AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The linear magnification for a spherical mirror is the ratio of the size of the
image to the size of the object, and is
denoted by m. Then \( m \) is equal to (symbols have their usual meanings)
A \( \cdot \frac{u}{u-f} \)
B. \( \frac{u f}{u-f} \)
c. \( \frac{f}{u+f} \)
D. None of these
Subject: Chemistry
Among the following, the number of
compounds that can react with \( P C l_{5} \) to
give \( P O C l_{3} \) is:
\( O_{2}, C O_{2}, S O_{2}, H_{2} O, H_{2} S O_{4}, P_{4} O_{10} \)
\( A \cdot 4 \)
B. 5
\( c \cdot 3 \)
D. 6
Subject: Chemistry
\( 0.303 \mathrm{g} \) of the organic compound in Duma's method on combustion gave
\( 32.27 \mathrm{ml} \) of moist nitrogen at \( 27^{\circ} \mathrm{C} \) and
at P mm of Hg pressure. The vapour
pressure at \( 27^{\circ} \mathrm{C} \) is \( 21 \mathrm{mm} \) of Hg. Find
the value of P.
A. \( 725 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. \( 746 \mathrm{mm} \) of \( \mathrm{Hg} \)
c. \( 710 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 760 \mathrm{mm} \) of \( \mathrm{Hg} \)
Subject: Chemistry
Complex compound
\( \left[\boldsymbol{C o}(\boldsymbol{S C N})_{2}\left(\boldsymbol{N H}_{3}\right)_{4}\right] \boldsymbol{C l} \) exhibits :
This question has multiple correct options
A. ionization isomerism
B. geometrical isomerism
c. optical isomerism
D. linkage isomerism
Subject: Physics
If the magnetic moment of magnet is \( 0.8 \times 10^{-3} A m^{2} \) and the force acting on
each pole in a uniform magnetic field strength of 0.48 gauss, is \( 0.512 \times 10^{-6} N \)
The distance between the poles of the magnet is : (in \( c m) \)
A . 25
в. 12.5
c. 15
D. 7.5
Subject: Physics
A body of mass \( 1 \mathrm{kg} \) has a kinetic energy
of motion 8 J. Its linear momentum is
equal to:
A \( \cdot 2 k g m s^{-1} \)
B. \( 4 k g m s^{-1} \)
c. \( 6 k g m s^{-1} \)
D. \( 8 k g m s^{-1} \)
Subject: Maths
Find general solution of \( \frac{2 d y}{d x}= \) \( \frac{y(x+1)}{x} \)
\( \mathbf{A} \cdot \log y^{2}=x+\log |x|+k \)
B. \( \log y^{2}=x+\log (x)+k \)
\( \mathbf{c} \cdot \log y=x+\log (x)+k \)
D . \( 2 \log y=x-\log |x|+k \)
Subject: Physics
A particle executes SHM with
amplitude \( 0.5 \mathrm{cm} \) and frequency \( 100 s^{-1} \) The maximum speed of the particle is \( (\operatorname{in} m / s) \)
\( A \)
B. 0.5
c. \( 5 \pi \times 10^{-5} \)
D. \( 100 \pi \)
Subject: Maths
If \( \boldsymbol{x}^{m}+\boldsymbol{y}^{m}=\mathbf{1} \) such that \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=-\frac{\boldsymbol{x}}{\boldsymbol{y}} \)
then what should be the value of \( m ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of the above
Subject: Physics
The displacement of a body executing SHM is given by \( x=A \sin \left(2 \pi t+\frac{\pi}{3}\right) . \) The first time from \( t=0 \) when the velocity is maximum is:
A. 0.33 sec
B. 0.16 sec
c. \( 0.25 \mathrm{sec} \)
D. \( 0.5 \mathrm{sec} \)
Subject: Chemistry
A one litre flask is full of reddish brown
bromine fumes. The intensity of brown colour of vapour will decrease appreciably on adding to the flask \( x \) number of species from the following
find \( x \)
(i) Marble pieces
(ii) Animal charcoal powder
(iii) \( \mathbf{C} \boldsymbol{C l}_{\mathbf{4}} \)
(iv) \( \mathbf{C} \boldsymbol{S}_{2} \)
(v) Water
\( A \cdot(3) \)
B. (2)
c. (1)
\( D \cdot(4) \)
Subject: Maths
A random variable \( \boldsymbol{X} \) has the following probability distribution:
\[
