AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \operatorname{Let} \boldsymbol{H}_{1}, \boldsymbol{H}_{2}, \boldsymbol{H}_{3}, \dots, \boldsymbol{H}_{n} \) be mutually
exclusive and exhaustive events with
\( \boldsymbol{P}\left(\boldsymbol{H}_{i}\right)>0 ; \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \boldsymbol{3}, \ldots, \boldsymbol{n} . \) Let \( \mathrm{E} \) be any
other event with \( 0<P(E)<1 \)
STATEMENT-1: \( \boldsymbol{P}\left(\boldsymbol{H}_{\boldsymbol{i}} \mid \boldsymbol{E}\right)> \)
\( \boldsymbol{P}\left(\boldsymbol{E} \mid \boldsymbol{H}_{i}\right) \cdot \boldsymbol{P}\left(\boldsymbol{H}_{i}\right) \) for \( \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \boldsymbol{3}, \dots, \boldsymbol{n} \)
STATEMENT-2 \( \sum_{i=1}^{n} P\left(H_{i}\right)=1 \)
A. Statement-1 is True, Statement-2 is True; Statement - is a correct explanation for Statement- -
B. Statement-1 is True, Statement-2 is True; Statement - is Not a correct explanation for Statement- 1
c. Statement- - - is True, Statement - 2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Physics
Three similar oscillators, \( A, B, C \) have the same small damping constant \( r \)
but different natural frequencies \( \omega_{0}= \) \( (k / m)^{\frac{1}{2}}: 1200 H z, 1800 H z, 2400 H z .1 f \)
all three are driven by the same source at \( 1800 H z, \) which statement is correct
for the phases of the velocities of the
three?
A \( \cdot \phi_{A}=\phi_{B}=\phi_{c} \)
в. \( \phi_{A}<\phi_{B}=0<\phi_{c} \)
\( \mathbf{c} \cdot \phi_{A}>\phi_{B}=0>\phi_{c} \)
D \( \cdot \phi_{A}>\phi_{B}>0>\phi_{c} \)
Subject: Physics
A body of mass \( M \) is attached to one
end of a rod of mass \( M \) and length \( L \)
The entire system is rotated about an axis passing through the other end of
the rod. The \( M . I . \) of the system about die given axis of rotation is:
\( ^{\mathrm{A}} \cdot \frac{M L^{2}}{3} \)
B. \( \frac{4}{3} M L^{2} \)
\( \mathbf{c} \cdot 2 M L^{2} \)
D. \( 3 M L^{2} \)
Subject: Physics
The diameter of a sphere is 4.24 m. Its
surface area with due regard to significant figures is :
A \( .5 .65 \mathrm{m}^{2} \)
в. \( 56.5 \mathrm{m}^{2} \)
\( c .565 m^{2} \)
D. \( 5650 m^{2} \)
Subject: Physics
toppr
Q Type your question
'Igure. Ine coemcıent \( \mu \) Is insurırcıent
to start pure rolling. The sphere slides a
length \( \ell \) on the incline from rest and its
kinetic energy becomes K. Then, the work done by friction will be
A. \( -\mu \) mglcos \( \theta \)
в. \( -m g \ell \sin \theta+K \)
\( c \)
\( D \)
Subject: Chemistry
For car battery which one is correct
statement?
