Subject: Maths
If \( \mathrm{E} \& \mathrm{F} \) are events with \( \boldsymbol{P}(\boldsymbol{E}) \leq \boldsymbol{P}(\boldsymbol{F}) \& \)
\( \boldsymbol{P}(\boldsymbol{E} \cap \boldsymbol{F})>0, \) then?
A. Occurrence of \( E \Rightarrow \) occurrence of \( F \)
B. Occurrence of F \( \Rightarrow \) occurrence of E
c. Non-occurrence of \( E \Rightarrow \) non-occurrence of \( F \)
D. None of the above implications holds
Subject: Maths
Twenty persons arrive in a town having
3 hotels \( x, y \) and \( z . \) If each person randomly chooses one of these hotels, then what is the probability that aleast 2 of them goes in hotel \( x, \) atleast 1 in hotel \( y \) and atleast 1 in hotel \( z ?( \) each
hotel has capacity for more than 20 guests).
\( ^{\mathbf{A}} \cdot \frac{^{18} C_{2}}{^{22} C_{2}} \)
B. \( \frac{20 C_{2} \cdot^{18} C_{1} \cdot^{17} C_{1} \cdot 3^{16}}{3^{20}} \)
C. \( \frac{^{20} C_{9}}{3^{9}} \)
D. \( \frac{3^{20}-13.2^{20}+43}{3^{20}} \)
Subject: Chemistry
The chemical reaction, \( 2 O_{3} \rightarrow 3 O_{2} \)
proceeds as follows;
\( O_{3} \rightleftharpoons O_{2}+O \dots(\text { Fast }) \)
\( \boldsymbol{O}+\boldsymbol{O}_{3} \rightarrow \boldsymbol{2} \boldsymbol{O}_{2} \ldots(\text { Slow }) \)
The rate law expression should be:
A \( \cdot r=K\left[O_{3}\right]^{2} \)
B . \( r=K\left[O_{3}\right]^{2}\left[O_{2}\right]^{-1} \)
\( \mathbf{c} \cdot r=K\left[O_{3}\right]\left[O_{2}\right] \)
D. unpredictable
Subject: Physics
Two persons of equal height are
carrying a long uniform wooden plank of length \( l . \) They are at distance \( \frac{l}{4} \) and \( \frac{l}{6} \)
from nearest end of the rod. The ratio of
normal reaction at their heads is-
\( \mathbf{A} \cdot 2: 3 \)
B. 1: 3
\( c \cdot 4: 3 \)
D. 1: 2
Subject: Physics
A simple pendulum, made of a string of
length \( l \) and a bob of mass \( m \), is
released from a small angle \( \theta_{0} . \) It
strikes a block of mass \( M, \) kept on a
horizontal surface at its lowest point of oscillations, elastically. It bounces back
and goes up to an angle \( \theta_{1} . \) Then \( M \) is given by :
A \( \cdot m\left(\frac{\theta_{o}+\theta_{1}}{\theta_{o}-\theta_{1}}\right) \)
B. \( \frac{m}{2} \frac{\theta_{o}-\theta_{1}}{\theta_{o}+\theta_{1}} \)
c. \( \frac{m_{o}+\theta_{1}}{2}\left(\frac{\frac{\theta_{o}}{\theta_{o}-\theta_{1}}}{)}\right. \)
D. \( \quad m\left(\frac{\theta_{o}-\theta_{1}}{\theta_{o}+\theta_{1}}\right) \)
Subject: Chemistry
In the following sequences of reactions, the compound \( Q \) formed will be?
\[
\mathbb{P} \stackrel{\text { Oleum }}{\longrightarrow} P \frac{(\mathrm{i}) \mathrm{NaOH}}{(\mathrm{ii}) \mathrm{H}^{+}} \rightarrow Q
\]
A . aniline
B. phenol
c. benzaldehyde
D. benzene sulphonic acid
Subject: Physics
Three equal resistors, connected across a source of e.m.f. together dissipate 10 watt of power. What will be the power
dissipated in watts if the same resistors are connected in parallel across the same source of e.m.f.
