AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Assertion : Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in
which the later motion occurs.

Reason: Simple harmonic motion is a uniform motion.
A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false
Subject: Physics
A body of mass \( m \) falls from rest
through a height \( h \) under gravitation acceleration \( g \) and is then brought to rest by penetrating through a depth \( d \) into some sand. The average
deceleration of the body during penetration into sand is
A \( \frac{g h^{2}}{d^{2}} \)
в. \( \frac{g h^{2}}{2 d^{2}} \)
c. \( \frac{g h}{d} \)
D. \( \frac{g d}{h} \)
Subject: Physics
Mass defect of 1 g gives energy equal to
This question has multiple correct options
\( \mathbf{A} \cdot 9 \times 10^{13} J \)
B \( .5 .625 \times 10^{32} e V \)
C \( .2 .15 \times 10^{10} \) kcal
D. \( 9 \times 10^{6} \) ergs
Subject: Physics
The velocity of a particle is \( \boldsymbol{v}=\boldsymbol{v}_{0}+ \)
\( g t+f t^{2} . \) If its position is \( x=0 \) at \( t=0 \)
then its displacement after unit time \( (t=1) \) is
A \( \cdot v_{0}+2 g+3 f \)
в. \( v_{0}+\frac{g}{2}+\frac{f}{3} \)
\( \mathbf{c} \cdot v_{0}+g+f \)
D. \( v_{0}+\frac{g}{2}+f \)
Subject: Physics
In the shown figure, length of the rod is
\( L, \) area of cross-section \( A, \) Young's
modulus of the material of the rod is \( Y \).
Then, \( B \) and \( A \) is subjected to a tensile
force \( \boldsymbol{F}_{A} \) while force applied at end
\( B, F_{B} \) is lesser than \( F_{A} \). Total change in length of the rod will be
\( A \)
\[
F_{A} \times \frac{L}{2 A Y}
\]
B.
\[
F_{B} \times \frac{L}{2 A Y}
\]
\( c \)
\[
\frac{\left(F_{A}+F_{B}\right) L}{2 A Y}
\]
\( D \)
\[
\frac{\left(F_{A}-F_{B}\right) L}{2 A Y}
\]
Subject: Maths
Consider the following statements in respect of the function \( f(x)=x^{3}- \)
\( \mathbf{1}, \quad \boldsymbol{x} \boldsymbol{\epsilon}[-\mathbf{1}, \mathbf{1}] \)
\( f(x) \) is increasing in [-1,1]
\( f^{\prime}(x) \) has no root in (-1,1) Which of the statements given above is/ are correct?
A. Onlyı
B. Only II
c. Both I and II
D. Neither I nor II
Subject: Maths
Two chords \( A B \) and \( A C \) of a circle with
centre \( O \) are on the opposite sides of
\( \boldsymbol{O} \boldsymbol{A} . \) Then:
A. \( \angle O A B=\angle O A C \).
в. \( \angle O A B \neq \angle O A C \).
c. Cannot be determined
D. None of the above
Subject: Chemistry
Water is brought to boil under the pressure of 1.0 atm. When an electric
current of \( 0.50 A \) from a \( 12 ~ V \) supply is
passed for \( 300 s \) through resistance in
thermal contact with it is found that
\( 0.798 g \) of water is vapourised. Calculate the molar internal energy
change at boiling point \( (373.15 K) \)
B. \( 3.75 k J \) mol \( ^{-1} \)
c. \( 42.6 k J \) mol \( ^{-1} \)
D. \( 4.26 k J \) mol \( ^{-1} \)
Subject: Chemistry
Malonic ester contains an active
methylene group and two hydrogen atoms of active methylene group which
are easily replaced by alkyl and acyl
groups in the presence of a strong base. The carbonation intermediate formed
makes \( S_{N} 2 \) attack on alkyl or acyl
groups. In the sequence of reactions
given above, the final product \( [S] \) is :
\[
[\mathrm{Q}] \stackrel{\mathbf{H}_{3} \mathbf{O}^{+}}{\longrightarrow}[\mathbf{R}] \stackrel{\text { heat }}{\longrightarrow}[\mathrm{s}]
\]
\( \mathbf{A} \cdot C H_{2}=C H-C H_{2}-C H_{2}-C O-C O O H \)
B \( \cdot C H_{2}=C H-C H_{2}-C O-C H_{2}-C O O H \)
c. \( C H_{2}=C H-C H_{2}-C H_{2}-C O O H \)
D. \( C H_{3}-C H=C H-C H_{2}-C O O H \)
Subject: Physics
A current I flows in a infinitely long wire with cross section in the form of a
semicircular ring of radius R. The magnitude of the magnetic induction at its axis is
A \( \cdot \frac{\mu_{0} I}{\pi^{2} R} \)
в. \( \frac{\mu_{0} \mathrm{I}}{2 \pi^{2} \mathrm{R}} \)
c. \( \frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{R}} \)
D. \( \frac{\mu_{0} I}{4 \pi \mathrm{R}} \)
Subject: Physics
A conducting ring of radius \( r \) and
resistance \( \boldsymbol{R} \) rolls on a horizontal
surface with constant velocity \( v \). The
magnetic field \( B \) is uniform and is
normal to the plane of the loop. Choose
the correct option.