A. Cathode is lead dioxide \( \left(P b O_{2}\right) \) and anode is copper \( (C u) \)
B. Cathode is copper \( (C u) \) and anode is lead dioxide \( \left(P b O_{2}\right) \)
C. Cathode is copper \( (C u) \) and anode is lead \( (P b) \)
D. cathode is lead dioxide \( \left(P b O_{2}\right) \) and anode is lead \( (P b) \)
Subject: Physics
A particle starts performing simple
harmonic motion. Its amplitude is \( A \). At one time its speed is half that of the maximum speed. At this moment the displacement is:
A \( \cdot \frac{\sqrt{2} A}{3} \)
B. \( \frac{\sqrt{3} A}{2} \)
c. \( \frac{2 A}{\sqrt{2}} \)
D. \( \frac{3 A}{\sqrt{2}} \)
Subject: Maths
For matrices \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{1} \\ \mathbf{3} & \mathbf{2}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right], \) write \( A+B \) and \( A-B \)
Subject: Physics
During the rocket propulsion, gases ejecting with velocity \( 1 k m / s \) relative to
rocket. The rate of fuel consumption is \( \frac{\boldsymbol{m}}{\mathbf{1 0}} \boldsymbol{k g} / \boldsymbol{s}, \) where \( \boldsymbol{m} \) is the instantaneous
mass of the rocket. If air resistance
varies according to equation \( \boldsymbol{f}= \) \( 0.15 m v, \) then terminal velocity of the
rocket is:-
A. \( 300 \mathrm{m} / \mathrm{s} \)
в. \( 600 \mathrm{m} / \mathrm{s} \)
c. \( 7.92 \mathrm{m} / \mathrm{s} \)
D. \( 11.2 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
In which case van't Hoff factor is
maximum (assuming no hydrolysis)?
A . \( K C l, \) 50\% ionised
B. \( K_{2} S O_{4}, 40 \% \) ionised
c. \( F e C l_{3}, \) 30\% ionised
D. \( S n C l_{4}, \) 20\% ionised
Subject: Physics
A circular loop of radius \( r, \) having \( N \)
turns of a wire, is placed in a uniform
and constant magnetic field \( \boldsymbol{B} \). The
normal loop makes an angle \( \theta \) with the
magnetic field. Its normal rotates with an angular velocity \( \omega \) such that the angle \( \theta \) is constant. Choose the correct
statement from the following. This question has multiple correct options
A . emf in the loop is \( N B \omega r^{2} / 2 \cos \theta \)
B. emf induced in the loop is zero
c. emf must be induced as the loop crosses magnetic lines
D. emf must not be induced as flux does not change with time
E. answer required
Subject: Maths
If the second term of the expansion \( \left[\boldsymbol{a}^{1 / 13}+\frac{\boldsymbol{a}}{\sqrt{\boldsymbol{a}^{-1}}}\right]^{n} \quad \boldsymbol{i s} 14 \boldsymbol{a}^{5 / 2}, \) then the
value of \( \frac{n_{\mathbf{S}}}{n_{\mathbf{C}_{2}}} \) is
A .4
B. 3
c. 12
D. 6
Subject: Maths
\( f(a, b, c \text { are in } A P \) then Prove that \( \left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{2} & \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}+\mathbf{2} \boldsymbol{a} \\ \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}+\mathbf{4} & \boldsymbol{x}+\mathbf{2} \boldsymbol{b} \\ \boldsymbol{x}+\mathbf{4} & \boldsymbol{x}+\mathbf{5} & \boldsymbol{x}+\mathbf{2} \boldsymbol{c}\end{array}\right|=\mathbf{0} \)
Subject: Physics
Q Type your question
equal area \( A \) are used at the four
openings to keep the water in
equilibrium. Now an additional force \( \boldsymbol{F} \) is applied at each piston. The increase
in the pressure at the centre of the
container due to this addition is
\( A \cdot F \)
\( \bar{A} \)
B. 2 \( A \)
c. \( \frac{4 F}{A} \)
\( D \)
Subject: Physics
Find the total acceleration of the sphere as a function of \( \boldsymbol{\theta}, \) the angle of deflection of the thread from the
vertical.