A . \( 10 V \)
в. \( 10 / 3 V \)
c. \( 30 V \)
D. \( 90 V \)
Subject: Maths
A letter is known to have come form
TATANAGAR or CALCUTTA. On the
envelope just two consecutive letters TA are visible. The probability that the letter has come from CALCUTTA is
A \( \cdot \frac{4}{11} \)
в. \( \frac{7}{11} \)
c. \( \frac{1}{22} \)
D. \( \frac{21}{22} \)
Subject: Physics
A car accelerates from rest at a
constant rate \( \alpha \) for some time, after
which it decelerates at a constant rate
\( \beta \) and comes to rest. If the total time
elapsed is \( t, \) then the maximum velocity acquired by car is
\( ^{\mathbf{A}} \cdot\left(\frac{\alpha^{2}+\beta^{2}}{\alpha \beta}\right) t \)
\( ^{\mathrm{B}}\left(\frac{\alpha^{2}-\beta^{2}}{\alpha \beta}\right) t \)
c. None of these
D. \( \left(\frac{\alpha \beta r}{\alpha \beta}\right) \)
Subject: Chemistry
The value of of \( K_{P} \) for dissociation
\( 2 H I \rightleftharpoons H_{2}+I_{2} \) is \( 1.84 \times 10^{-2} . \) If the
equilibrium concentration of \( \boldsymbol{H}_{2} \) is
0.4789 mole \( L^{-1}, \) calculate the
concentration of \( \boldsymbol{H} \boldsymbol{I} \) at equilibrium.
A \( . a=0.25 \)
В. \( a=3.53 \)
c. \( a=88 \)
D. \( a=2.22 \)
Subject: Physics
Q Type your question-
having track, is \( M=1 k g \) and rests
over a smooth horizontal floor. \( A \)
cylinder of radius \( r=10 \mathrm{cm} \) and mass
\( m=0.5 k g \) is hanging by thread such
that axes of cylinder and track are in
same level and surface of cylinder is in contact with the track as shown in
figure. When the thread is burnt cylinder starts to move down the track.
Sufficient friction exists between
surface of cylinder and track, so that cylinder does not slip.Calculate velocity of axis of cylinder and velocity of the block when it reaches bottom of the
track. Also find force applied by block on
the floor at that moment \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
Subject: Maths
In the given figure, \( A C \) is diameter of \( a \)
circle with radius \( 5 \mathrm{cm} \). if \( \mathrm{AB}=\mathrm{BC} \) and
\( \mathrm{CD}=8 \mathrm{cm}, \) the area of the shaded region
to the nearest whole number is-
\( A \cdot 28 c m^{2} \)
B \( \cdot 29 c m^{2} \)
\( c \cdot 30 c m^{2} \)
\( \mathbf{D} \cdot 45 \mathrm{cm}^{2} \)
Subject: Maths
The determinant
\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{\alpha}+\boldsymbol{b} & \boldsymbol{b} \boldsymbol{\alpha}+\boldsymbol{c} & \boldsymbol{0}\end{array}\right| \) is equal to
zero, if-
\( \mathbf{A} \cdot a, b, c \) are in \( A P \)
B. \( a, b, c \) are in GP
\( \mathrm{C} \cdot \alpha \) is a root of the equation \( a x^{2}+b x+c=0 \)
D. \( (x-\alpha) \) is a factor of \( a x^{2}+2 b x+c \)
Subject: Physics
What name is given to the type of astronomy having the following characteristics.
I. It is carried out in the waveband 300
nm to 10 nm.
II. The atmosphere is opaque to the incoming radiation from space
III. Observations are to be carried out
from above the earth's atmosphere.
