AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \boldsymbol{A}(\boldsymbol{x})=\left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{1} & \mathbf{2} \boldsymbol{x}+\mathbf{1} & \mathbf{3} \boldsymbol{x}+\mathbf{1} \\ \mathbf{2} \boldsymbol{x}+\mathbf{1} & \mathbf{3} \boldsymbol{x}+\mathbf{1} & \boldsymbol{x}+\mathbf{1} \\ \boldsymbol{3} \boldsymbol{x}+\mathbf{1} & \boldsymbol{x}+\mathbf{1} & \boldsymbol{2} \boldsymbol{x}+\mathbf{1}\end{array}\right| \)
\( \operatorname{then} \int_{0}^{1} \boldsymbol{A}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}= \)
A . -15
\( B \cdot \frac{-1}{2} \)
\( c .-30 \)
\( D \)
Subject: Maths
If \( A \) and \( B \) mutually exclusive events associated with a random experiment such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \)
then find \( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \overline{\boldsymbol{B}}) \)
Subject: Physics
Velocity of a body moving along a straight line with uniform acceleration
(a) reduces by \( \frac{3}{4} \) of its initial velocity in
time \( t_{0} . \) The total time of motion of the
body till its velocity becomes zero is
A \( \cdot \frac{4}{3} t_{0} \)
в. \( \frac{3}{2} t_{0} \)
c. \( \frac{5}{3} t_{0} \)
D. \( \frac{8}{3} t_{0} \)
Subject: Chemistry
Study the given reaction and identify the process which is carried out.
\[
\left.\rangle \mathrm{c}=\mathrm{O}+\mathrm{NaHSO}_{3} \rightarrow \lambda_{\mathrm{SO}_{3} \mathrm{Na}}^{/ \mathrm{OH}} \frac{\mathrm{Na}_{2} \mathrm{CO}_{3}}{\rightarrow}\right\rangle \mathrm{C}=0
\]
A. It is used for purification of aldehydes and ketones
B. It is used to distinguish aldehydes from ketones
c. It is used to prepare cyclic aldehydes and ketones
D. It is used to study polar nature of aldehydes and ketones
Subject: Biology
The correct sequence of stages in the
evolution of the modern man (Homo
sapiens) is
A. Neanderthal man, Australopithecus, Cro-magnon man, Homoerectus, Modern man
B. Australopithecus, Homo sapiens, Neanderthal man, Cro-magnon man, Modern man
C. Homo erectus, Australopithecus, Neanderthal man, Cro-magnon man, Modern man
D. Australopithecus, Homo erectus, Neanderthal man, Cro-magnon man, Modern man
Subject: Maths
If \( \int \frac{3 x+4}{x^{3}-2 x-4} d x=\log |x-2|+ \)
\( \boldsymbol{K} \log \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{C}, \) then
This question has multiple correct options
A. \( K=-1 / 2 \)
B . \( f(x)=x^{2}+2 x+2 \)
C \( . f(x)=\left|x^{2}+2 x+2\right| \)
D. \( K=1 / 4 \)
Subject: Physics
If a magnet is suspended at an angle
\( 30^{\circ} \) to the magnetic meridian, the dip
needle makes an angle of \( 45^{\circ} \) with the horizontal. The real dip is:
A \( \cdot \tan ^{-1}(\sqrt{3 / 2}) \)
B. \( \tan ^{-1} \sqrt{3} \)
\( ^{\mathrm{c}} \tan ^{-1}(\sqrt{\frac{2}{3}}) \)
D \( \cdot \tan ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)
Subject: Chemistry
Two elements A and B have the
following configuration: \( \boldsymbol{A}: \mathbf{2}, \mathbf{7} ; \boldsymbol{B} \)
\( 2,8,7 . \) Both of them belong to:
A. the same group and are chemically similar
B. different groups but are chemically similar
C. the same group but are chemically dissimilar
D. the same period and are chemically similar
Subject: Physics
In the circuit shown in figure. Current
through \( R_{2} \) is zero if \( R_{4}=2 \Omega \) and
\( \boldsymbol{R}_{3}=\mathbf{4} \boldsymbol{\Omega} \)