A. The induced emf between \( O \) and \( Q \) is \( B r v \)
B. \( _{\text {An induced current } I}=\frac{2 B v r}{R} \) flows in the clockwise
direction
Conduced current \( I=\frac{2 B v r}{R} \) flows in the
anticlockwise direction
D. No current flows
E. answer required
Subject: Physics
Find the speed of sound in a mixture of
mole of \( H e \) and 2 mole of \( O_{2} \) at \( 27^{\circ} C \)
A \( \cdot 480 m s^{-1} \)
B. \( 621 m s^{-1} \)
c. \( 401 \mathrm{ms}^{-1} \)
D. \( 601 m s^{-1} \)
Subject: Maths
If \( \frac{\sin A}{\sin B}=\frac{\sqrt{3}}{2} \) and \( \frac{\cos A}{\cos B}=\frac{\sqrt{5}}{2}, 0< \)
\( A, B<\frac{\pi}{2}, \) then find the value of
\( \tan A+\tan B \)
A \( \cdot \frac{\sqrt{5}-\sqrt{3}}{\sqrt{3}} \)
B. \( \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}} \)
c. \( \frac{\sqrt{3}+\sqrt{5}}{\sqrt{5}} \)
D. \( \frac{\sqrt{3}+\sqrt{5}}{\sqrt{3}} \)
Subject: Maths
Which one of the following statement is meaningless?
\( ^{\mathbf{A}} \cdot \cos ^{-1}\left(\ln \left(\frac{2 e+4}{3}\right)\right) \)
B. \( \operatorname{cosec}^{-1}\left(\frac{\pi}{3}\right) \)
c. \( \cot ^{-1}\left(\frac{\pi}{2}\right) \)
D \( \cdot \sec ^{-1}(\pi) \)
Subject: Chemistry
Assertion
\( \beta \) -particles are deflected less than \( \alpha \) particles in electrical field.
Reason
\( \beta \) -particles have very low mass.
A. \( A \) is correct but \( R \) is wrong
B. \( A \) is wrong but \( R \) is correct
c. Both \( A \) and \( R \) are correct and \( R \) is correct explanation of \( A \)
D. Both \( A \) and \( R \) are correct but \( R \) is not correct explanation of \( A \)
Subject: Maths
For the next three (03) items that follow
The number of telephone calls received
in 245 successive one minute intervals
at an exchange is given below in the following frequency distribution.
Number of calls 0 2
Frequency
\( \begin{array}{llll}\text { 21 } & \text { 25 } & \text { 43 } & \text { 35 } & \text { 43 }\end{array} \)
What is the median of the distribution
\( ? \)
A . 3.5
B. 4
c. 4.5
D. 5
Subject: Physics
A sparrow flies around a circular path
at a constant speed. If the radius of the
circular path is \( 15.0 \mathrm{m} \) and the sparrow takes 10 seconds to complete one lap. how fast is the sparrow flying?