A. \( w=g \sqrt{1+2 \cos ^{2} \theta} \)
В. \( w=g \sqrt{2+3 \cos ^{2} \theta} \)
c. \( w=g \sqrt{1+3 \cos ^{2} \theta} \)
D. \( w=g \sqrt{3+2 \cos ^{2} \theta} \)
Subject: Physics
Among the following, which one is isotope
A. \( N H_{3} \) and \( N_{2} H_{4} \)
B. 160 and \( ^{17} O \)
c. \( N H_{4} C l \) and \( N H_{4} N O_{3} \)
D. \( C H_{3} O C H_{3} \) and \( C H_{3} C H_{2} O H \)
E. \( O_{2} \) and \( O_{3} \)
Subject: Chemistry
Assertion
Boiling and melting points of amides are higher than corresponding acids.
Reason
It is due to strong intermolecular hydrogen bonding in their molecules
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
If \( D \) is a point on the side \( A B \) of \( \triangle A B C \) such that \( A D: D B=3: 2 \) and \( E \) is a point
on BC such that DE \( \| \) AC. Find the ratio of areas of \( \triangle \mathrm{ABC} \) and \( \triangle \mathrm{BDE} \)
Subject: Chemistry
Q Type your question
\( \mathbf{A} \cdot 2 C H_{3} C O O H+N a_{2} C O_{3} \rightarrow 2 C H_{3} C O O N a+H_{2} O+ \)
\( C O_{2} \) (Test tube \( B \) )
\( \left.C a(O H)_{2}+C O_{2} \rightarrow C a C O_{3}+H_{2} O \text { (Test tube } A\right) \)
B \( \cdot 2 C H_{3} C O O H+N a_{2} C O_{3} \rightarrow 2 C H_{3} C O O N a+H_{2} O+ \)
\( C O_{2}(\text { Test tube } A) \)
\( \left.C a(O H)_{2}+C O_{2} \rightarrow C a C O_{3}+H_{2} O \text { (Test tube } B\right) \)
\( \mathbf{c} \cdot C H_{3} C O O H+N a_{2} C O_{3} \rightarrow C H_{3} C O O N a+H_{2} O+ \)
\( C O_{2}(\text { Test tube } A) \)
\( \left.C a(O H)_{2}+C O_{2} \rightarrow C a C O_{3}+H_{2} \text { (Test tube } B\right) \)
D \( \cdot 2 C H_{3} C O O H+N a_{2} C O_{3} \rightarrow 2 C H_{3} C O O N a+H_{2} O+ \)
\( C O \text { (Test tube } A) \)
\( \left.\mathrm{Ca}(\mathrm{OH})_{2}+\mathrm{CO}_{2} \rightarrow \mathrm{CaCO}_{3}+\mathrm{H}_{2} \mathrm{O} \text { (Test tube } B\right) \)
Subject: Physics
The radius of a sphere is \( 1.41 \mathrm{cm} \). Its volume to an appropriate number of significant figures is then
\( \mathbf{A} \cdot 11.73 \mathrm{cm}^{3} \)
B . 11.736 \( c m^{3} \)
\( \mathrm{c} \cdot 11.7 \mathrm{cm}^{3} \)
D. \( 117 \mathrm{cm}^{3} \)
Subject: Physics
Two conducting rings \( P \) and \( Q \) of radi and \( r \) and \( 2 r \) rotate uniformly in opposite directions with centre of mass
velocities \( 2 \mathrm{v} \) and \( \mathrm{v} \) respectively on a conducting surface S. There is a uniform magnetic field of magnitude B perpendicular to the plane of the rings.