In this case:
A . current through \( R_{3} \) is \( 2 A \)
B. current through \( R_{4} \) is 3 A
\( c . \) both (1) and (2) are correct
D. both (1) and (2) are wrong
Subject: Physics
If metal section of shape H is inserted in
between two parallel plates as shown in figure and \( A \) is the area of each plate then the equivalent capacitance is :
A \( \cdot \frac{A \epsilon_{0}}{a}-\frac{A \epsilon_{0}}{b} \)
В. \( \frac{A \epsilon_{0}}{a+b} \)
c. \( \frac{A \epsilon_{0}}{a}+\frac{A \epsilon_{0}}{b} \)
D. \( \frac{A \epsilon_{0}}{a-b} \)
Subject: Physics
A copper wire of negligible mass, \( 1 \mathrm{m} \) length and cross-sectional area
\( l 0^{-6} m^{2} \) is kept on a smooth horizontal
table with one end fixed. A ball of mass
kg is attached to the other end. The wire and the ball are rotating with an angular velocity of 20 rad/s. If the
elongation in the wire is \( 10^{-3} \mathrm{m} \)
a. Find the Young's modulus of the wire (in terms of \( \left.\times 10^{11} N / m^{2}\right) \)
Subject: Chemistry
If \( S_{0}, S_{1}, S_{2} \) and \( S_{3} \) are the solubilities
in water of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \)
\( \mathbf{0 . 0 1} \boldsymbol{M} \boldsymbol{C a C l}_{2}, \mathbf{0 . 0 1} \boldsymbol{M} \boldsymbol{N a C l} \) and
\( \mathbf{0 . 5} \boldsymbol{M} \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} \) solutions, respectively
then which of the following is true?
A \( . S_{0}>S_{2}>S_{1}>S_{3} \)
B. \( S_{0}=S_{2}=S_{1}>S_{3} \)
c. \( S_{3}>S_{1}>S_{2}>S_{0} \)
D. none of these
Subject: Physics
A bullet when fired into a target loses half of its velocity after penetrating 20 cm. Further distance of penetration
before it comes to rest is :
A. \( 6.66 \mathrm{cm} \)
B. 3.33 сm
\( c \cdot 12.5 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
E. \( 5 \mathrm{cm} \)
Subject: Physics
The dimensions of \( \epsilon_{0} \mu_{0} \)
\( \mathbf{A} \cdot\left[L T^{-1}\right] \)
B . \( \left[L T^{-2}\right] \)
c. \( \left[L^{2} T^{-2}\right] \)
\( \mathbf{D} \cdot\left[L^{-2} T^{-2}\right] \)
Subject: Maths
If \( \boldsymbol{A}=\left|\begin{array}{ll}\mathbf{1 0} & \mathbf{2} \\ \mathbf{3 0} & \mathbf{6}\end{array}\right| \)
then \( |\boldsymbol{A}|= \)
\( A \cdot O \)
B. 10
\( c \cdot 12 \)
D. 60
Subject: Chemistry
Chemical \( A \) is used for water softening
to remove temporary hardness. \( A \) reacts
with \( N a_{2} C O_{3} \) to generate caustic soda.
When \( C O_{2} \) is bubbled through \( A \), it
turns cloudly. What is the chemical
formula of \( \boldsymbol{A} \) ?
A \( \cdot C a C O_{3} \)
в. \( C a O \)
\( \mathbf{c} \cdot \operatorname{Ca}(O H)_{2} \)
D. \( \operatorname{Ca}\left(H C O_{3}\right)_{2} \)
Subject: Physics
A slab \( X \) is placed between the two parallel isolated charged plates as
shown in the figure. If \( E_{p} \) and \( E_{q} \) denotes the intensity of electric field at
\( P \) and \( Q, \) then :
A. \( E_{p} \) is reduced by the presence of \( x \), if \( x \) is metallic
B. \( E_{q} \) is increased by presence of \( X \), if \( X \) is dielectric
\( \mathrm{c} . E_{q} \) is in the opposite sense to \( E_{p}, \) if \( \mathrm{X} \) is dielectric
D. \( E_{q} \) is zero, if \( x \) is metallic
Subject: Physics
Two identical uniform solid spherical
balls \( A \) and \( B \) of mass \( m \) each are placed
on a the fixed wedge as shown in figure.
