AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
ff \( \boldsymbol{y}=\tan ^{-1} \frac{1}{1+x+x^{2}}+ \)
\( \tan ^{-1} \frac{1}{x^{2}+3 x+3}+ \)
\( \tan ^{-1} \frac{1}{x^{2}+5 x+7}+\ldots+ \) upto \( n \) terms
then \( y^{\prime}(0) \) is equal to
A \( \cdot-\frac{1}{1+n^{2}} \)
B. \( -\frac{n^{2}}{1+n^{2}} \)
c. \( \frac{n}{1+n^{2}} \)
D. none of these
Subject: Chemistry
Select the correct order with respect to
acidic nature of the given compounds.
\( \mathbf{A} \cdot A l_{2} O_{3}<\operatorname{In}_{2} O_{3}<T l_{2} O<B_{2} O_{3} \)
B. \( T l_{2} O< \)In\( _{2} O_{3}<A l_{2} O_{3}<B_{2} O_{3} \)
\( \mathbf{c} \cdot A l_{2} O_{3}<B_{2} O_{3}<\operatorname{In}_{2} O_{3}<T l_{2} O \)
\( \mathbf{D} \cdot T l_{2} O<A l_{2} O_{3}<B r_{2} O_{3}<I n_{2} O_{3} \)
Subject: Physics
The vector \( \hat{B}=4 \hat{i}+2 \hat{j}-S \hat{k} \) is
perpendicular to the vector \( \overrightarrow{\boldsymbol{A}}=\mathbf{3} \hat{\mathbf{i}}+ \)
\( \hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}} \) if \( \boldsymbol{S}= \)
\( A \)
B. 7
\( c \cdot 6 \)
D. 8
Subject: Physics
An ice cube floats on water in a beaker with \( \frac{9}{10} \) th of its volume submerged under water. What fraction of its volume
will be submerged if the beaker of water is taken to the moon where the gravity is \( 1 / 6^{t h} \) that on the earth?
\( A \cdot \frac{9}{10} \)
в. \( \frac{27}{50} \)
\( c \cdot \frac{2}{3} \)
D. zero
Subject: Physics
In a Young's double slit experiment set
up, source \( S \) of wavelength \( 500 n m \)
illuminates two slits \( S_{1} \) and \( S_{2} \) which
act as two coherent sources. The source
\( S \) oscillates about its own position
according to the equation \( y=0.5 \sin \pi t \)
where \( y \) is in \( \mathrm{mm} \) and \( t \) in seconds. The
minimum value of time \( t \) for which the
intensity at point \( P \) on the screen
exactly infront of the upper slit becomes minimum is :
\( A \cdot 1 s \)
B. \( 2 s \)
\( c .3 s \)
D. \( 1.5 s \)
Subject: Chemistry
Freundlich equation for adsorption of gases (in amount of \( g \) ) on a solid (in
amount of \( \mathrm{mg} \) ) at constant temperature can be expressed as:
\( ^{\mathbf{A}} \cdot \log \frac{x}{m}=\log P+\frac{1}{n} \log K \)
B. \( \log \frac{x}{m}=\log K+\frac{1}{n} \log P \)
c. \( \frac{x}{m} \propto P^{n} \)
D \( \cdot \frac{x}{m}=P+\frac{1}{n} \log K \)
Subject: Physics
A particle is projected vertically upwards from a point \( A \) on the ground. It \( \operatorname{takes} t_{1} \) time to reach a point \( B \) but it still continues to move up. If it takes
further \( t_{2} \) time to reach the ground from point B then height of point B from the
ground is
A \( \cdot \frac{1}{2} g\left(t_{1}+t_{2}\right)^{2} \)
B. \( g t_{1} t_{2} \)
c. \( \frac{1}{8} g\left(t_{1}+t_{2}\right)^{2} \)
D. \( \frac{1}{2} g t_{1} t_{2} \)
Subject: Maths
ff \( \boldsymbol{y}=\boldsymbol{A} \boldsymbol{e}^{-\boldsymbol{k} t} \cos (\boldsymbol{p} \boldsymbol{t}+\boldsymbol{c}), \) then prove
that \( \frac{d^{2} y}{d t^{2}}+2 k \frac{d y}{d t}+n^{2} y=0, \) where
\( \boldsymbol{n}^{2}=\boldsymbol{p}^{2}+\boldsymbol{k}^{2} \)
Subject: Chemistry
Assertion
The surface tension of water is more
than other liquid.