The potential difference between the
highest points of the two rings is
\( A \cdot(a) \) zer
\( B \cdot(b) 4 B v \)
\( c \cdot(c) 8 \) Bv
D. (d)16 Bv
Subject: Physics
On the pole of the Earth a body is
imparted velocity \( v_{0} \) directed vertically
up. Knowing the radius of the Earth and
the free-fall acceleration on its surface,
the height to which the body will ascend is given as \( h=\frac{R v_{0}^{2}}{x g R-v_{0}^{2}} . \) The air drag
is to be neglected. Find \( x \)
Subject: Maths
Find the value of \( p \) such that quadratic
equation \( (\boldsymbol{p}-\mathbf{1 2}) \boldsymbol{x}^{2}-\boldsymbol{2}(\boldsymbol{p}-\mathbf{1 2}) \boldsymbol{x}+ \)
\( 2=0 \) has equal
Subject: Maths
If \( \boldsymbol{P}=(8,6) \) and \( \mathrm{R} \) is the rotation
through \( 90^{\circ} \) about \( 0, \) then \( R_{-90} O(P) \) is
A. (6,-8)
()
в. (-8,-6)
\( c \cdot(8,6) \)
D. (-8,6)
Subject: Physics
A proton goes undeflected in a crossed electric and magnetic field (the fields
are perpendicular to each other) at a speed of \( 10^{5} \mathrm{m} / \mathrm{s} \). The velocity is
perpendicular to both the fields. When
the electric field is switched off, the
proton moves along a circle of radius 2
\( \mathrm{cm} . \) Find the magnitude of the electric and the magnetic fields. Take the mass of the proton \( =1.6 \times 10^{-27} \mathrm{kg} \)
Subject: Physics
A conductor \( A B \) carries a current \( i \) in a magnetic field \( \vec{B} . \) If \( \overrightarrow{A B}=\vec{r} \) and the force on the conductor is \( \vec{F} \). Then
This question has multiple correct options
A \( \cdot \vec{F} \) does not depend on the shape of \( A B \)
В \( \cdot \vec{F}=i(\vec{r} \times \vec{B}) \)
c. \( \vec{F}=i(\vec{B} \times \vec{r}) \)
D \( \cdot|\vec{F}|=i(\vec{r} \cdot \vec{B}) \)
Subject: Physics
A turn of radius \( 20 m \) is banked for the
vehicles going at a speed of \( 10 m s^{-1} . \) If the coefficient of static friction between
the road and the tyre is \( 0.4, \) what is the
possible speed of a vehicle so that it does not slips down?
(Take \( \left.g=10 m s^{-2}\right) \)
A. \( 50 k / h \)
в. \( 48 k / h \)
c. \( 54 k / h \)
D. \( 10 k / h \)
Subject: Biology
toppr OG
Q Type your question
these alphabets have been correctly
matched with the parts which they
indicate
A. A- Root hair, B- Epiblema, C- Cortex, D- Endodermis, EPassage cell, F- Pericycle, G- Pith, H- Phloem, IMetaxylem, J- Protoxylem
B. A- Root hair, B- Epiblema, C- Cortex, D- Endodermis, EPassage cell, F- Pith, G- Pericycle, H- Metaxylem, IPhloem, J- Protoxylem
C. A- Root hair, B- Epiblema, C- Cortex, D- Endodormis, EPericycle, F- Passage cell, G- Phloem, H- Pith, IProtoxylem, J- Metaxylem
D. A- Root hair, B- Cortex, C- Epiblema, D- Pericycle, EEndodermis, F- Pith, G- Passage cell, H- Phloem, Protoxylem, J- Metaxylem
Subject: Maths