Ball B is kept at rest and it is released just before two balls collides. Ball A rolls
down without slipping on inclined plane and collide elastically with ball B. The kinetic energy of ball Ajust after the collision with ball B is:
A \( \cdot \frac{m g h}{7} \)
в. \( \frac{m g h}{2} \)
c. \( \frac{2 m g h}{5} \)
D. \( \frac{7 m g h}{5} \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined as
\( \left\{\begin{array}{lll}2 x & \text { if } & x>3 \\ x^{2}, & \text { if } & 1<x \leq 3 \text { . Then, find } \\ 3 x, & \text { if } & x \leq 1\end{array}\right. \)
\( \boldsymbol{f}(-1)+\boldsymbol{f}(2)+\boldsymbol{f}(4) \)
\( A \cdot S \)
B . 14
\( c .5 \)
D. none of these
Subject: Chemistry
Balance the following redox reactions:
\( \boldsymbol{S}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{I}_{2}(\boldsymbol{s}) \longrightarrow \boldsymbol{S} \boldsymbol{O}_{4}^{2-}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
A \( \cdot S^{2-}(a q)+4 I_{2}(s)+4 H_{2} O(l) \rightarrow 8 I^{-}(a q)+S O_{4}^{2-}(a q)+ \)
\( 8 H^{+}(a q) \)
B . \( S^{2-}(a q)+6 I_{2}(s)+4 H_{2} O(l) \longrightarrow 8 I^{-}(a q)+4 S O_{4}^{2-}(a q)+ \)
\( 8 H^{+}(a q) \)
\( \mathbf{c} \cdot 3 S^{2-}(a q)+4 I_{2}(s)+4 H_{2} O(l) \longrightarrow \)
\( 8 I^{-}(a q)+5 S O_{4}^{2-}(a q)+8 H^{+}(a q) \)
D \( \cdot 2 S^{2-}(a q)+4 I_{2}(s)+H_{2} O(l) \rightarrow 8 I^{-}(a q)+S O_{4}^{2-}(a q)+ \)
\( 8 H^{+}(a q) \)
Subject: Physics
A disc of mass \( \mathrm{M} \) and radius \( \mathrm{R} \) is rolling
with angular speed \( \omega \) on a horizontal
plane as shown. The magnitude of
angular momentum of the disc about
the origin 0 is
A \( \cdot \frac{1}{2} M R^{2} \omega \)
B. \( M R^{2} \omega^{\omega} \)
c. \( \frac{3}{2} M R^{2} \omega \)
D. \( 2 M R^{2} \omega \)
Subject: Maths
If 5,7,6 are the sums of the \( x, y \)
intercepts; \( \boldsymbol{y}, \boldsymbol{z} \) intercepts, \( \boldsymbol{z}, \boldsymbol{x} \)
intercepts respectively of a plane then the perpendicular distance from the origin to that plane is
A \( \cdot \frac{144}{61} \)
в. \( \frac{12}{\sqrt{61}} \)
c. \( \frac{\sqrt{61}}{12} \)
D. \( \frac{61}{144} \)
Subject: Chemistry
Consider the following reactions:
\( \boldsymbol{C a C O}_{3} \rightarrow \boldsymbol{C a O}+\boldsymbol{C O}_{2} \)
\( \boldsymbol{E}+\boldsymbol{C O}_{2} \rightarrow \boldsymbol{F} \)
\( N a C l+F \rightarrow A+N a H C O_{3} \)
where \( \boldsymbol{E} \) and \( \boldsymbol{F} \) are respectively:
A. \( N H_{4} H C O_{3} \) and \( N H_{4} C l \)
B. \( N a O H \) and \( N a H C O_{3} \)
c. \( c a(O H)_{2} \) and \( C a\left(H C O_{3}\right)_{2} \)
D. none of the above
Subject: Maths
A solar energy system uses a photovoltaic panel to convert solar energy into electricity, to charge a battery, and provide electricity as needed by the consumer. The photovoltaic pannel intercepts 1000 units of solar energy and convert \( 20 \% \) of that into electricity. There is a loss of 10 \( \% \) energy while charging the battery. The battery can be used to supply only half of the stored energy to the consumer. Assuming \( 40 \% \) energy loss in the distribution, the number of units of
energy received by the customers is
\( A \cdot 6 \)
в. 36
\( c \cdot 54 \)
D. 80
Subject: Physics
Which of the following is the most precise instrument for measuring length?