\( A \cdot 15 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 1.5 \mathrm{m} / \mathrm{s} \)
D. \( 9 \mathrm{m} / \mathrm{s} \)
\( E .5 \mathrm{m} / \mathrm{s} \)
Subject: Maths
Express \( 25 \sin h x-24 \sin h x \) in the
form \( R \cos h 2(x-\alpha) \) giving the values
of \( \boldsymbol{R} \) and \( \tan \boldsymbol{h} \boldsymbol{\alpha} \)
Hence write down the minimum value
of \( 25 \cos h x-24 \sin h x \) and find the
value of \( x \) at which this occurs, and give
your answer in terms of a natural
logarithms.
Subject: Maths
A particle starts at the origin and moves along the \( x \) -axis in such a way
that its velocity at the point \( (x, 0) \) is
given by the formula \( \frac{d x}{d t}=\cos ^{2} \pi x \)
Then the particle never reaches the point on:
A \( \cdot x=\frac{1}{4} \)
в. \( _{x}=\frac{3}{4} \)
c. \( _{x}=\frac{1}{2} \)
D. \( x=1 \)
Subject: Maths
A line makes an angle \( \alpha, \beta, \gamma \) with the
\( X, Y, Z \) axes. Then \( \sin ^{2} \alpha+\sin ^{2} \beta+ \)
\( \sin ^{2} \gamma= \)
A .
B. 2
\( c \cdot \frac{3}{2} \)
D.
Subject: Maths
Consider the following statements:
\( S_{1}: \lim _{x \rightarrow 0^{-}} \frac{[x]}{x} \) is an indeterminate from
(where [] denotes greatest integer function).
\( \boldsymbol{S}_{2}: \lim _{x \rightarrow \infty} \frac{\sin \left(3^{x}\right)}{3^{x}}=0 \)
\( S_{3}: \lim _{x \rightarrow \infty} \sqrt{\frac{x-\sin x}{x+\cos ^{2} x}} \) does not exist.
\( \boldsymbol{S}_{4} \)
\( \lim _{n \rightarrow \infty} \frac{(n+2) !+(n+1) !}{(n+3) !}(n \in N)=0 \)
Which of the statements \( S_{1}, S_{2}, S_{3}, S_{4} \)
are true or false:
A. \( F T F T \)
в. \( F T T T \)
c. \( F T F F \)
D. \( T T F T \)
Subject: Maths
\( \vec{a}=4 \hat{i}-\hat{j}+\hat{k} \quad \) and \( \quad \vec{b}=p \hat{i}+2 \hat{j}+ \)
\( 3 \hat{k} \) are mutually perpendicular, then
find the value of \( \mathrm{p} \)
Subject: Maths
\( \mathbf{f} \mathbf{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{0} & -\mathbf{2} \\ \mathbf{2} & \mathbf{- 3} & \mathbf{4}\end{array}\right], \) then the matrix
\( X \) for which \( 2 X+3 A=0 \) holds true is
\( \mathbf{A} \cdot\left[\begin{array}{ccc}-\frac{3}{2} & 0 & -3 \\ -3 & -\frac{9}{2} & -6\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{ccc}\frac{3}{2} & 0 & -3 \\ 3 & -\frac{9}{2} & -6\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{lll}\frac{3}{2} & 0 & 3 \\ 3 & \frac{9}{2} & 6\end{array}\right] \)
\( ^{\mathrm{D}} \cdot\left[\begin{array}{ccc}-\frac{3}{2} & 0 & 3 \\ -3 & \frac{9}{2} & -6\end{array}\right] \)
Subject: Maths
If a function \( f(x) \) has \( f^{\prime}(a)=0 \) and
\( f^{\prime \prime}(a)=0, \) then
A. \( x=a \) is a maximum for \( f(x) \)
B. \( x=a \) is minimum for \( f(x) \),
c. It is difficult to say \( (a) \) and \( (b) \)
D. \( f(x) \) is necessarily a constant function.
Subject: Physics
A car increases its speed from 20 km /
to \( 50 k m / h \) in 10 seconds. Its
acceleration is
A \( \cdot 30 m s^{-2} \)
B . \( 3 m s^{-2} \)
\( \mathrm{c} \cdot 18 \mathrm{ms}^{-2} \)
D. None of these
Subject: Chemistry
In the sequence of reactions (A) is:
\( (A) \stackrel{N a}{\rightarrow}(B)^{C_{2} H_{5} I / h e a t} \)
\( (\boldsymbol{C}) \stackrel{\boldsymbol{H I} / \text {heat}}{\rightarrow} \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{I} \)
A . acetic acid
B. methyl alcohol
c. ethyl alcohol
D. propionic acid
Subject: Chemistry
When a graph is plotted between \( \log x / m \) and \( \log p, \) it is a straight line
with an angle \( 45^{\circ} \) and intercept 0.3010
on y-axis. If the initial pressure is 0.3
atm, what will be the amount of gas adsorbed per gram of the adsorbent?