\( \ln \) a \( \mathrm{G} . \mathrm{P}, ., \mathrm{T}_{2}+\mathrm{T}_{5}=216 \) and \( \boldsymbol{T}_{4}: \boldsymbol{T}_{6}= \)
1: 4 and all terms are integers, then its
first term is:
A . 16
B. 14
c. 12
D. 15
Subject: Physics
A block of mass \( 20 \mathrm{kg} \) is slowly slid up on a smooth incline of inclination53 \( ^{o} \) by
a person. Calculate the work done by the person in moving the block through a distance \( 4 \mathrm{m}, \) if the driving force is \( (\mathrm{a}) \) parallel to the incline and (b) in the
horizontal direction. \( \left[\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right] \)
Subject: Physics
At what height above the ground must a mass of \( 5 \mathrm{kg} \) be to have its P.E. equal in value to the K.E. possessed by it when it moves with a velocity of \( 10 \mathrm{m} / \mathrm{s} ? \)
(Assume \( \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2} \)
A. \( 1 \mathrm{m} \)
B. \( 5 \mathrm{m} \)
\( c \cdot 10 m \)
D. 50 \( m \)
Subject: Physics
When 5 V potential difference is applied
across a wire of length \( 0.1 \mathrm{m} \), the drift speed of electrons is \( 2.5 \times 10^{-4} m s^{-1} . \) If
the electron density in the wire is \( 8 x \)
\( 10^{28} m^{-3}, \) the resistivity of the material
is close to:
A \( \cdot 1.6 \times 10^{-7} \Omega \) m
В \( \cdot 1.6 \times 10^{-6} \Omega \) m
c. \( 1.6 \times 10^{-5} \Omega \) m
D. \( 1.6 \times 10^{-8} \Omega \) m
Subject: Maths
If \( y=\log \left(\frac{1-x^{2}}{1+x^{2}}\right), \) then \( \frac{d y}{d x} \) is equal
to
A \( \cdot \frac{-4 x}{1-x^{4}} \)
в. \( \frac{4 x^{3}}{1-x^{4}} \)
c. \( \frac{1}{4-x^{4}} \)
D. \( \frac{-4 x^{3}}{1-x^{4}} \)
Subject: Maths
Solve graphically the pair of equations \( x+3 y=6, \) and \( 3 x-5 y=18 . \) Hence
find the value of \( \boldsymbol{K} \) if \( \mathbf{7} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\boldsymbol{K} \)
A. \( x=-3, y=1, K=13 \)
В. \( x=-8, y=5, K=8 \)
c. \( x=1, y=2, K=29 \)
D. \( x=6, y=0, K=42 \)
Subject: Maths
\( \int_{-1 / 2}^{1 / 2}(\cos x)\left[\log \left(\frac{1-x}{1+x}\right)\right] d x \) is equal
to :
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot e^{1 / 2} \)
D. \( 2 e^{1 / 2} \)
Subject: Maths
Divide the first expression by the second. Write the quotient and the remainder.
\( x^{2}-\frac{1}{4 x^{2}} ; x-\frac{1}{2 x} \)
A \( \cdot \) Quotient \( =x+\frac{2}{2 x}, \) Remainder \( =1 \)
B. Quotient \( =2 x+\frac{1}{2 x} \), Remainder = 0
c. quotient \( =x-\frac{1}{2 x}, \) Remainder \( = \)
D. Quotient \( =x+\frac{1}{2 x}, \) Remainder \( =0 \)
Subject: Maths
Let \( x^{k}+y^{k}=a^{k},(a, k>0) \) and
\( \frac{d y}{d x}+\left(\frac{y}{x}\right)^{1 / 3}=0, \) then \( k \) is :
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{4}{3} \)
\( D \cdot 3 \)
\( \overline{2} \)
Subject: Physics
Assuming that in an atom, neutron
\( \left(m_{n}\right) \) and electron \( \left(m_{e}\right) \) are bound to