A. X-ray astronomy
B. Ultra-violet astronomy
c. Infra-red astronomy
D. Gamma ray astronomy
Subject: Maths
The area of a parallelogram is \( y c m^{2} \) and its height is \( h \) cm. The base of
another parallelogram is \( x \) cm more
than the base of the first parallelogram
and its area is twice the area of the first.
Find, in terms of \( y, h \) and \( x, \) the expression for the height of the
second parallelogram.
A \( \cdot \frac{2 h y}{y+x h} c m \)
B. \( \frac{2 h y}{x+x h} \) cm
c. \( \frac{2 y}{y+x h} c m \)
D. None of these
Subject: Biology
Assertion
Protons or hydrogen ions produced by photolysis of water accumulate in the lumen of thylakoids.
Reason
Photolysis of water takes place in inner membrane of thylakoid.
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
How many grams of \( C O_{2} \) gas is dissolved in a 1 It bottle of carbonated
water if the manufacturer uses a
pressure of 2.4 atmosphere in the
bottling process at \( 25^{\circ} \mathrm{C} ? \) Given \( \boldsymbol{K}_{\boldsymbol{H}} \) of
\( C O_{2} \) water \( =29.76 \) atm/mole/l at \( 25^{\circ} \mathrm{C} \)
A . 3.52
B. 4.2
\( c .3 . \)
D. 2.5
Subject: Physics
Light of wavelength \( 6000 A^{\circ} \) from a distant source falls on a slit 0.5 mm
wide. The distance between two dark
bands on each side of the central
bright band of the diffraction pattern observed on a screen placed at a distance \( 2 m \) from the slit is:
A . 1.2 nm
B. 2.4 nm
\( c .3 .6 n m \)
D. \( 4.8 \mathrm{mm} \)
Subject: Maths
If \( f(x y-1)=f(-x) f(-y)+f(x)- \)
\( \boldsymbol{y}+\mathbf{1} \) and if \( \boldsymbol{f}(\mathbf{0})=\mathbf{1}, \) then \( \boldsymbol{f}(\boldsymbol{x})=? \)
\( \mathbf{A} \cdot x-1 \)
B. \( -x+1 \)
\( c \cdot-x-1 \)
D. \( x+1 \)
E \( .1-2 x \)
Subject: Maths
Discuss the applicability of Rolle's theorem for the following function on the indicated interval:
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}-\mathbf{4} \boldsymbol{x}+\mathbf{5}, \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{1} \\ \mathbf{2} \boldsymbol{x}-\mathbf{3}, \quad \mathbf{1}<\boldsymbol{x} \leq \mathbf{2}\end{array}\right. \)
Subject: Physics
toppr
Q Type your question_
spool has mass \( m \), edge radius \( K \) and
is wound up to a radius \( r, \) its moment of
inertia about its own axis is \( \boldsymbol{I} \). The free
end of the thread is attached as shown
in figure. So that the thread is parallel
to the inclined plane. \( T \) is the tension in
the thread. Which of the following is
correct?
This question has multiple correct options
A. The linear acceleration of the spool axis down the
slope is \( \frac{m g \sin \theta-T}{m} \)
B. Angular accelerations is \( \frac{T r}{2 I} \)
C. The linear acceleration of the spool axis down the
plane is \( \frac{T r^{2}}{I} \)
D. The acceleration of the spool axis down the slope is
\( \frac{\frac{1}{1} \theta}{m r^{2}} \)
Subject: Physics
An artificial satellite is revolving round the earth. The radius of its circular orbit is half the orbital radius of moon. The
time taken by this satellite in completing one revolution will be
A. 2 lunar months
B \( \cdot 2^{-2 / 3} \) lunar months
\( \mathrm{c} \cdot 2^{-3 / 2} \) lunar months
D. \( 1 / 2 \) lunar months
Subject: Chemistry
What is the empirical formula of a compound that contains 0.05 mole of magnesium, 0.05 mole of sulfur, and 0.20 mole of oxygen?