A . 0.4
B. 0.6
c. 0.8
D. \( 0 . \)
Subject: Maths
If \( f(x)=(x)^{\frac{1}{x-1}} \) for \( x \neq 1 \) and \( f \) is
continuous at \( \mathbf{x}=1 \) then \( \mathbf{f}(\mathbf{1})= \)
\( A \)
B . e-
\( c \cdot e^{-2} \)
D. e \( ^{2} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{5} \\ \mathbf{0} & \mathbf{0}\end{array}\right] \) and \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}+\boldsymbol{x}+ \)
\( \boldsymbol{x}^{2}+\ldots \ldots+\boldsymbol{x}^{6}, \operatorname{then} \boldsymbol{f}(\boldsymbol{A})= \)
A . 0
в. \( \left[\begin{array}{ll}1 & 5 \\ 0 & 1\end{array}\right] \)
c. \( \left[\begin{array}{ll}1 & 5 \\ 0 & 0\end{array}\right] \)
D. \( \left[\begin{array}{ll}0 & 5 \\ 1 & 1\end{array}\right] \)
Subject: Physics
A fourth charge with charge \( +3 q \) is
slowly moved in from infinity to point \( \boldsymbol{P} \)
How much work must be done in this
process?
\( A \)
в. \( \frac{3 q^{2}}{2 \pi \epsilon_{0} a} \)
c. \( \frac{3 q^{2}}{\sqrt{3} \pi \epsilon_{0} a} \)
D. \( \frac{3 q^{2}}{4 \pi \epsilon_{n}} \)
Subject: Physics
Consider a capacitor-charging circuit.
Let \( Q_{1} \) be the charge given to the capacitor in a time interval of \( 10 m s \)
and \( Q_{2} \) be the charge given in the next time interval of 10 ms. Let \( 10 \mu C \) charge be deposited in a time interval \( t_{1} \) and
the next \( 10 \mu C \) charge is deposited in
the next time interval \( t_{2} \)
A. \( Q_{1}>Q_{2}, t_{1}>t_{2} \)
в. \( Q_{1}>Q_{2}, t_{1}<t_{2} \)
c. \( Q_{1}<Q_{2}, t_{1}>t_{2} \)
D. \( Q_{1}<Q_{2}, t_{1}<t_{2} \)
Subject: Chemistry
\( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} C \mathrm{H}_{3} \mathrm{COOH} \) is mixed
with \( 50 \mathrm{ml} \) of \( 0.1 \mathrm{M} \) NaOH solution and
pH of the resulting solution is 5. The change in pH if \( 100 \mathrm{ml} \) of \( 0.05 \mathrm{M} \) NaOH
is added in the above solution is:
A . 1.30
B. 4.74
\( c \cdot 5 \)
D. 3.8
Subject: Chemistry
Assertion
An elements nuclear charge is equal to
the number of protons in the nucleus
Reason
The only charged particles in the
nucleus are neutrons
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
Assertion
For a reaction, \( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}(\boldsymbol{g}) \longrightarrow \boldsymbol{N}_{\mathbf{2}}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \)
\( \triangle \boldsymbol{H}>\triangle \boldsymbol{E} \)
Reason
Enthalpy change is always greater than
internal energy change.
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
An object of mass \( m \) slides down a hil
of height \( h \) and of arbitrary shape and stop at the bottom because of friction.
The coefficient of friction may be different for different segments of the path. Find the work required to return the object to its initial position along the same path by by a tangential force
A \( . m g h \)
в. 2 тун
c. \( -m g h \)
D. It cant be calculated
Subject: Chemistry
(I) Ref. images
(II) \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{N} \boldsymbol{H}_{2} \)
(III) \( \left(\boldsymbol{C H}_{3}\right)_{2} \)
\( o \)
\( (\mathrm{IV}) C H_{3}-\stackrel{\|}{C}-N H_{2} \)
What is the correct order of basicity among the following compounds?