each other by gravitational force only and electron are moving around neutron and assuming Bohr's quantization rule to be valid.The expression for energy of
electron in \( n^{t h} \) level comes out to be
\( \left.\frac{(a-4) G^{2} m_{n}^{2} m_{e}^{2}}{4 n^{2} h^{2}} V \quad \text { (where } h=\frac{h}{2 \pi}\right) \)
Find the value of ' \( a \) '
Subject: Maths
Suppose \( g(x)=2 x+1 \) and \( h(x)= \)
\( 4 x^{2}+4 x+5 \) and \( h(x)=(f o g)(x) \) The
area enclosed by the graph of the function \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) and the pair of
tangents drawn to it from the origin is
\( A \cdot 8 / 3 \)
B. \( 16 / 3 \)
c. \( 32 / 3 \)
D. none
Subject: Maths
A rectangular hyperbola whose cente is C is cut by any circle of radius \( r \) in four
point \( P, Q, R, \) S. The value of \( C P^{2}+ \)
\( C Q^{2}+C R^{2}+C S^{2} \) is equal to:
A \( \cdot r^{2} \)
B . \( 2 r^{2} \)
\( c \cdot 3 r^{2} \)
D. \( 4 r^{2} \)
Subject: Chemistry
The triad of nuclei that is isotonic is :
A \( \cdot \frac{14}{6} C, \frac{15}{7} N, \frac{17}{9} F \)
В \( \cdot \frac{12}{6} C, \frac{74}{7} N, \frac{19}{9} F \)
C \( \cdot \frac{14}{6} C, \frac{14}{7} N, \frac{17}{9} F \)
D \cdot \( _{6}^{14} C, \frac{14}{7} N, \frac{19}{9} F \)
Subject: Physics
Mean free path in kinetic theory can be
written as: ( every symbol has standard
meaning
A \( \cdot l=\frac{\mu}{2 p} \sqrt{\frac{\pi K_{B} T}{m}} \)
B. \( l=\frac{\mu}{2 p} \sqrt{\frac{3 \pi K_{B} T}{2 m}} \)
\( \mathbf{c} \cdot l=\frac{\mu}{p} \sqrt{\frac{\pi K_{B} T}{2 m}} \)
D \( \cdot l=\frac{3 \mu}{2 p} \sqrt{\frac{\pi K_{B} T}{2 m}} \)
Subject: Maths
The variance of the first \( n \) natural
number is
A \( \cdot \frac{1}{12}\left(n^{2}-1\right) \)
B \( \cdot \frac{1}{6}\left(n^{2}-1\right) \)
c. \( \frac{1}{6}\left(n^{2}+1\right) \)
D. \( \frac{1}{12}\left(n^{2}+1\right) \)
Subject: Maths
Prove that: \( \left|\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b} & \boldsymbol{c}\end{array}\right|=(\boldsymbol{a}+\boldsymbol{b}+ \)
\( c)(a-c)^{2} \)
Subject: Physics
A spring-mass oscillator has a total
energy \( E_{0} \) and an amplitude \( x_{0} . \) For
what value of \( \boldsymbol{x} \) will \( \boldsymbol{K}=\boldsymbol{U} \) ?
A \( . x=x_{0} \)
в. \( x=\frac{x_{0}}{\sqrt{2}} \)
c. \( x=2 \)
D. \( x=0 \)
Subject: Chemistry
The atomic masses of two elements \( P \)
and \( Q \) are 20 and 40 , respectively. If
\( a^{\prime} g \) of \( P \) contains \( ^{\prime} b^{\prime} \) atoms, how many
atoms are present in \( ^{\prime} 2 a^{\prime} g \) of \( Q ? \)
\( A \)
B. \( b \)
c. \( 2 a \)
D. \( 2 b \)
Subject: Physics
Consider the nuclear reaction
\( \boldsymbol{X}^{200} \rightarrow \boldsymbol{A}^{110}+\boldsymbol{B}^{90}+ \)energy
If the binding energy per nucleon for \( X, A \) and \( B \) is \( 7.4 M e V, 8.2 M e V \) and
\( 8.2 M e V \) respectively. What is the
energy released?