\begin{array}{ccccc}
\boldsymbol{X} & 0 & 1 & 2 & 3 \\
P(X) & 0.1 & k & 2 k & 2 k
\end{array}
\]
Determine:
(i) \( k \)
(ii) \( P(X \geq 2) \)
Subject: Physics
The position of a particle is given by \( \vec{r} \) \( =3 t \hat{i}+2 t^{2} \hat{j}+5 \hat{k}, \) where \( t \) is in seconds and the coefficients have the proper
units for \( r \) to be in metres. The direction
of velocity of the particle at \( t=1 \) s is:
\( A \cdot 53^{\circ} \) with \( x \) -axis
B. 37 \( ^{\circ} \) with \( x \) -axis
c. \( 30^{\circ} \) with \( y \) -axis
D. \( 60^{\circ} \) with \( y \) -axis
Subject: Maths
Evaluate the following:
\( [\mathbf{2} \hat{\mathbf{i}} \hat{\mathbf{j}} \hat{\mathbf{k}}]+[\hat{\mathbf{i}} \hat{\mathbf{k}} \hat{\mathbf{j}}]+[\hat{\boldsymbol{k}} \hat{\mathbf{j}} \mathbf{2} \hat{\mathbf{i}} \)
Subject: Physics
The least value of magnetic moment
(where \( m \) is the mass of the electron, \( e \) is
the charge of electron) is :
A \( \cdot \frac{e h}{m} \)
в. \( \frac{e h}{4 \pi m} \)
c. \( \frac{2 e h}{\pi m} \)
D. \( \frac{e h}{\pi m} \)
Subject: Maths
Calculate the volume of the hemisphere.
A. \( 1095.23 \mathrm{cm}^{3} \)
B . \( 2095.23 \mathrm{cm}^{3} \)
c. \( 3095.23 \mathrm{cm}^{3} \)
D. \( 4095.23 \mathrm{cm}^{3} \)
Subject: Chemistry
X-rays emitted from a copper target and
a molybdenum target are found to
contain a line of wavelength \( 22.85 \mathrm{nm} \) attribute to the \( K_{\alpha} \) lines of an impure
element. The \( K_{\alpha} \) lines of copper \( (\mathrm{Z}=29 \)
and molybdenum \( (\mathrm{Z}=42) \) have a
wavelength 15.42 nm and 7.12 nm respectively. Using Moseley's law, \( v^{1 / 2}=a(Z-b), \) calculate the atomic
number of the impure element:
A .24
B . 28
c. 30
D. 32
Subject: Chemistry
\( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} \) solution of a weak acid
\( H A \) has molar conductivity
\( 5 S c m^{2} m o l^{-1} . \) The osmotic pressure of
the resulting solution obtained after
dilution of original solution upto 1 litre at \( 500 \mathrm{K}, \) assuming ideal solution is:
\( \left(G i v e n: \lambda_{m}^{\infty}\left(H^{+}\right)=\right. \)
\( 450 S c m^{2} m o l^{-1}, \lambda_{m}^{\infty}\left(A^{-}\right)= \)
\( \mathbf{5 0} \boldsymbol{S c m}^{2} \boldsymbol{m o l}^{-1}, \boldsymbol{R}= \)
\( \left.0.08 L \text { atm } \operatorname{mole}^{-1} K^{-1}, \sqrt{10}=3.2\right) \)
A. 0.3128 atm
B. 0.4128 atm
c. 0.5128 atm
D. 0.6128 atm
Subject: Maths
In the given figure, two connectric circles with centre \( \boldsymbol{O} \) have radii \( 21 \mathrm{cm} \)
and \( 42 \mathrm{cm}, \) If \( \angle A O B=60^{\circ}, \) find the
area of the shaded region \( \left[\mathbf{U} \mathbf{s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)
Subject: Maths
Let \( 0<\theta<\pi / 2 \) and
\( \boldsymbol{\Delta}(\boldsymbol{x}, \boldsymbol{\theta})=\left|\begin{array}{ccc}\boldsymbol{x} & \tan \boldsymbol{\theta} & \cot \boldsymbol{\theta} \\ -\tan \boldsymbol{\theta} & -\boldsymbol{x} & \mathbf{1} \\ \cot \boldsymbol{\theta} & \boldsymbol{1} & \boldsymbol{x}\end{array}\right| \)
then
This question has multiple correct options
A \( \cdot \Delta(0, \theta)=0 \)
B. \( \Delta\left(x, \frac{\pi}{4}\right)=x-x^{3} \)
c. \( \operatorname{Min}_{0<\theta<\pi / 2} \Delta(1, \theta)=0 \)
D. \( \Delta(x, \theta) \) is independent of \( x \)
Subject: Physics
A circular loop of radius \( 1 \mathrm{m} \) is kept in a magnetic field of strength 2 T directed
perpendicular to the plane of loop.