A. \( I I>I>I I I>I V \)
В. \( I>I I>I I I>I V \)
c. \( I I I>I>I I>I V \)
\( . I>I I I>I I>I V \)
\( V \)
Subject: Chemistry
A solution contains \( 0.4 M C H_{3} C O O H \)
and \( 0.2 M C H_{3} C O O N a . \) Calculate the
concentration of \( \boldsymbol{H}^{+} \) ions. The
ionisation constant of acetic acid is
\( 1.8 \times 10^{-5} \)
Subject: Physics
Electrons used in an electron
microscope are accelerated by a voltage of \( 25 \mathrm{kV} \). If the voltage is increased to \( 100 \mathrm{kV} \) then the de-Broglie wavelength associated with the electrons would?
A. Increase by 2 times
B. Decrease by 2 times
c. Decrease by 4 times
D. Increase by 4 times
Subject: Maths
The distance, from the origin, of the
normal to the curve, \( \boldsymbol{x}=\mathbf{2} \cos \boldsymbol{t}+ \)
\( \mathbf{2} t \sin t, y=2 \sin t-2 t \cos t \) at \( t=\frac{\pi}{4}, \) is
\( A \cdot 2 \)
B. 4
\( c \cdot \sqrt{2} \)
D. \( 2 \sqrt{2} \)
Subject: Physics
A body of \( 6 k g \) rests in limiting equilibrium on an inclined plane whose
slope is \( 30^{\circ} . \) If the plane is raised to
slope of \( 60^{\circ}, \) then force \( (\operatorname{in} k g-w t) \)
along the plane required to support it is
A . 3
B. \( 2 \sqrt{3} \)
\( c \cdot \sqrt{3} \)
D. \( 3 \sqrt{3} \)
Subject: Chemistry
Q Type your question
school organised a seminar in which he invited parents and principle. They all resolved this issue by strictly banning junk food in schools and introducing healthy snacks and drinks like soup, lassi, milk etc. in school canteens. They
also decided to make compulsory half an hour of daily physical activities for the students in the morning assembly. After six months, Mr. Chopra conducted
the health survey in most of the schools and discovered a tremendous
improvement in the health of the
students.

After reading the above passage, answer the following questions:
(i) What are the values (at least two)
displayed by Mr. Chopra?
(ii) As a student, how can you spread awareness about this issue?
(iii) Why should antidepressant drugs not be taken without consulting a
doctor?
(iv) Give two examples of artificial
sweeteners.
Subject: Maths
If a wire is bent into the shape of a
square, then the area enclosed by the square is \( 81 \mathrm{cm}^{2} \). When the same wire
is bent into a semi-circular shape, then the area enclosed by the semi circle will be
\( \mathbf{A} \cdot 81 c m^{2} \)
B. \( 44 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 77 c m^{2} \)
D. \( 154 c m^{2} \)
Subject: Biology
Read the following statements carefully
and select the incorrect statement
A. Carbon monoxide binds to Hb with higher affinity than oxygen and forms carboxyhemoglobin
B. Nearly \( 23 \% \) of oxygen is transported as oxyhemoglobin in RBC's of blood.
C. \( 100 \mathrm{ml} \) of deoxygenated blood delivers approximately \( 4 \mathrm{ml} \) of \( \mathrm{CO}_{2} \) to the alveoli under normal physiological conditions.
D. About 72\% of \( C O_{2} \) gets transported via blood plasma.
Subject: Chemistry
Which product is formed when 3
methylpentane-1,3,4-triol is heated under reflux with an excess of acidified
potassium dichromate(VI)?
A \( \cdot H O_{2} C C H_{2} C\left(C H_{3}\right)(O H) C O C H_{3} \)
в. \( H O_{2} C C H_{2} C O C(O H)\left(C H_{3}\right)_{2} \)
c. \( O H C C H_{2} C\left(C H_{3}\right)(O H) C O C H_{3} \)
D. \( H O_{2} C C H_{2} C O\left(C H_{3}\right) C O C H_{3} \)
Subject: Chemistry
Which of the following statements is
correct for \( \left[M n(C N)_{6}\right]^{3-} \) according to
valence bond theory?