Reason
Water molecules have strong inter molecular \( \boldsymbol{H}- \) bonding as attractive
force.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
A man and a child are holding a uniform rod of length \( L \) in the horizontal direction in such a way that one fourth weight is supported by the child. If the child is at one end of the rod then the
distance of man from another end will
be:
A \( \cdot \frac{3 L}{4} \)
в. \( \frac{L}{4} \)
c. \( \frac{L}{3} \)
D. \( \frac{2 L}{3} \)
Subject: Chemistry
The value of \( \square_{e q}^{\infty} \) for \( N H_{4} C l, \) NaOH and NaCl are respectively, 149.74,248.1 and \( 126.4 \Omega^{-1} c m^{2} e q u i v^{-1} . \) The value of \( \square_{e q}^{\infty} \)
of \( N H_{4} O H \) is
A . 371.44
B. 271.44
\( c \cdot 71.44 \)
D. Cannot be predicted from given data
Subject: Maths
A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who
applied. Each Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-l's name, 1 time.
What is the probability that a Year-III's name will be chosen?
\( A \cdot \)
B.
\( c \cdot \frac{3}{3} \)
\( D \)
Subject: Chemistry
The pair(s) of coordination
complexes/ions exhibiting the same kind of isomerism is(are):
This question has multiple correct options
\( \mathbf{A} \cdot\left[C r\left(N H_{3}\right)_{5} C l\right] C l_{2} \) and \( \left[C r\left(N H_{3}\right)_{4} C l_{2}\right] C l \)
\( \mathbf{B} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right]^{+} \) and \( \left[P t\left(N H_{3}\right)_{2}\left(H_{2} O\right) C l\right]^{+} \)
\( \mathbf{c} \cdot\left[\operatorname{CoBr}_{2} C l_{2}\right]^{2-} \) and \( \left[P t B r_{2} C l_{2}\right]^{2-} \)
\( \mathbf{D} \cdot\left[P t\left(N H_{3}\right)_{3}\left(N O_{3}\right)\right] C l \) and \( \left[P t\left(N H_{3}\right)_{3} C l\right] B r \)
Subject: Maths
By selling an article for \( R s .225 \), the shopkeeper losses \( 25 \% \). Find the \( \% \) gain or loss, if be article be sold for \( \boldsymbol{R} \boldsymbol{s} \). \( \boldsymbol{3} \boldsymbol{6} \boldsymbol{0} \)
A. \( 20 \% \) gain
B. \( 20 \% \) loss
c. \( 10 \% \) loss
D. \( 10 \% \) gain
Subject: Maths
Evaluate: \( \frac{x\left(8 x^{2}-32\right)}{8 x(x-4)} \)
\( \mathbf{A} \cdot x+2 \)
B. \( x+4 \)
c. \( \frac{x^{2}-4}{x-4} \)
D. \( x^{2}-4 \)
Subject: Physics
A radioactive nucleus has specific
binding energy' \( E_{1} \) '. It emits an \( \alpha \) particle. The resulting nucleus has
specific binding energy' \( E_{2} \) '. Then
A \( \cdot E_{2}=E_{1} \)
в. \( E_{2}<E_{1} \)
c. \( E_{2}>E_{1} \)
D. \( E_{2}=0 \)
Subject: Physics
In the given arrangement, the loop is moved with constant velocity \( v \) in a
uniform magnetic field \( B \) in a restricted
region of width \( a \). The time for which the
emf is induced in the circuit is
A \( -\frac{2 b}{v} \)
в. \( \frac{2 a}{v} \)
c. \( \frac{(a+b)}{v} \)
D.