A. \( M g S O \)
в. \( M g S O_{2} \)
\( \mathrm{c} \cdot \mathrm{MgSO}_{3} \)
D. \( M g S O_{4} \)
Subject: Maths
If \( \left[\begin{array}{ccc}3 & 2 & -1 \\ 4 & 9 & 2 \\ 5 & 0 & -2\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}0 \\ 7 \\ 2\end{array}\right], \) then
\( (x, y, z)= \)
В. (2,-1,-4)
c. (3,0,6)
\( \mathbf{D} \cdot(2,-1,4) \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cl}\boldsymbol{\alpha}+\frac{\sin [\boldsymbol{x}]}{\boldsymbol{x}} & \boldsymbol{i f} \boldsymbol{x}>0 \\ \boldsymbol{2} & \boldsymbol{i f} \boldsymbol{x}=\mathbf{0} \\ \boldsymbol{\beta}+\left[\frac{\sin \boldsymbol{x}-\boldsymbol{x}}{\boldsymbol{x}^{3}}\right] & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x}<0\end{array}\right. \)
where \( [x] \) denotes the integral part of \( y \) If \( f \) is continuous at \( x=0, \) then \( \beta-\alpha= \)
\( A \)
B. 1
\( c \cdot 0 \)
\( D \)
Subject: Physics
A sound wave has a frequency of \( 192 \mathrm{Hz} \) and travels the length of a football field, \( 91.4 \mathrm{m}, \) in \( 0.27 \mathrm{s} . \) What is the speed of the wave?
A. \( 338.5 \mathrm{m} / \mathrm{s} \)
В. \( 348.5 \mathrm{m} / \mathrm{s} \)
c. \( 358.5 \mathrm{m} / \mathrm{s} \)
D. \( 368.5 \mathrm{m} / \mathrm{s} \)
Subject: Maths
For two events, \( A \) and \( B \), it is given that \( \boldsymbol{P}(\boldsymbol{A})=\frac{\mathbf{3}}{\mathbf{5}}, \boldsymbol{P}(\boldsymbol{B})=\frac{\mathbf{3}}{\mathbf{1 0}} \) and \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B})= \)
\( \mathbf{2} \)
\( \frac{2}{3} . \) If \( \bar{A} \) and \( \bar{B} \) are the complementary
events of \( A \) and \( B \), then what is \( P(\bar{A} \mid \bar{B}) \)
equal to?
\( A \cdot \frac{3}{7} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{1}{3} \)
D.
Subject: Maths
If \( \alpha \) and \( \beta \) are the roots of \( a x^{2}+b x+ \)
\( c=0, a \neq 0 \) then the wrong statement
is
\( ^{A} \cdot \alpha^{2}+\beta^{2}=\frac{b^{2}-2 a c}{a^{2}} \)
B . \( \alpha \beta=\frac{c}{a} \)
\( \mathbf{c} \cdot \alpha+\beta=\frac{b}{a} \)
D. \( \frac{1}{\alpha}+\frac{1}{\beta}=-\frac{b}{c} \)
Subject: Biology
The enzymes catalysing reactions 1,2 and 3 respectively in the above steps
are
Glucose
Triose phospate (3-phosphoglyceric acid)
2-phosphoglyceric acid 2-phosphoenol pyruvate
pyruvic acid
A. Phosphoglyceromutase, Enolase, Pyruvate kinase
B. Enolase, Phosphofructoknase, Pyruvate kinase
C. Phosphoglycerokinase, Enolase, Pyruvate kinase
D. G-3-P dehydrogenase, Enolase, Phosphoglyceromutase
Subject: Physics
Calculate the inductance of a unit
length of a double tape line as shown in
figure. The tapes are separated by a
distance \( h \) which is considerably less
than their width \( b \)
A \( \cdot \frac{\mu_{0}}{b} \)
B. \( \frac{\mu_{0} h}{\text { sh } h} \)
c. \( \frac{2 \mu_{0} h}{b} \)
D. \( \frac{\sqrt{2} \mu_{0} h}{b} \)