\( \mathbf{A} \cdot d^{2} s p^{3}, \) inner orbital complex, paramagnetic, 2.87 B.M.
B. \( d^{2} s p^{3}, \) inner orbital complex, diamagnetic, zero magnetic moment.
C \( \cdot d^{2} s p^{3} \), outer orbital complex, paramagnetic, 3.87 B.M.
D. \( d s p^{2} \), outer orbital complex, diamagnetic, zero magnetic moment.
Subject: Physics
A small object of mass \( m \) is attached to a light string which passes through a hollow tube. The tube is hold by one hand and the string by the other. The object is set into rotation in a circle of
radius \( R \) and velocity \( v \). The string is
then pulled down, shortening the radius of path to \( r . \) What is conserved?
A. Angular momentum
B. Linear momentum
c. Kinetic energy
D. None of these
Subject: Chemistry
Cell equation \( : \boldsymbol{A}+\mathbf{2} \boldsymbol{B}^{+} \rightarrow \boldsymbol{A}^{2+}+\mathbf{2} \boldsymbol{B} \)
\( \boldsymbol{A}^{2+}+\boldsymbol{2} \boldsymbol{e} \rightarrow \boldsymbol{A} \boldsymbol{E}^{\circ}=+\mathbf{0 . 3 4} \boldsymbol{V} \)
and \( \log _{10} K=15.6 \) at \( 300 K \) for cell reactions
Find \( \boldsymbol{E}^{\circ} \) for \( \boldsymbol{B}^{+}+\boldsymbol{e} \rightarrow \boldsymbol{B} \)
Given \( \left[\frac{2.303 R T}{n F}=0.059\right]_{a t 300 K} \)
A . 0.80
B. 1.26
c. -0.54
D. +0.94
Subject: Physics
A light pointer fixed to one prong of a tuning fork touched a vertical plate. The fork is set vibrating and plate is allowed
to fall freely. 8 complete oscillations are counted when the plate falls through 10cm. What is the frequency of the
tuning fork?
A. \( 40 \sqrt{2} \)
в. \( 40 \sqrt{3} \)
c. \( 20 \sqrt{2} \)
D. \( 70 \sqrt{2} \)
Subject: Physics
Assertion: A combination of two simple
harmonic motions with arbitrary amplitudes and phases is not necessarily periodic. Reason: A periodic motion can always be expressed as a sum of infinite number of harmonic motions with
appropriate amplitudes.
A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true and reason is not the correct explanation of assertion
c. If assertion is true but reason is false.
D. If both assertion and reason are false
Subject: Chemistry
Among the following complexes (K-P):
\( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{C} \boldsymbol{N}_{6}\right]-\boldsymbol{K} \) and \right.
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3}-\boldsymbol{L} \)
\( N a_{3}\left[C o(\text {oxalate})_{3}\right]-M \) and
\( \left[\boldsymbol{N} \boldsymbol{i}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{2}-\boldsymbol{N} \)
\( \boldsymbol{K}_{2}\left[\boldsymbol{P t}(\boldsymbol{C N})_{4}\right]-\boldsymbol{O} \) and
\( \left[\boldsymbol{Z} \boldsymbol{n}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}-\boldsymbol{P} \)
the diamagnetic complexes are:
A. K.L,M,N
в. к,м,о,
c. L,M,O,
D. all
Subject: Physics
An aeroplane is flying horizontally with a velocity of \( 600 k m / h \) and at a height
of \( 1960 m . \) When it is vertically at a
point \( A \) on the ground a bomb is
released from it. The bomb strikes the
ground at point \( B \). The distance \( A B \) is:
A \( .1200 m \)
в. \( 0.33 k m \)
\( c .3 .33 k m \)
D. \( 33 k m \)
Subject: Physics
The maximum speed of a particle o a
trailing wave is \( v_{0}, \) then find the speed
of a particle wen the displacement is half of the maximum value