A. Metre rod of least count \( 0.1 \mathrm{cm} \)
B. Vernier calipers of least count \( 0.01 \mathrm{cm} \)
c. Screw gauge of least count \( 0.001 \mathrm{cm} \)
D. None of these
Subject: Maths
\( f(x)=1, \) if \( x \) is rational and \( f(x)=0 \)
if \( x \) is irrational
then \( (\text { fof })(\sqrt{5})= \)
\( A \cdot 0 \)
B.
\( c \cdot \sqrt{5} \)
D. \( \frac{1}{\sqrt{5}} \)
Subject: Physics
An arrangement for YDSE is shown in
figure. S is a light source then find the
position of central maxima from point 0
on screen B.
A. \( 5 \mathrm{mm} \) below
B. \( 5 \mathrm{mm} \) above 0
c. \( 30 \mathrm{mm} \) below
\( D \cdot \alpha \)
Subject: Chemistry
Write equations for the reaction of dil HCl with each of the following. Sodium sulphite
A \( \cdot 2 H C l+N a_{2} S O_{3} \rightarrow 2 N a C l+S O_{2}+H_{2} O \)
в. \( 4 H C l+N a_{2} S O_{3} \rightarrow 2 N a C l+S O_{2}+2 H_{2} O \)
c. \( 2 H C l+N a_{2} S O_{3} \rightarrow N a C l+S O_{2}+H_{2} O \)
D. \( 2 H C l+N a_{2} S O_{3} \rightarrow 2 N a C l+S O_{3}+H_{2} O \)
Subject: Maths
\( \int \frac{\sqrt{4+x^{2}}}{x^{6}} d x= \)
\( \frac{\boldsymbol{A}\left(\boldsymbol{4}+\boldsymbol{x}^{2}\right)^{\frac{3}{2}}\left(\boldsymbol{B} \boldsymbol{x}^{2}-\boldsymbol{6}\right)}{\boldsymbol{x}^{5}}+\boldsymbol{C} \)
This question has multiple correct options
A \( \cdot A=\frac{1}{120} \)
B. \( B=1 \)
c. \( A=-\frac{1}{120} \)
D. \( B=-1 \)
Subject: Physics
A semicircular wire of radius \( \boldsymbol{R} \) is
rotated with constant angular velocity about an axis passing through one end and perpendicular to the plane of the wire. There is a uniform magnetic field
of strength \( B \). The induced emf between
the ends is
\( \mathbf{A} \cdot B \omega R^{2} / 2 \)
в. \( 2 B \omega R^{2} \)
C. is variable
D. none of these
Subject: Physics
Two small equal point charges of magnitude \( q \) are suspended from a
common point o the ceiling by insulating massless strings of equal lengths. They come to equilibrium with
each string making angle \( \theta \) from the
vertical. If the mass of each charge is \( m \)
\( \mathrm{m}, \) then the electrostatic potential at
the center of line joining them will be \( \left(\frac{1}{4 \pi \epsilon_{0}}=K\right) \)
A \( .2 \sqrt{k / m g \tan \theta} \)
B . \( \sqrt{k m g \tan \theta} \)
c. \( 4 \sqrt{k / m g \tan / \theta} \)
D. \( 4 \sqrt{k m g \tan \theta} \)
Subject: Chemistry
If the energy of the second Bohr's orbit
in H-atom is \( -328 k J \) mol\( ^{-1} \), then what
is the energy of the fourth Bohr orbit?