Subject: Chemistry
The heat of neutralization of HCl by NaOH is \( -55.9 \mathrm{kJ} / \mathrm{mol} \). If the heat of
neutralization of HCN by NaOH is -12.1 kJ/ mol.

The energy of dissociation of HCN is :
A. -43.8 kJ
B. 43.8 kJ
c. 68 kJ
D . -68kJ
Subject: Maths
If we apply mean value theorem for
\( \boldsymbol{f}(\boldsymbol{x})=\log \boldsymbol{x} \boldsymbol{x} \in[\mathbf{1}, \mathbf{2}], \) then the value of
\( c \) is
A \( \cdot \sqrt{3} \)
B. \( \log _{e} 2 \)
\( \mathbf{c} \cdot \log _{2} e \)
D.
Subject: Maths
Consider the function \( \left\{\begin{array}{c}x \sin \frac{\pi}{x} \text { for } x>0 \\ \text { 0 for } x=0\end{array} \) then the number \right.
of points in (0,1) where the derivative \( f^{\prime}(x) \) vanishes, is
A . 0
B. 1
\( c \cdot 2 \)
D. infinite
Subject: Physics
Two wires carrying equal current \( I \) in opposite directions are placed a distance \( a \) apart. The wires experience a force \( F \) due to the current. The wires are moved to a distance \( \frac{\boldsymbol{a}}{\mathbf{2}} \) If the current in wire one remains the
same, which of the following values of \( \boldsymbol{I}_{2} \) would result in the same force \( \boldsymbol{F} \)
between the wires?
A \( \cdot \frac{1}{4} I \)
B \( \cdot \frac{1}{2} I \)
c. \( I \)
D. 2I
E . \( 4 I \)
Subject: Chemistry
Consider the following equilibrium:
\( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{N} \boldsymbol{H}_{3} \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{4}^{+}+\boldsymbol{N} \boldsymbol{H}_{2}^{-} \)
Why \( N H_{3} \) undergo self ionization?
Subject: Maths
Assertion
The equation \( 3 x^{2}-2 y^{2}+4 x-6 y=0 \)
represents a hyperbola.
Reason
The second degree equation \( a x^{2}+ \) \( 2 h x y+b y^{2}+2 g x+2 f y+c=0 \)
represents a hyperbola if \( a b c+2 f g h- \)
\( \boldsymbol{a} \boldsymbol{f}^{2}-\boldsymbol{b} \boldsymbol{g}^{2}-\boldsymbol{c h}^{2} \neq \boldsymbol{0} \& \boldsymbol{h}^{2}>\boldsymbol{a b} \)
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
A beam of white light shows no dispersion on emerging from a glass slab.
Reason
Dispersion in a glass slab is 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: Chemistry
Assertion: Aryl halides undergo electrophilic substitution more readily than benzene.

Reason: Aryl halide gives a mixture of
\( o-, p- \) products when they undergo electrophilic substitution.
A. Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Assertion and Reason are correct but Reason is not the correct explanation of Assertion
c. Assertion is true and Reason is false
D. Assertion is false and Reason is true
Subject: Maths
Solve the following:
¡¡) \( \sqrt{99} \times \sqrt{396} \)
ii) \( \sqrt{\mathbf{0 . 0 3 2 4}} \)
\( \mathbf{A} \cdot 192 ; 0.18 \)
B. \( 192 ; 0.12 \)
c. \( 198 ; 0.18 \)
D. \( 198 ; 0.12 \)
Subject: Physics
The amplitude of the magnetic field of a harmonic electromagnetic wave in
vacuum is \( B_{0}=510 \) nT. The amplitude of
the electric field part of the wave is
\( \mathbf{A} \cdot 120 \mathrm{N} C^{-1} \)
B . \( 163 \mathrm{N} C^{-1} \)
c. \( 510 \mathrm{N} C^{-1} \)
D. 153 N \( C^{-1} \)
Subject: Physics
A hemispherical body is placed in a uniform electric field E. What is the flux
linked with the curved surface if the
field is perpendicular to the curved surface at every points as in figure.