A \( .200 \mathrm{MeV} \)
В. \( 160 \mathrm{MeV} \)
c. \( 110 M e V \)
D. 90 MeV
Subject: Physics
A transformer has an efficiency of \( 80 \% \) It works at \( 4 \mathrm{kW} \) and \( 100 \mathrm{V} \). If the
secondary voltage is \( 240 \mathrm{V} \), the current in primary coil is
\( \mathbf{A} \cdot 0.4 \mathrm{A} \)
B. 4 A
c. 10 А
D. 40 A
Subject: Maths
Let \( \boldsymbol{f}=\boldsymbol{R} \rightarrow \boldsymbol{R} \) be a continuous
function defined by \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\boldsymbol{e}^{\boldsymbol{x}}+\mathbf{2} \boldsymbol{e}^{-\boldsymbol{x}}} \)
Statement \( 1: f(c)=\frac{1}{3}, \) for some \( c \epsilon R \) Statement \( 2: 0<f(x) \leq \frac{1}{2 \sqrt{2}}, \) for al
\( \boldsymbol{x} \epsilon \boldsymbol{R} \)
Subject: Physics
A metallic solid sphere is rotating about is diameter as axis of rotation. If
the temperature is increased by \( 200^{\circ} \mathrm{C} \)
the percentage increased in its moment
of inertia is (Coefficient of linear
expansion of the metal \( =10^{-5} /^{\circ} \mathrm{C} \)
A . \( 0 . \)
B. 0.2
c. 0.3
D. 0.4
Subject: Chemistry
A mixture of \( S O, \) and \( O_{2} \) under
atmospheric pressure in the ratio of 2:
1 is passed over a catalyst at \( 1170^{\circ} \mathrm{C} \) After equilibrium has reached, the gas coming out has been found to contain
\( 87 \% S O_{3} \) by volume. Calculate \( K_{p} \) for \( \boldsymbol{S O}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3} \)
Subject: Chemistry
Assertion
An emulsion becomes stable if soap is
added to it.
Reason
Soap contains hydrophobic and hydrophilic parts.
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: Maths
Using section formula, show that the
points \( \boldsymbol{A}(\mathbf{2},-\mathbf{3}, \mathbf{4}), \boldsymbol{B}(-\mathbf{1}, \mathbf{2}, \mathbf{1}) \) and
\( C\left(0, \frac{1}{3}, 2\right) \) are collinear.
Subject: Maths
Which of the following statements are true and which are false? In each case
give a valid reason for saying so
(i) \( p: \) Each radius of a circle is a chord of the circle
(ii) \( \mathrm{q}: \) The centre of a circle bisects each chord of the circle
(iii) \( r: \) Circle is a particular case of an ellipse
(iv) \( s: \) If \( x \) and \( y \) are integers such that
\( \boldsymbol{x}>\boldsymbol{y} \) then \( -\boldsymbol{x}<-\boldsymbol{y} \)
\( (v) t: \sqrt{11} \) is a rational number
Subject: Physics
andiscilicia du
consists of two identical uniform solid
cylinders, each of mass \( m, \) on which two
light threads are wound symmetrically.
The friction in the axle of the upper
cylinder is assumed to be absent. If the
tension of each thread in the process of motion is \( \boldsymbol{T}=\frac{\boldsymbol{m} \boldsymbol{g}}{\boldsymbol{x}}, \) then the value of \( \boldsymbol{x} \)
is :
A . 10
B. 20
c. 15
\( D \)
Subject: Physics
A radioactive substance after 48 days
remains \( 25 \% \) of initial. Find
disintegration constant
A \( \cdot 2.89 \times 10^{-2} T^{-1} \)
В. \( 3.89 \times 10^{-3} T^{-1} \)
c. \( 4.89 \times 10^{-2} T^{-1} \)
D. none of these
Subject: Biology
If \( ^{\prime} 1^{\prime} \) represents the extracellular
digestion, '2' represent the intracellular
digestion and \( ^{\prime} 3^{\prime} \) represent both type
then for coelentrata, ctenophore and
porifera, select the correct option.