Subject: Physics
Two identical short magnets having magnetic moment M are placed perpendicular to each other centres
coinciding as shown in adjacent figure. The magnitude of the magnetic field at
a point \( P \) at angle distance 'd' on the bisector of right angle will be :
A. \( \frac{\sqrt{2} \mu_{0} M}{4 \pi d^{3}} \)
B. \( \frac{2 \sqrt{2} \mu_{0} M}{4 \pi d^{3}} \)
c. \( \frac{2 \mu_{0} M}{4 \pi d^{3}} \)
D. \( \frac{\sqrt{3} \mu_{0} M}{4 \pi d^{3}} \)
Subject: Chemistry
Out of \( 1.0 \mathrm{g} \) dioxygen, \( 1.0 \mathrm{g} \) atomic oxygen and \( 1.0 \mathrm{g} \) ozone, the maximum number of oxygen atoms are contained
in
A. \( 1.0 g \) of atomic oxygen
B. 1.0 g of ozone
c. \( 1.0 g \) of oxygen gas
D. All contain the same number of atoms
Subject: Physics
A man of mass \( 50 ~ k g \) carries a bag of
weight \( 40 N \) on his shoulder. The force
with which the floor pushes up his feet
will be
\( \mathbf{A} \cdot 882 N \)
в. \( 530 N \)
\( \mathbf{c} .90 N \)
D. \( 600 N \)
Subject: Chemistry
Two first order reaction have half-lives
in the ration \( 8: 1 . \) Calculate the ration
of time intervals \( t_{1} \) and \( t_{2} \) are the time period for the \( \left(\frac{1}{4}\right)^{t h} \) and \( \left(\frac{3}{4}\right)^{t h} \) completion.
A. 1: 0.30
в. 0.125: 0.602
c. 1: 0.602
D. none of these
Subject: Maths
The value of \( x \) at which tangent to the
curve \( \boldsymbol{y}=\boldsymbol{x}^{3}-\boldsymbol{6} \boldsymbol{x}^{2}+\boldsymbol{9} \boldsymbol{x}+\boldsymbol{4}, \boldsymbol{0} \leq \boldsymbol{x} \leq \)
5 has maximum slope is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
\( c \cdot \frac{5}{2} \)
\( D \)
Subject: Physics
Q Type your question
Who did
at the four corners of a square with
sides of length D.

What is the electric potential at the
center of the square? (k is Coulomb constant.)
\( A \cdot \frac{4 k Q}{D} \)
в.
c. \( \frac{2 k Q}{\left(D \cos 45^{\circ}\right)} \)
\( D \)
\( E \)
Subject: Maths
The median of the following distribution
is
\( \begin{array}{lllll}\text { Class } & 35- & 45- & 55- & 65- \\ \text { interval } & 45 & 55 & 65 & 70\end{array} \) Frequency \( \quad 8 \quad 12 \quad \) 20 10
A . 56.
B. 57.5
c. 58.7
D. 59
Subject: Physics
In Youngs expt., the distance between two slits is \( \mathrm{d} / 3 \) and the distance
between the screen and the slits is \( 3 D \)
The number of fringes in \( 1 / 3 \) m on the screen, formed by monochromatic light of wavelength \( 3 \lambda, \) will be?
A \( \cdot \frac{d}{9 D \lambda} \)
B. \( \frac{d}{27 D \lambda} \)
c. \( \frac{d}{81 D \lambda} \)
\( D \cdot \frac{d}{D \lambda} \)
Subject: Maths
The principal value of arg z where \( z= \) \( 1+\cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \) is given by
A \( \cdot \frac{3 \pi}{5} \)
B. \( -\frac{\pi}{5} \)
\( c \cdot-\frac{3 \pi}{5} \)
D.