Resistance of the loop wire is \( 2 \mathrm{m} . \mathrm{A} \)
conductor of length \( 2 \mathrm{m} \) is sliding with a speed \( 1 \mathrm{m} / \mathrm{s} \) as shown in the figure. Find
the instantaneous force acting on the rod [Assume that the rod has negligible resistance]
\( A \cdot 8 N \)
B. 16 N
\( c .24 \mathrm{N} \)
D. 32
Subject: Chemistry
The correct order of increasing atomic
size of element \( N, F, S i \& P \) is:
\( \mathbf{A} \cdot N<F<S i<P \)
B \( . F<N<P<S i \)
\( \mathbf{c} \cdot F<N<S i<P \)
D. \( N<S i<F<P \)
Subject: Chemistry
Excess of KI reacts with \( C u S O_{4} \)
solution and then \( N a_{2} S_{2} O_{3} \) solution is
added to it. Which of the statement is
incorrect for this reaction?
A \( \cdot C u_{2} I_{2} \) is formed
B. \( C u I_{2} \) is formed
c. \( N a_{2} S_{2} O_{3} \) is oxidised
D. Evolved \( I_{2} \) is reduced
Subject: Physics
Consider the following statements A and \( \mathrm{B} \) and identify the correct answer
A) The speed acquired by a body when falling in a vacuum for a given time is dependent on the mass of the falling body
B) A stone falls freely from rest and the total distance covered by it in the last
second of its motion equals the distance covered by it in the first three seconds of its motion. The stone
remains in the air for \( 5 s .\left[g=10 m s^{-2}\right] \)
A. Both A \& B are true
B. A is true but B is false
c. B is true but A is false
D. Both A \& B are false
Subject: Physics
A metallic wire bent into a right \( \Delta \) abc
moves with a uniform velocity \( \boldsymbol{v} \) as
shown in figure. B is the strength of
uniform magnetic field perpendicular
outwards the plane of triangle. The net
emf is ................. and emf along ab is
A. zero, zero
B. zero, \( B v(b c) \) with \( b \) positive
C. zero, \( B v(b c) \) with \( a \) positive
D. \( B v(b c) \) with \( c \) positive, zero
E. \( B v(b c) \) with \( b \) positive, zero
Subject: Maths
n given figure \( C \) is centre of circle. \( A O \)
and \( B O \) are tangents to circle. \( C M \perp \)
\( A B \)
\( \mathbf{f} \boldsymbol{A} \boldsymbol{C}=\boldsymbol{A} \boldsymbol{B}=\mathbf{6} \boldsymbol{c m}, \) then find \( \boldsymbol{A} \boldsymbol{M} \)
\( A \cdot 3 c m \)
8. 4 ст
\( c .5 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)
Subject: Physics
An ionization chamber with parallel conducting plates as anode and
cathode, has \( 5 \times 10^{7} \) electrons and the
same number of singly charged positive ions per \( c m^{3} . \) The electrons are moving
towards the anode with velocity \( 0.4 \mathrm{m} / \mathrm{s} \) The current density from anode to
cathode is \( 4 \mu A / m^{2} . \) The velocity of positive ions moving towards cathode is
A. \( 0.4 m s^{-1} \)
B. zero
c. \( 1.6 m s^{-1} \)
D. \( 0.1 m s^{-1} \)
Subject: Physics
The resistance of a wire is 5 ohm at \( 50^{\circ} \)