A. 1,2,3 respectively
B. 3,3,2 respectively
c. 3,2,1 respectively
D. 3,2,2 respectively
Subject: Maths
Tangents PA and PB drawn to \( x^{2}+y^{2}= \)
9 from any arbitrary point 'P' on the line \( x+y=25 . \) Locus of midpoint of chord
AB is
A \( \cdot 25\left(x^{2}+y^{2}\right)=9(x+y) \)
B . \( 25\left(x^{2}+y^{2}\right)=3(x+y) \)
C. \( 5\left(x^{2}+y^{2}\right)=3(x+y) \)
D. None of these
Subject: Chemistry
Ref. image Half-life is independent of concentration of reactant. After minutes
volume of \( N_{2} \) gas is \( 10 L \) and after
complete reaction it is \( 50 L \). Hence rate
constant is :
A \( \cdot(2.303 / 10) \log 5 \min ^{-1} \)
B . \( (2.303 / 10) \log 1.25 \mathrm{min}^{-1} \)
c. \( (2.303 / 10) \log 2 \) min \( ^{-1} \)
D. \( (2.303 / 10) \log 4 \min ^{-1} \)
Subject: Maths
If \( x=n \pi-\tan ^{-1} 3 \) is a solution of the
equation \( 12 \tan 2 x+\frac{\sqrt{10}}{\cos x}+1=0 \)
then
A. \( n \) is any integer
B. n is an even integer
c. \( n \) is a positive integer
D. \( n \) is an odd integer
Subject: Physics
If two bodies of different masses \( m_{1} \)
and \( m_{2} \) are dropped from different
heights \( h_{1} \) and \( h_{2} \), then ratio of the
times taken by the two to drop through these distances is
B. \( h_{2} / h_{1} \)
c. \( \sqrt{h_{1}}: \sqrt{h_{2}} \)
D. \( h_{1}^{2}: h_{2}^{2} \)
Subject: Physics
Heat is flowing through two cylindrical rods made of same materials whose
ends are maintained at similar
temperatures. If diameters of the rods are in ratio 1: 2 and lengths in the ratio \( 2: 1, \) then the ratio of thermal current
through in steady state is:
A \( \cdot 1: 8 \)
B. 1: 4
\( c \cdot 1: 6 \)
D. 4: 1
Subject: Physics
Explain why
(a) The blood pressure in humans is
greater at the feet than at the brain
(b) Atmospheric pressure at a height of about \( 6 \mathrm{km} \) decreases to nearly half of its value at the sea level, though the
height of the atmosphere is more than \( 100 \mathrm{km} \)
(c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area
Subject: Chemistry
How many elements are possible for the
\( 1^{s t} \) period of periodic table if azimuthal quantum number can have integral values from 0 to \( (n+1) .[n= \) shell number and other rules are remaining same to form period table?
A . 4
B. 6
\( c \cdot 2 \)
\( D \cdot 8 \)
Subject: Chemistry
Correct formula of
tetraamminechloronitroplatinum (IV) sulphate can be written as:
A \( \cdot\left[P t\left(N H_{3}\right)_{4}(O N O) C l\right] S O_{4} \)
B . \( \left[P t\left(N H_{3}\right)_{4} C l_{2} N O_{2}\right]_{2} S O_{4} \)
\( \mathrm{c} \cdot\left[\operatorname{Pt}\left(N H_{3}\right)_{4}\left(\mathrm{NO}_{2}\right) \mathrm{Cl}\right] \mathrm{SO}_{4} \)
D \cdot \( \left[P t C l(O N O) N H_{3}\left(S O_{4}\right)\right] \)
Subject: Chemistry
What would happen when a solution of
potassium chromate is treated with an excess of dilute nitric acid?
A \( \cdot C r^{3+} \) and \( C r_{2} O_{7}^{2-} \) are formed
B. \( C r_{2} O_{7}^{2-} \) and \( H_{2} O \) are formed
C. \( C r_{2} O_{4}^{2-} \) is reduced to +3 state of \( c r \)
D. \( C r_{2} O_{4}^{2-} \) oxidised to +7 state of \( c r \)