A \( \cdot \phi=E 4 \pi R^{2} \)
В. \( \phi=E 2 \pi R^{2} \)
c. \( \phi=E 7 \pi R^{2} \)
D. \( \phi=E 9 \pi R^{2} \)
Subject: Maths
The age distribution of 400 persons in a colony having median age 32 is given below
\[
\begin{array}{llll}
\text { Age } \sin & 20- & 25- & 30- \\
\text { Years) } & 25 & 30 & 35
\end{array}
\]
Frequency
75
Then, \( (x-y) \) is :
A .10
в. 20
c. -10
D. - 20
Subject: Chemistry
The standard oxidation potential of Zn referred to SHE is \( 0.76 \mathrm{V} \) and that of \( \mathrm{Cu} \)
is \( -0.34 V \) at \( 25^{\circ} \mathrm{C} . \) When excess of Zn
is added to \( C u S O_{4}, Z n \) displaces
\( C u^{2+} \) till equilibrium is reached. What
is the ratio of \( Z n^{2+} \) to \( C u^{2+} \) ions at
equilibrium? Express the ans in the form \( \left[Z n^{2+}\right] /\left[C u^{2+}\right]=k \times 10^{37}, \) and find \( k \)
A .1 .94
в. 2.34
c. 1.45
D. none of these
Subject: Chemistry
An organic compound has \( C \) and \( H \) percentage in the ratio 6: 1 by mass
and \( \mathrm{C} \) and 0 percentage in the ratio 3: 4
by mass. The compound is:
A. \( H C H O \)
в. \( C H_{3} O H \)
c. \( C H_{3} C H_{2} \) ОН
D. \( (C O O H)_{2} \)
Subject: Physics
What is a pressure on the smaller piston if both the pistons are at same
horizontal level? (Take \( \left.\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}\right) \)
\( A \cdot 3 P a \)
В. \( 4 \times 10^{3} P a \)
\( \mathbf{c} \cdot 6 \times 10^{5} P a \)
D. 1000 Pa
Subject: Maths
The product of two consecutive natural
numbers is \( 12 . \) The equation form of this statement is
A. \( x^{2}+2 x-12=0 \)
B . \( x^{2}+1 x-12=0 \)
c. \( x^{2}+1 x+12=0 \)
D. \( x^{2}+2 x+12 \)
Subject: Maths
A box contains 32 coloured marbles. 8 of
them are red marbles and the rest are
either blue or green marbles. A marble is drawn at random. Calculate the
probability of drawing a marble which is not red in colour.
\( A \cdot \frac{2}{3} \)
в. \( \frac{5}{8} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{7}{16} \)
Subject: Physics
A circular disc \( D_{1} \) of mass \( \mathrm{M} \) and radius
R has two identical discs \( D_{2} \) and \( D_{3} \) of
the same mass \( \mathrm{M} \) and radius \( \mathrm{R} \)
attached rigidly at its opposite ends(see figure). The moment of inertia of the system about the axis 00 ',
passing through the centre of \( D_{1}, \) as
shown in the figure, will be?
\( \mathbf{A} \cdot 3 M R^{2} \)
B. \( \frac{2}{3} M R^{2} \)
c. \( M R^{2} \)
D. \( \frac{4}{5} M R^{2} \)
Subject: Physics
A person pulls a bucket of water from a well of depth \( h . \) If the mass of uniform
rope is \( m \) and that of the bucket full of
water is \( M, \) then work done by the
person is:
A \( \cdot\left(M+\frac{m}{2}\right) g h \)
B \( \cdot \frac{1}{2}(M+m) g h \)
c. \( (M+m) g h \)
D. \( \left(\frac{M}{2}+m\right) g h \)
Subject: Chemistry
Choose the correct answer among the alternatives given :
Haloalkanes contain halogen atom(s)
attached to the \( s p^{3} \) hybridised carbon
atom of an alkyl group. Identify haloalkane from the following compounds.