\( \mathrm{C} \) and 6 ohm at \( 100^{\circ} \mathrm{C} \). The resistance of
the wire at \( 0^{\circ} \mathrm{C} \) will be:
\( A \cdot 2 \) ohm
B. 1 ohm
c. 4 ohm
D. 3 ohm
Subject: Physics
In the figure a potential of \( +1200 \mathrm{V} \) is
given to point \( A \) and point \( B \) is
earthed,what is the potential at the
point
A . \( 100 \mathrm{V} \)
B. 200
c. \( 400 \mathrm{v} \)
D. 600 v
Subject: Chemistry
Lanthanoid contraction is caused due
to:
A. the same effective nuclear charge from \( C e \) to \( L u \)
B. the imperfect shielding on outer electrons by \( 4 f \) electrons from the nuclear charge
C. the appreciable shielding on outer electrons by \( 4 f \) electrons from the nuclear charge
D. the appreciable shielding on outer electrons by \( 5 d \) electrons from the nuclear charge
Subject: Chemistry
A list of reactions are given below.
(a) \( \boldsymbol{F e}+\mathbf{2 H C l} \rightarrow \boldsymbol{F e C l}_{2}+\boldsymbol{H}_{2} \)
(b) \( \boldsymbol{F e} \boldsymbol{S}+\boldsymbol{2} \boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{2}+\boldsymbol{H}_{2} \boldsymbol{S} \)
(c) \( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{S} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \)
(d) \( \boldsymbol{N a C l}+\boldsymbol{H}_{2} \boldsymbol{S O}_{4} \stackrel{<200^{\circ} \boldsymbol{C}}{\longrightarrow} \)
\( N a H S O_{4}+H C l \)
\( (e) C u S O_{4}+H_{2} S \rightarrow C u S+H_{2} S O_{4} \)
\( (f) S+H_{2} S O_{4} \rightarrow 3 S O_{2}+H_{2} O \)
Identify redox reactions.
\( A \cdot a, c \) and \( f \)
B. d and f
\( c \cdot c \) and \( d \)
D. c, d and f
Subject: Physics
The parallel plate capacitor on the left \( C L \) has a separation distance of \( 1 \mathrm{cm} \)
and the sides of the square plate are each \( 0.5 m . \) While the smaller paralle
plate capacitor on the right \( C R \) has a
separation distance of \( 0.2 \mathrm{cm} \) and each
side of the square plate is \( 0.1 m \) in length. Determine the ratio of capacitance
\( \boldsymbol{C} \boldsymbol{L}: \boldsymbol{C} \boldsymbol{R} \)
A . 1:
B. 5:
\( c .1: 5 \)
\( D .3 \)
Subject: Chemistry
Decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O} \) is a first order
reaction. A 16 volume solution of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
of half-life period 30 minutes is present at the start. When will the solution
become one volume?
A. After 120 minutes
B. After 90 minutes
c. After 60 minutes
D. After 140 minutes
Subject: Chemistry
In a \( H- \) like atom for an electron
revolving in nth orbit, the variation of
\( \log _{10} K E \) versus \( \log _{10} z \) is plotted as
following Where \( z \) is an atomic number
and kinetic energy of the electron (in
\( \mathrm{eV} \) ). If \( \boldsymbol{O} \boldsymbol{A}=\log _{10} \mathbf{3} . \boldsymbol{4} \) then find the
value of principal quantum number of the electron.