A \( \cdot \frac{v_{0}}{2} \)
в. \( \frac{\sqrt{3} v_{0}}{2} \)
c. \( \frac{\sqrt{3} v_{0}}{4} \)
D. \( v_{0} \)
Subject: Maths
Find the approximate value of mode for the following data:
\( \begin{array}{lllll}\text { Class } & 7- & 14- & 21- & 28 \\ \text { interval } & 14 & 21 & 28 & 35\end{array} \)
Frequency 4 3
A . 30
B. 32
c. 31
D. 35
Subject: Physics
The force \( F \) acting on a particle of mass
1 kg is indicated by the force-time graph
as shown. If the partial starts from rest,
then the speed of the particle at the end
of 6 s will be
\( \mathbf{A} \cdot 3 \mathrm{m} \cdot^{-1} \)
B. \( 12 \mathrm{m} \mathrm{s}^{-1} \)
\( \mathbf{C} \cdot 9 m s^{-1} \)
D. \( 18 \mathrm{m} \mathrm{s}^{-1} \)
Subject: Maths
If \( \left(\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}+\mathbf{1}\right)^{\boldsymbol{6}}=\boldsymbol{a}_{\boldsymbol{0}}+\left(\boldsymbol{a}_{\boldsymbol{1}} \boldsymbol{x}+\frac{\boldsymbol{b}_{\boldsymbol{1}}}{\boldsymbol{x}}\right)+ \)
\( \left(a_{2} x^{2}+\frac{b_{2}}{x^{2}}\right)+\ldots+\left(a_{6} x^{6}+\frac{b_{6}}{x^{6}}\right) \) the
find the value of \( a_{0} \)
Subject: Chemistry
Two solvent \( A \) and \( B \) have \( K_{f} \) values 1.86
and \( 2.79 \mathrm{K} \) mol\( ^{-1} \) kg respectively.
given amount of substance when
dissolved in 500 g of \( A, \) it completely dimerizes and when same mass of
substance is dissolved in 500 g of \( \mathrm{B} \), the solute undergoes trimerization.
The ratio of observed lowering of freezing points in two cases is \( 1:(?) \)
Subject: Maths
If \( f(x)=\ln \left(\frac{1+x}{1-x}\right), \) then \( f\left(\frac{2 x}{1+x^{2}}\right) \)
equals.
\( \mathbf{A} \cdot[f(x)]^{2} \)
B. \( f(x)^{3} \)
c. \( 2 f(x) \)
D. \( 3 f(x) \)
Subject: Chemistry
Consider the reaction at \( 300 K \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow 2 \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \)
\( \Delta H^{o}=-185 k J / m o l \)
If 3 mole of \( H_{2} \) completely react with 3
mole of \( C l_{2} \) to form \( H C l . \) What is \( \Delta U^{\circ} \)
for this process?
A. \( 0 k J \)
\( J \)
в. \( 185 k J \)
c. \( 555 k J \)
D. \( -553.8 k J \)
Subject: Physics
A sphere of radius \( \boldsymbol{R} \) and mass \( \boldsymbol{M} \)
collides elastically with a cubical block
of mass \( M \) and side \( 2 R \). The entire
system is on a smooth horizontal
ground. Given that the sphere was rolling without slipping with an angular velocity \( \omega \) at the time of collision. The
velocities of the sphere and the block
after the collision are :
\( \mathbf{A} \cdot \omega_{\text {sphere}}=0, v_{\text {sphere}}=0, v_{\text {block}}=v \)
B. \( \omega_{\text {sphere}}=\omega, v_{\text {sphere}}=0, v_{\text {block}}=v \)
C. \( \omega_{\text {sphere}}=0, v_{\text {sphere}}=0, v_{\text {block}}=0 \)
D. \( \omega_{\text {sphere}}=\frac{\omega}{2}, v_{\text {sphere}}=\frac{v}{2}, v_{\text {block}}=\frac{v}{2} \)
Subject: Chemistry
At certain temperature, the \( \mathrm{H}^{+} \) ion
concentration of water is \( 4 \times 10^{-7} \mathrm{M} \)
then the value of \( K_{w} \) at the same
temperature is :
A \( \cdot 10^{-14} \mathrm{M}^{2} \)
B. \( 4 \times 10^{-14} \mathrm{M}^{2} \)
c. \( 1.6 \times 10^{-13} \mathrm{M}^{2} \)
D. \( 4 \times 10^{-7} \mathrm{M}^{2} \)