Subject: Physics
The velocity \( V \) of a body moving along a
straight line varies with time \( t \) as \( v= \)
\( 2 t^{2} e^{-t}, \) where \( v \) is in \( m / s \) and \( t \) in second
The acceleration of body is zero at \( t= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B . \( 2 s \)
\( c .3 \)
D. Both (A) and (B)
Subject: Maths
If \( \boldsymbol{A}-\boldsymbol{B}=\emptyset, \) then relation between \( \mathbf{A} \)
and B is :
\( \mathbf{A} \cdot A \neq B \)
в. \( B \subset A \)
\( c . A \subset B \)
D. \( A=B \)
Subject: Physics
A charge \( q \) is moving with a velocity \( \bar{v}_{1}= \) 1 ìm / \( s \) at a point in a magnetic field and experiences a force \( \overline{\boldsymbol{F}}_{\mathbf{1}}=\boldsymbol{q}[-\mathbf{1} \hat{\boldsymbol{j}}+ \)
\( \mathbf{1} \hat{\boldsymbol{k}}] \boldsymbol{N} . \) If the charge is moving with a
velocity \( \bar{v}_{2}=1 \hat{j} m / s \) at the same point
it experiences a force \( \overline{\boldsymbol{F}}_{2}=\boldsymbol{q}[\mathbf{1} \hat{\boldsymbol{i}}-\mathbf{1} \hat{\boldsymbol{k}}] \boldsymbol{N} \)
The magnetic induction \( \bar{B} \) at that
point is
\( \mathbf{A} \cdot(\hat{i}+\hat{j}+\hat{k}) W b / m^{2} \)
B \( \cdot(\hat{i}-\hat{j}+\hat{k}) W b / m^{2} \)
\( \mathbf{c} \cdot(-\hat{i}+\hat{j}-\hat{k}) W b / m^{2} \)
D. \( (\hat{i}+\hat{j}-\hat{k}) W b / m^{2} \)
Subject: Physics
A small block oscillates back and forth
on a smooth concave surface of radius
\( \boldsymbol{R} \). The time period of small oscillation
of the block is :
\( ^{\mathbf{A}} \cdot T=2 \pi \sqrt{\frac{R}{g}} \)
В \( \cdot T=2 \pi \sqrt{\frac{2 R}{g}} \)
c. \( T=2 \pi \sqrt{\frac{R}{2 g}} \)
D. none of these
Subject: Chemistry
The conditions for the combination of
atomic orbitals to form molecular
orbitals are stated below. Mark the
incorrect condition mentioned here.
A. The combining atomic orbitals must have nearly same energy
B. The combining atomic orbitals must overlap to maximum extent
c. combining atomic orbitals must have same symmetry about the molecular axis.
D. Pi ( \( \pi \) ) molecular orbitals are symmetrical around the bond axis
Subject: Biology
Assertion
Genes are stretches of DNA that make
up the different codes for the different
proteins.
Reason
DNA is the complex bio molecule made up of sugars,phosphorus and nitrogen
bases
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
Find the direction cosines \( l, m, n \) of a line which are connected by the relation \( l+m-n=0 \) and \( 2 m l-2 m n+n l= \)
0
This question has multiple correct options
A \( \cdot \frac{-2}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-1}{\sqrt{6}} \)
в. \( \frac{2}{\sqrt{6}}, \frac{-1}{\sqrt{6}}, \frac{1}{\sqrt{6}} \)
c. \( \frac{-2}{\sqrt{6}}, \frac{-1}{\sqrt{6}}, \frac{-1}{\sqrt{6}} \)
D. \( \frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}} \)
Subject: Maths
The real and imaginary parts of \( \frac{a+i b}{a-i b} \)
are:
A \( \cdot a^{2}-b^{2}, 2 a b \)
B. \( \frac{a^{2}+b^{2}}{a^{2}-b^{2}}, \frac{2 a b}{a^{2}-b^{2}} \)
c. \( \frac{a^{2}-b^{2}}{a^{2}+b^{2}}, \frac{2 a b}{a^{2}+b^{2}} \)
D. \( \frac{a^{2}+b^{2}}{a^{2}-b^{2}}, \frac{2 a b}{a^{2}+b^{2}} \)
Subject: Chemistry
In a reaction, \( \boldsymbol{A} \rightarrow \boldsymbol{B}+\boldsymbol{C}, \) the following
data were obtained:
t in seconds
\( \mathbf{0} \quad \mathbf{9 0 0} \)
Concentration of \( \boldsymbol{A} \quad \mathbf{5 0 . 8} \quad \mathbf{1 9 . 7} \quad \mathbf{7 . 6} \)
Prove that it is a first order reaction.