(i) 2-Bromopentane
(ii) Vinyl chloride
(iii) 2-Chloroacetophenone
(iv) Trichloromethane
A. Only (ii)
B. (ii) and (iv) only
c. (i) and (iv) only
D. (i), (ii) and (iii) only
Subject: Chemistry
Which equation represents the time to complete \( 90 \% \) of first order reaction?
A \( \cdot \frac{k}{2.303} \log \frac{4}{3} \)
в. \( \frac{2.303}{k} \log _{\frac{3}{4}} \)
c. \( \frac{2.303}{k} \)
D. \( \frac{2.303}{k} \log 3 \)
Subject: Physics
A body has an initial velocity of \( 3 m / s \)
and has an acceleration of \( 1 \mathrm{ms}^{-2} \)
normal to the direction of the initial
velocity. Then its velocity \( 4 s \) after the
start is
A \( \cdot 7 m s^{-1} \) along the direction of initial velocity
B. \( 7 m s^{-1} \) along the normal to the direction of the initial velocity
c. \( 7 m s^{-1} \) mid-way between the two directions
D \( \cdot 5 m s^{-1} \) at an angle of \( \tan ^{-1} \frac{4}{3} \) with the direction of the initial velocity
Subject: Physics
The intensity at the maximum in a
Young's double slit experiment is \( \boldsymbol{I}_{\mathbf{0}} \)
Distance between two slits is \( d=5 \lambda \)
,where \( \lambda \) is the wavelength of light used in the experiment. What will be the intensity in front of one the slits on the
screen place at a distance \( \mathrm{D}=2 \mathrm{m} \)
Subject: Maths
Find the value of \( k \) if \( f(x)= \) \( \left\{\begin{array}{ll}\frac{1-\cos 2 x}{1+\cos 2 x}, & x \neq 0 \\ k, & x=0\end{array} \) is continuous at \right.
\( \boldsymbol{x}=\mathbf{0} \)
Subject: Maths
In the given figure, 0 is the centre of the
circle. If \( \angle A O D=140^{\circ} \) and \( \angle C A B= \)
\( 50^{\circ}, \) Then
(i) \( \angle \boldsymbol{E} \boldsymbol{D} \boldsymbol{B} \) (ii) \( \angle \boldsymbol{E} \boldsymbol{B} \boldsymbol{D} \) are
respectively
\( \begin{array}{lll}A & -70^{\circ} & \ & 50\end{array} \)
\( \begin{array}{lll}\text { B } \cdot 50^{\circ} & 110^{\circ}\end{array} \)
\( \begin{array}{lll}c \cdot 30^{\circ} & \ & 70^{\circ}\end{array} \)
\( \begin{array}{lll}\text { D. } 120^{\circ} & \text { \& } 130^{\circ}\end{array} \)
Subject: Physics
A coil of cross-sectional area \( \boldsymbol{A} \) having
\( \boldsymbol{n} \) turns is placed in a uniform magnetic
field \( B \). When it is rotated with an
angular velocity \( \omega, \) the maximum e.m.f.
induced in the coil will be
\( \mathbf{A} \cdot n B A \omega \)
В \( \cdot \frac{3}{2} n B A \omega \)
\( c .3 n B A \omega \)
D. \( \frac{1}{2} n B A \)
Subject: Chemistry
Identify the correct order of boiling
point:
This question has multiple correct options
\( \mathbf{A} \cdot H F<H C l<H B r<H I \)
B. \( N H_{3}<P H_{3}<A s H_{3}<S b H_{3} \)
\( \mathbf{c} \cdot C H_{4}<S i H_{4}<G e H_{4}<S n H_{4} \)
D. \( H_{2} S<H_{2} S e<H_{2} T e<H_{2} O \)
Subject: Chemistry
The energy of hydrogen atom in \( n^{t h} \) orbit
is \( E_{n} \) then the energy in \( n^{t h} \) orbit of singly ionised helium atom will be:
\( A \cdot 4 E_{n} \)
в. \( 2 E_{n} \)
c. \( E_{n} / 4 \)
D. \( E_{n} / 2 \)
Subject: Maths
The mean of the numbers \( a, b, 8,5,10 \) is
6 and the variance is \( 6.80 . \) Then which
one of the following gives possible values of \( a \) and \( b ? \)
A \( . a=0, b=7 \)
В. \( a=5, b=2 \)
c. \( a=1, b=6 \)
D. \( a=3, b=4 \)
Subject: Maths
A sum of money lent at simple interest amounts to \( R s 3224 \) in 2 years and
Rs 4160 in 5 years. Find the sum and
the rate of interest.