В. \( -41 k J \) mol\( ^{-1} \)
c. \( -1312 k J \) mol \( ^{-1} \)
D. \( -164 k J \) mol \( ^{-1} \)
Subject: Chemistry
The structural formula of iso-butene is:
A. \( C H_{3} C H_{2} C H=C H_{2} \)
B. \( C H_{3} C H=C H-C H_{3} \)
c. \( C H_{3}-C H-C H_{3} \)
\[
\begin{array}{l}_{c H_{3}}\end{array}
\]
D. \( C H_{2}=\underset{c H_{3}}{C}-C H_{3} \)
Subject: Chemistry
Platinum forms two different
compounds with chlorine. One contains
\( 26.7 \% C l \) by mass, and the other contains 42.1 per \( C l \) by mass \( (P t= \)
195). The empirical formulae of the two
compounds are \( \boldsymbol{P t C l}_{2} \) and \( \boldsymbol{P t C l}_{4} \) respectively. If true enter 1 , else enter 0 .
Subject: Chemistry
Monazite sample contains \( 9 \% T h O_{2} \)
and \( 0.35 \% U_{3} O_{8} . P b^{208} \) and \( P b^{208} \) are
the stable end products in the radioactive decay series of \( \boldsymbol{T} \boldsymbol{h}^{238} \boldsymbol{q u a d a n d} \quad \mathbf{2 3 8} \) respectively. All
the lead in monazite is of radiogenic origin.

The isotopic ratio of \( P b^{208} T h^{232} \) was
found to be 0.104 . The half lives of Th
and \( U \) are \( 1.4 \times 10^{10} \) years and \( 4.47 \times \)
\( 10^{9} \) years, respectively. The time elapsed since the formation of monazite sample will be :
A. \( 1.34 \times 10^{9} \) years
B . \( 2.01 \times 10^{9} \) years
c. \( 1.41 \times 10^{10} \) years
D. \( 4.47 \times 10^{9} \) years
Subject: Chemistry
\( N a C l \) and \( C a C l_{2} \) are also added to
fused \( M g C l_{2} \) in the electrolysis of
\( M g C l_{2} . \) Select the correct statement.
This question has multiple correct options
A. melting point is decreased and conductivity is increased
B. melting point is increased and conductivity is decreased
c. melting point and conductivity both are decreased
D. melting point and conductivity both are increased
Subject: Chemistry
Which of the following pairs of isomers is not correctly matched with its type of isomerism?
A \( \cdot\left[C r\left(N H_{3}\right)_{6}\right]\left[C r(C N)_{6}\right] \) and
\( \left[C r\left(N H_{3}\right)_{4}(C N)_{2}\right]\left[C r\left(N H_{3}\right)_{2}(C N)_{4}\right] \) - coordination
isomerism
в. \( \operatorname{Co}\left[\left(N H_{3}\right)_{5} N O_{2}\right] C l_{2} \) and \( \left[C o\left(N H_{3}\right)_{5} O N O\right] C l_{2}- \) Linkage
isomerism
\( \mathbf{c} \cdot\left[\operatorname{Co}(p y)_{2}\left(H_{2} O\right)_{2} C l_{2}\right] C l \) and
\( \left[\cos (p y)_{-} 2\left(H_{-} 20\right) C_{-} 3\right] H_{-} 20 \$ \$- \) coordination
isomerism
D \cdot \( \left[P t\left(N H_{3}\right)_{4} B r_{2}\right] C l_{2} \) and \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] B r_{2} \) -lonisation isomerism
Subject: Chemistry
10 g of cane sugar (molecular mass =
342) in \( 1 \times 10^{-3} m^{3} \) of solution
produces an osmotic pressure of \( 6.68 \times 10^{4} N m^{-2} \) at \( 273 \mathrm{K} . \) Calculate
the value of \( \mathrm{R} \) in SI units.