Subject: Maths
If \( \boldsymbol{f}\left(\frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{2}}\right)=\frac{\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})}{2} \) for all
\( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{o})=-\mathbf{1}, \boldsymbol{f}(\boldsymbol{o})=\mathbf{1} \)
then \( \boldsymbol{f}(2)= \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot-1 \)
D. \( \frac{-1}{2} \)
Subject: Chemistry
The correct relationship between free energy change in a reaction and the corresponding equilibrium constant Kc
is:
\( \mathbf{A} \cdot \Delta G=R T \ln K c \)
в. \( -\Delta G=R T \ln K c \)
c. \( \Delta G^{0}=R T l n K c \)
D. \( -\Delta G^{0}=R T l n K c \)
Subject: Maths
The contrapositive of \( (\boldsymbol{p} \vee \boldsymbol{q}) \Rightarrow \boldsymbol{r} \) is
A \( \cdot r \Rightarrow(p \vee q) \)
в. \( r \Rightarrow(p \vee q) \)
c. \( r \Rightarrow(\sim p \wedge \sim q) \)
D. \( p \Rightarrow(q \vee r) \)
Subject: Physics
In aerial mapping a camera uses a lens with a \( 100 \mathrm{cm} \) focal length. The height
at which the airplane must fly, so that
the photograph of a \( 1 k m \) long strip on the ground fits exactly on the \( 20 \mathrm{cm} \) long filmstrip of the camera, is
A . \( 200 \mathrm{km} \)
B. \( 20 \mathrm{km} \)
\( c .5 k m \)
D. \( 1 \mathrm{km} \)
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\tan ^{2} \boldsymbol{a} \boldsymbol{x}\right) \)
A \( \cdot 2 a \tan a x \sec ^{2} a x \)
B. \( -2 a \tan a x \sec ^{2} a x \)
\( \mathbf{c} \cdot a \tan a x \sec ^{2} a x \)
D. \( 2 a \cot a x \sec ^{2} a x \)
Subject: Physics
An electron revolves along a circular
path of radius \( 20 \mathrm{cm} \) with constant
angular velocity 120 rads \( ^{-1} \) about an axis passing through the centre and perpendicular to the plane of the circle. If the external magnetic field is absent,
then the potential difference between the centre of the circle and a point on
the circumference of the circle is (Mass
of the electron \( \left.=9.1 \times 10^{-31} k g\right) \)
\( \mathbf{A} \cdot 3.691 \times 10^{-9} V \)
B . \( 1.638 \times 10^{-9} V \)
C \( .4 .278 \times 10^{-9} V \)
D . \( 2.347 \times 10^{-9} V \)
Subject: Chemistry
How many mL of \( 0.3 \mathrm{M} K_{2} C r_{2} O_{7}(\text { acidic }) \)
is required for complete oxidation of 5
\( \mathrm{mL} \) of \( 0.2 \mathrm{M} \) Sn \( C_{2} \mathrm{O}_{4} \) solution.
(Round off to 1 decimal place)