Subject: Physics
Position vector that defines position of
vector in three dimensions having
formula of
A \( \cdot \sqrt{\left(a^{2}+b^{2}+c^{2}\right)} \)
B. \( \sqrt{(a+b+c)} \)
C \( \cdot \sqrt{\left(a^{2}-b^{2}+c^{2}\right)} \)
D. \( \left(a^{2}+b^{2}+c^{2}\right) \)
Subject: Physics
The refracting angle of a prism is \( A, \) and refractive index of the material of the
prism is cot (A/2). The angle of minimum deviation is :
A \( \cdot 90^{\circ}-A \)
\( A \)
В. \( 180^{\circ}+2 A \)
D. \( 180^{\circ}-2 A \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{A}=\left\{\boldsymbol{y}: \boldsymbol{0} \leq \boldsymbol{y}<\frac{\boldsymbol{\pi}}{2}\right\} \) be a
function such that \( f(x)=\tan ^{-1}\left(x^{2}+\right. \)
\( \boldsymbol{x}+\boldsymbol{k}), \) where \( \boldsymbol{k} \) is a constant. The value
of \( k \) for which \( f \) is an onto function is
A . 1
B.
c. \( \frac{1}{4} \)
D. none of these
Subject: Maths
If the variable takes values
\( \mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \cdots, \boldsymbol{n} \) with frequencies
proportional to \( ^{n} c_{0},^{n} c_{1},^{n} c_{2}, \cdots,^{n} c_{n} \)
respectively, the variance is
A \( \cdot \frac{n}{4} \)
в. \( \frac{n}{3} \)
\( c \cdot \frac{2 n}{5} \)
D. none of these
Subject: Maths
The following table shows the
distribution of weights of 100 candidates appearing for a competition Determine the model weight.
\( \begin{array}{llll}\text { Weight } & \mathbf{5 0}- & \mathbf{5 5}- & \mathbf{6 0}- \\ (\mathbf{i n k g}) & \mathbf{5 5} & \mathbf{6 0} & \mathbf{6 5}\end{array} \)
Number of 13 candida
18
Subject: Chemistry
\( 100 \mathrm{ml} \) of a hydrocarbon on combustion gave \( 300 \mathrm{ml} \) of \( C O_{2} \) and \( 400 \mathrm{ml} \) of
water vapor measured under similar conditions of temperature and pressure. Find out the molecular
formula of hydrocarbon.
A \( \cdot C_{2} H_{4} \)
в. \( C_{3} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{3} H_{4} \)
Subject: Chemistry
For an ideal solution with \( \boldsymbol{p}_{\boldsymbol{A}}^{\boldsymbol{o}}>\boldsymbol{p}_{\boldsymbol{B}}^{\boldsymbol{o}} \)
which of the following is true?
A \( \cdot\left(x_{A}\right)_{\text {liquid}}=\left(x_{A}\right)_{\text {vapour}} \)
В . \( \left(x_{A}\right)_{\text {liquid }}>\left(x_{A}\right)_{\text {vapour }} \)
C \( \cdot\left(x_{A}\right)_{\text {liquid}}<\left(x_{A}\right)_{\text {vapour}} \)
D \cdot \( \left(x_{A}\right)_{\text {liquid }} \) and \( \left(x_{A}\right)_{\text {vapour }} \) cannot be correlated with each other
Subject: Physics
An object comprises of a uniform ring of
radius \( R \) and a uniform chord \( A B \) (not
necessarily made of the same material) as shown. Which of the following cannot
be the centre of mass of the object?
\( \mathbf{A} \cdot(\mathrm{R} / 3, \mathrm{R} / 3) \)
в. \( (R / 2, R / 2) \)
c. \( (\mathrm{R} / 4, \mathrm{R} / 4) \)
D. none of the above
Subject: Chemistry
Which of the following set of reaction
\( R-C-O H \) as the can not prepare
final product?