A. \( R s .2500 \)
B. \( R s .2000 \)
c. \( R s .2600 \)
D. \( R s .1600 \)
Subject: Maths
The set of values of \( x \) for which the
inequality \( [\boldsymbol{x}]^{2}-\mathbf{5}[\boldsymbol{x}]+\boldsymbol{6} \leq \mathbf{0} \) (where [
denote the greatest integral function) holds good are
A \( .2 \leq[x]<3 \)
в. \( 2 \leq x<4 \)
c. \( 2 \leq[x] \leq 3 \)
D. \( (b) \) and \( (c) \) both
Subject: Maths
Assertion
If the postman delivers 1332 card to the students then number of students are
36.
Reason
If there are n students then total
number of cards are \( n(n-1) \)
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A),
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A)
c. (A)is true but (R) is false
D. (A)is false but (R) is true.
Subject: Physics
A man standing on a platform holds
weights in his outstretched arms. The
system rotates freely about a central
vertical axis. If he now draws the
weights inwards close to his body,
This question has multiple correct options
A. the angular velocity of the system will increase.
B. the angular momentum of the system will decrease.
C. the kinetic energy of the system will increase.
D. he will have to expend some energy to draw the weights in.
Subject: Maths
The equation of the image of the circle \( x^{2}+y^{2}+16 x-24 y+183=0 \) by the
line mirror \( 4 x+7 y+13=0 \) is:
A \( \cdot x^{2}+y^{2}+32 x-4 y+235=0 \)
B. \( x^{2}+y^{2}+32 x+4 y-235=0 \)
C. \( x^{2}+y^{2}+32 x-4 y-235=0 \)
D. \( x^{2}+y^{2}+32 x+4 y+235=0 \)
Subject: Physics
Assertion
While measuring the thermal conductivity of liquid experimentally, the upper layer is kept hot and the lower
layer is kept cold.
Reason
This avoids heating of liquid by
convection.
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 area bounded by the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) and the ordinates \( x=0 \)
and \( x=a e, \) where \( b^{2}=a^{2}\left(1-e^{2}\right) \) and
\( e<1 \)
Subject: Chemistry
Assertion: o-phenol sulphonic acid on heating at \( 100^{0} C \) changes to \( \mathrm{p} \)
phenol sulphonic acid. Reason: Sulphonation of phenol is a reversible process.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct
Subject: Maths
Points on the line \( y=x \) whose
perpendicular distance from the line
\( 3 x+4 y=12 \) is 4 have the coordinates
\( ^{A} \cdot\left(-\frac{8}{7},-\frac{8}{7}\right),\left(-\frac{32}{7},-\frac{32}{7}\right) \)
в. \( \left(\frac{8}{7}, \frac{8}{7}\right),\left(\frac{32}{7}, \frac{32}{7}\right) \)
\( ^{\mathbf{c}} \cdot\left(-\frac{8}{7},-\frac{8}{7}\right),\left(\frac{32}{7}, \frac{32}{7}\right) \)
D. None of these
Subject: Physics
Assertion
The graph between velocity and displacement for a harmonic oscillator is an ellipse.
Reason
Velocity does not change uniformly with displacement in harmonic motion.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
A rod of length \( l \) rotates with a uniform
angular velocity \( \omega \) rad/s about an axis passing through its middle point but normal to its length in a uniform magnetic field of induction \( B \)
with its direction parallel to the axis of rotation. The induced emf between the
two ends of the rod is :
\( ^{A} \cdot \frac{B l^{2} \omega}{2} \)
в. zero
c. \( \frac{B l^{2} \omega}{4} \)
D \( \cdot 2 B l^{2} \omega \)
Subject: Maths
Consider the following statements in respect of histogram:
1. Histogram is an equivalent graphical
representation of the frequency
distribution.