A. \( 8.3684 J K^{-1} \mathrm{mol}^{-1} \)
B . \( 9.3684 J K^{-1} \) mol \( ^{-1} \)
c. \( 7.3684 J K^{-1} \) mol \( ^{-1} \)
D. \( 5.3684 J K^{-1} \) mol \( ^{-1} \)
Subject: Maths
\( A \) is older than B. Taking present ages of \( A \) and \( B \) as \( x \) years and \( y \) years
respectively, find in terms of \( x \) and \( y \)
(i) the difference between the ages of \( A \)
and B.
(ii) the age of B when A was of \( y \) years. If the age of \( B \), obtained, in step (ii), is
half the present age of \( A \) and \( B \) is 42 years; find the present ages of A and B.
Subject: Maths
If \( A, B \) and \( C \) are mutually exclusive and exhaustive events, then \( \boldsymbol{P}(\boldsymbol{A})+ \)
\( P(B)+P(C) \) equals to
A \( \cdot \frac{1}{3} \)
B. 1
\( c .0 \)
D. Any value between 0 and 1
Subject: Physics
The velocity time graph of a particle moving along a straight line has the
form of a parabola \( t^{2}-6 t+8 \mathrm{m} / \mathrm{s} \). Find
the velocity (in \( \mathrm{m} / \mathrm{s} \) ) when acceleration of particle is zero:
A . -1
B. -2
c. -3
D. -
Subject: Maths
\( \left(x^{2}+y^{2}\right) d x+2 x y d y=0 \)
Solve the above equation.
A \( \cdot x\left(x^{2}+3 y^{2}\right)=c \)
B. \( x\left(3 x^{2}+y^{2}\right)=c \)
C \( \cdot y\left(3 x^{2}+y^{2}\right)=c \)
D. \( y\left(x^{2}+3 y^{2}\right)=c \)
Subject: Physics
You have three resistors of values
\( 2 \Omega, 3 \Omega, \) and \( 5 \Omega . \) If they are in parallel then the total resistance is :
\( \mathbf{A} \cdot 0.97 \Omega \)
в. \( 2 \Omega \)
\( c .10 \Omega \)
D. 3.
Subject: Maths
The length of the latus rectum of the parabola
\( \mathbf{1 6 9}\left\{(\boldsymbol{x}-\mathbf{1})^{2}+(\boldsymbol{y}-\mathbf{3})^{2}\right\}=(\mathbf{5} \boldsymbol{x}- \)
\( 12 y+17)^{2} \) is
A \( \cdot \frac{14}{11} \)
в. \( \frac{12}{13} \)
c. \( \frac{28}{13} \)
D. none of these
Subject: Chemistry
The relative atomic mass of an element \( A \) is \( 16.2 . \) There are two isotopes \( _{8}^{16} A \) and \( _{8}^{18} A \) of the element. Calculate the percentage of \( _{8}^{16} A \) present in the
element.
A. 90\%
в. 60 \%
c. \( 45 \% \)
D. 80\%
Subject: Chemistry
A conductance cell was calibrated by
filling it with a \( 0.02 M \) solution of
potassium chloride (specific conductance \( =0.2768 \) oh \( m^{-1} m^{-1} \)
and measuring the resistance at \( 298 K \)
which was found to be 457.3 ohm. The
cell was then filled with a calcium
chloride solution containing \( 0.555 g \) of
\( \mathrm{CaCl}_{2} \) per litre. The measure
resistance was 1050 ohm. Calculate
the molar conductivity of \( C a C l_{2} \)
solution.