A \( \cdot R-M g X+O=C=O \frac{d r y \cdot e t h e r}{\longrightarrow} A \frac{H_{3} O^{+}}{\longrightarrow} \)
в. \( R-C N \frac{S n\left(l_{2}+H C l\right.}{(i i) H_{2} O / H^{+}} \)
\( c \)
D. \( C H_{3}\left(C H_{2}\right)_{8} C H_{2} O H \frac{C r O_{3}}{H_{2} S O_{4}} \)
Subject: Physics
Two rigid boxes containing different ideal gases are placed on a table. Box \( A \)
contains one mole of \( N_{2} \) at temperature
\( T_{0}, \) while box \( \mathrm{B} \) contains one mole of \( \boldsymbol{H}_{2} \)
at temperature \( 7 / 3 T_{0} . \) The boxes
are then put into thermal contact with
each other and heat flows between them
until the gases reach a common final temperature [lgnore the heat capacity of boxes]. Then the final
temperature of the gases \( T_{f} \) in terms of
\( \boldsymbol{T}_{0} \) is
A \( \cdot T_{f}=\frac{5}{2} \) To
B \( T_{f}=\frac{3}{7} T o \)
c. \( T_{f}=\frac{5}{3} \) To
D. \( T_{f}=\frac{3}{2} \) To
Subject: Maths
The probability that at least one of the events \( A \) and \( B \) occur is \( 0.6 . \) If \( A \) and \( B \)
occur simultaneously with probability
0.2, then \( \boldsymbol{P}(\overline{\boldsymbol{A}})+\boldsymbol{P}(\overline{\boldsymbol{B}})= \)
A . 0.4
B. 0.8
c. 1.2
D. 1.
Subject: Maths
In a set of \( 2 n \) observations, half of them
are equal to ' \( \alpha \) ' and the remaining half
are equal to ' - \( \boldsymbol{\alpha} \) '. If the standard
deviation of all the observations is 2 then the value of \( |\boldsymbol{\alpha}| \) is equal to
A .2
B. \( \sqrt{2} \)
\( c \cdot 2 \sqrt{2} \)
D. 4
Subject: Physics
A condenser of capacity \( C \) is charged to a potential difference of \( V_{1} . \) The plates
of the condenser are then connected to
an ideal inductor of inductance L. The
current through the inductor when the potential difference across the
condenser reduces to \( V_{2} \) is:
A \( \cdot \frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L} \)
B. \( \frac{C\left(V_{1}^{2}+V_{2}^{2}\right)}{L} \)
c. \( \sqrt{\frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L}} \)
D. \( \sqrt{\frac{C\left(V_{1}-V_{2}\right)^{2}}{L}} \)
Subject: Physics
The final velocity of a body starts from rest and moving with an acceleration
\( 2 m s^{-2} \) and covering a distance of \( 10 \mathrm{m} \)
is \( m s^{-1} \)
A \( \cdot \sqrt{98} \)
в. \( \sqrt{40} \)
\( c \cdot \sqrt{20} \)
D. \( \sqrt{12} \)
Subject: Physics
Velocity-time graph of a particle moving
in a straight line is as shown in figure.
Mass of the particle is \( 2 k g . \) Work done
by all the forces acting on the particle in
time interval between \( t=0 \) to \( t=10 \) is
A. \( 300 J \)
в. \( -300 J \)
\( c .400 \)
D. \( -400 J \)
Subject: Physics
Assertion
Magnetic force is always perpendicular to the magnetic field.
Reason
Electric force is along the direction of electric field.
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
Four resistors, \( 100 \Omega, 200 \Omega, 300 \Omega, \) and
\( 400 \Omega \) are connected to form four sides
of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square?
A \( .210 \Omega \)
в. 240\Omega
\( \mathbf{c} .300 \Omega \)
D. 250\Omega
Subject: Maths
If \( f o g=|\sin x| \) and \( g o f=\sin ^{2} \sqrt{x}, \) then
\( f(x) \) and \( g(x) \) are
A \( \cdot f(x)=\sqrt{\sin x}, g(x)=x^{2} \)
B. \( f(x)=|x|, g(x)=\sin x \)
c. \( f(x)=\sqrt{x}, g(x)=\sin ^{2} x \)
D. \( f(x)=\sin \sqrt{x}, g(x)=x^{2} \)
Subject: Physics
A positively charged croquet ball rolls at
\( 4.0 m / s \) northward through a \( 2.00 T \)
magnetic field which points westward.