2. Histogram is suitable for continuous random variables, where the total
frequency of an interval is evenly distributed over the interval.
Which of the statements given above is/are correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Maths
Choose the correct answer from the
alternatives given :

Directions for questions 71 to 75: The
graph shows the production of wheat in different years of a particular State
The year which had the percentage of
decrease vis-a-vis its previous year
in production
A. \( 1996-1997 \)
B. \( 1995-1996 \)
c. \( 1999-2000 \)
D. \( 2000-2001 \)
Subject: Chemistry
Number of \( K^{+} \) ions and number of
moles of \( K^{+} \) ions present in \( 1 L \) of \( \frac{N}{5} K M n O_{4} \) solution respectively, in acidic medium are :
A \( \cdot 0.04 \) and \( 2.4 \times 10^{2} \)
B . 2.4 \( \times 10^{22} \) and 0.04
c. 200 and \( 6.023 \times 10^{23} \)
D. \( 6.023 \times 10^{23} \) and 200
Subject: Physics
A transverse sinusoidal wave moves
along a string in the positive x-direction at a speed of \( 10 \mathrm{cm} / \mathrm{s} \). The wavelength
of the wave is \( 0.5 m \) and its amplitude is
10cm. At a particular time \( t \), the snap shot of the wave is shown in figure.
The velocity of point P when its
displacement is \( 5 c m \) is
A \( \cdot \frac{\sqrt{3} \pi}{50} \hat{j} m / s \)
B. \( -\frac{\sqrt{3} \pi}{50} \hat{j} m / s \)
c. \( \frac{\sqrt{3} \pi}{50} \hat{i} m / s \)
D. \( -\frac{\sqrt{3} \pi}{50} \hat{i} m / s \)
Subject: Physics
In Young's double slit experiment, distance between two slits is \( 0.28 \mathrm{mm} \)
and distance between slits and screen
is \( 1.4 \mathrm{m} \). Distance between central bright hinge and third bright fringe is \( 0.9 \mathrm{cm}, \) what is the wavelength of light used?
A \( .4000 A^{\circ} \)
в. \( 6000 A^{\circ} \)
c. \( 3000 A^{\circ} \)
D. \( 5000 A^{\circ} \)
Subject: Physics
Gita arranges some mirrors in group- 1
and group- 2 according to the magnification, type of image and size of image from the following data.
Sr. Group-1 \( \quad \) Group- 2
No.
\( <1 \) and \( \quad \) Real, inverted and
(1) \( \quad \) nocative \( \quad \) small negative
\( >1 \) and \( \quad \) Real, inverted and
(2) \( \quad \) positive \( \quad \) enlarged
\( >1 \) and \( \quad \) Virtual, erect and
(3)\( \quad \) negative \( \quad \) enlarged
\( <1 \) and Virtual, erect and
positive \( \quad \) small
For which of the pairs from the group 1
and 2 you disagree.
A. 1 and 3
B. 2 and 3
c. 3 and 4
D. 1 and 2
Subject: Chemistry
Which of the following statements is
incorrect?
\( \mathbf{A} \cdot \) Among \( O_{2}^{+}, O_{2}, \) and \( O_{2} \) the stability decreases as \( O_{2}^{-}>O_{2}^{+}>O_{2} \)
B. \( H e_{2} \) molecule does not exist as the effect of bonding and anti-bonding orbitals cancel each other
\( \mathbf{c} \cdot C_{2}, O_{2}^{2-} \) and \( L i_{2} \) are diamagnetic
D. \( \ln F_{2} \) molecule, the energy of \( \sigma_{2 p_{z}} \) is more than \( \pi_{2 p_{x}} \) and
\( \pi_{2 p_{y}} \)