Subject: Chemistry
For a particular reaction, \( \Delta \boldsymbol{H}^{o}= \)
\( -38.3 k J \) and \( \Delta S^{o}= \)
\( -113 J K^{-1} m o l^{-1} . \) This reaction is:
A. spontaneous at all temperatures
B. non-spontaneous at all temperatures
C. spontaneous at temperatures below \( 66^{\circ} \mathrm{C} \)
D. spontaneous at temperatures above \( 66^{\circ} \mathrm{C} \)
Subject: Chemistry
The decreasing basic order of the following is:
\( \boldsymbol{i} . \boldsymbol{C H}_{3} \quad \boldsymbol{i} \boldsymbol{i} . \boldsymbol{O H} \)
iii.C \( H_{3} \) COO \( ^{\ominus} \) iv. \( H_{2} \) O
A \( \cdot(i)>(i i)>(i i i)>(i v) \)
B. \( (i v)>(i i i)>(i i)>(i) \)
C. \( (i i i)>(i)>(i i)>(i v) \)
D. \( (i v)>(i i)>(i)>(i i i) \)
Subject: Physics
The electronic potential \( V \) at a point on the circumference of a thin non-
conducting disk of radius r and uniform charge density \( \sigma \) is given by equation \( \boldsymbol{V}=\mathbf{4} \boldsymbol{\sigma} \boldsymbol{r} . \) Which of the following
expression correctly represents
electrostatic energy store in the electric
field of a similar charge disk of radius
R?
Subject: Chemistry
The charge required for reduction of
1 mol of \( C r_{2} O_{7}^{2-} \) ions to \( C r^{3+} \) is:
A . \( 9650 C \)
в. \( 2 \times 96500 C \)
c. \( 3 \times 96500 C \)
D. \( 6 \times 96500 C \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}=\{(1, \boldsymbol{a}),(\boldsymbol{2}, \boldsymbol{c}),(\boldsymbol{4}, \boldsymbol{d}),(\boldsymbol{3}, \boldsymbol{b})\} \) and
\( \boldsymbol{g}^{-1}=\{(\boldsymbol{2}, \boldsymbol{a}),(\boldsymbol{4}, \boldsymbol{b}),(1, c),(\boldsymbol{3}, \boldsymbol{d})\}, \) then
show that \( (\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})^{-1}=\boldsymbol{f}^{-1} \boldsymbol{o g}^{-1} \)
Subject: Physics
The parallel rays of white light are made an incident normally on an air film of uniform thickness. 250 fringes are seen in the transmitted light between
\( 4000 A^{\circ} \) and \( 6500 A^{\circ} . \) Thickness of air
film is
A . \( 1.3 m m \)
в. \( 1.5 \mathrm{mm} \)
c. \( 0.13 m m \)
D. \( 0.11 m m \)
Subject: Maths
Points \( (a, 0),(0, b) \) and (1,1) are
collinear, if:
A \( \cdot \frac{1}{a}+\frac{1}{b}=1 \)
B. \( \frac{1}{a}-\frac{1}{b}=1 \)
c. \( a+b=1 \)
\( \mathbf{D} \cdot a-b=a b \)
Subject: Maths
The greatest value of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( (x+1)^{1 / 3}-(x-1)^{1 / 3} \) on [0,1] is
\( A \)
B. 2
\( c \cdot 3 \)
D. \( 1 / 3 \)
Subject: Physics
A sphere 'P' of mass 'm' moving with velocity 'u' collides head-on with another sphere 'Q' of mass 'm' which is at rest. The ratio of final velocity of 'Q' to initial velocity of 'P' is \( . \cdot(e= \)
coefficient of restitution)
A \( \cdot \frac{e-1}{2} \)
\( ^{\mathrm{B}}\left[\frac{e+1}{2}\right]^{1 / 2} \)
c. \( \frac{e+1}{2} \)
\( ^{\mathrm{D} \cdot}\left[\frac{e+1}{2}\right]^{2} \)
Subject: Physics
A block of weight \( 5 N \) is pushed against
a vertical wall by a force \( 12 N \).The coefficient of friction between the wall
and block is \( 0.6 . \) The magnitude of the force exerted by the wall on block is
A. \( 12 N \)
B. \( 5 N \)
\( c .7 .2 N \)
D. \( 13 N \)
Subject: Maths
If \( y \) and \( z \) are the functions of \( x \) and if \( \boldsymbol{y}^{2}+\boldsymbol{z}^{2}=\boldsymbol{\lambda}^{2}, \) then \( \boldsymbol{y} \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\frac{\boldsymbol{y}}{\boldsymbol{\lambda}}\right)+ \)
\( \frac{d}{d x}\left(\frac{z^{2}}{\lambda}\right) \) is equal to
A \( \cdot \frac{z}{\lambda} \frac{d z}{d x} \)
B. \( \frac{z}{\lambda} \frac{d x}{d z} \)
c. \( \frac{\lambda}{z} \frac{d z}{d x} \)
D. None of these
Subject: Physics
The above figure shows a toroidal
solenoid whose cross-section is
rectangular. Find the magnetic flux (in \( \mu W b) \) through this cross-section if the
current through the winding equals \( I=1.7 A \) the total number of turns is
\( N=1000, \) the ratio of the outside
diameter to the inside one is \( \eta=1.6 \)
and the height is equal to \( h=5.0 \mathrm{cm} \)
Subject: Physics
A transformer has 500 turns in its
primary and 1000 turns in its secondary winding.The primary voltage is \( 200 \mathrm{V} \) and the load in the secondary is 100
ohm.Calculate the current in the
primary,assuming it to be a ideal transformer.
A . 25 A
B. 45 A
\( c \cdot 8 A \)
D. 22 A
Subject: Physics
A charge \( Q \) is distributed over two concentric hollow spheres of radii r and \( R(>r) \) such that the surface charge densities are equal. Find the potential
at the common centre,
A \( \cdot \frac{Q}{4 \pi \varepsilon_{0}}\left(\frac{R-r}{R^{2}+r^{2}}\right) \)
в. \( \frac{Q}{4 \pi \varepsilon_{0}}\left(\frac{R+r}{R^{2}+r^{2}}\right) \)
c. \( \frac{Q}{4 \pi \varepsilon_{0}}\left(\frac{-R+r}{R^{2}+r^{2}}\right) \)
D.
Subject: Chemistry
toppr
Q Type your question_
\( (\mathbf{B}) \)
This question has multiple correct options
\( \mathbf{A} \)
B.
\( c \)
D. In E2 elimination, the acidic H atoms is removed. The
inductive effect (-I) of Br atom increases the acidity of H atoms to which Br atoms bonded.
Decreasing acidity of \( \mathrm{H} \) atom in (B) is as follows:
\( \mathrm{H} \) at \( \mathrm{C}-1>\mathrm{H} \) at \( \mathrm{C}-2>\mathrm{H} \) at \( \mathrm{C}-3 \)
Subject: Maths
The polynomial \( a x^{3}+b x^{2}+x-6 \) has
\( (x+2) \) as a factor and leaves a
remainder 4 when divided by \( (x-2) \)
Find \( a \) and \( b \)
This question has multiple correct options
\( \mathbf{A} \cdot a=0 \)
в. \( b=2 \)
\( \mathbf{c} \cdot a=2 \)
\( \mathbf{D} \cdot b=0 \)
Subject: Physics
For a heater rated at \( 4.4 \mathrm{kW} ; 220 \mathrm{V} \) Calculate the energy consumed by the heater in 4 hours?
A. \( 12 \mathrm{kWh} \)
B. 17.6 kWh
\( c \cdot \) okwh
D. \( 4.4 \mathrm{kWh} \)
Subject: Physics
Fill the blanks with the correct option:
position potential mechanical chemical light kinetic.
1.An electric fan converts electrical
energy into \( _{\text {一一一一一一一吃 }} \) ergy.
2.Coking gas converts_- - energy
into heat energy.
3.The energy possessed by a spring is \( _{\text {therg. }} \)
4.The energy possessed by a body due to its \( _{\text {the called potential energy }} \)
5.The energy possessed by a body due to its motion is called_- - - energy