If the charge on the croquet ball is \( 1.0 C \)
how much force acts on the croquet ball
due to the magnetic field and in what
direction?
A. Amount of Force \( -2.00 N \), Direction of Force - up
B. Amount of Force \( -8.00 N \), Direction of Force - south
C. Amount of Force \( -8.00 N \), Direction of Force - down
D. Amount of Force \( -0.500 N \), Direction of Force - up
E. Amount of Force \( -8.00 N \), Direction of Force - up
Subject: Physics
A uniform disc of mass \( M \) and radius \( R \)
is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward pull \( T \) is exerted on the cord, the tangential acceleration of a point on the rim is
A \( \cdot \frac{T}{M} \)
в. \( \frac{M}{T} \)
c. \( \frac{2 T}{M} \)
D. \( \frac{M}{2 T} \)
Subject: Physics
The half life, \( T \), of a substance is related
to the decay constant by the equation
\( A \cdot T=\frac{1}{\lambda} \)
в. \( \frac{1}{0.693 \lambda} \)
c. \( \frac{0.693}{\lambda} \)
D. \( \frac{2.303}{\lambda} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{1} \\ -\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{6}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}5 & 4 & 6 \\ 4 & 1 & 2 \\ -5 & -1 & 1\end{array}\right], \) then
A. \( A+B \) exists
B. \( A B \) exists
c. \( B A \) exists
D. none of these
Subject: Physics
A black body calorimeter filled with hot
water cools from \( 60^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in 4 min
and \( 40^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \) in 8 min. The
approximate temperature of surrounding is :
A \( \cdot 10^{\circ} \mathrm{C} \)
В. \( 15^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 20^{\circ} C \)
D. \( 25^{\circ} \mathrm{C} \)
Subject: Chemistry
Which of the following pairs of ions have the same electronic configuration?
A \( \cdot C u^{2+}, C r^{2+} \)
B . \( F e^{3+}, M n^{2+} \)
c. \( C o^{3+}, N i^{3+} \)
D. \( S c^{3+}, C r^{3+} \)
Subject: Chemistry
Which of the follwoing does not have \( \boldsymbol{S}-\boldsymbol{S} \) linkage \( ? \)
A \( \cdot H_{2} S_{2} O_{5} \)
в. \( H_{2} S_{2} O_{7} \)
c. \( H_{2} S_{2} O_{3} \)
D. \( H_{2} S_{2} O_{6} \)
Subject: Chemistry
The first ionisation potential of \( \boldsymbol{N}, \boldsymbol{P}, \boldsymbol{O} \) and \( S \) are in the order of
\( \mathbf{A} \cdot S>P<O>N \)
В . \( N>O>P>S \)
c. \( N>O<P>S \)
D. \( N<O<P<S \)
Subject: Chemistry
Aldehydes and ketones are
differentiated by using:
\( \mathbf{A} \cdot N a O H / I_{2} \)
B. \( N a H S O_{3} \)
\( \mathbf{c} \cdot A g N O_{3} / N H_{4} O H \)
D. \( N H_{2}-N H_{2} \)
Subject: Maths
Factorise the following \( : 27(a-b)^{3}+ \)
\( (2 a-b)^{3}+(4 b-5 a)^{3} \)
A \( \cdot(a-b)(a-b)(4 b-8 a) \)
В. \( 9(a-b)(2 a-b)(4 b-5 a) \)
c. \( 9(a-b)(a-2 b)(4 b-a) \)
D. \( 94-b)(2 a-b)(b-a) \)
Subject: Biology
Match the column I with column II
What is and \( \begin{array}{lllll} & \text { Column I } & & \text { Column II } \\ \text { A. } & \text { Ethylene } & \text { 1. } & \text { Pigment } \\ \text { B. } & \text { Cytokinin } & \text { 2. } & \begin{array}{l}\text { Growth } \\ \text { inhibitor }\end{array} \\ \text { C. } & \text { Phytochrome } & \text { 3. } & \begin{array}{l}\text { Flowering } \\ \text { hormone }\end{array} \\ \text { D. } & \text { Florigen } & \text { 4. } & \text { Zeatin }\end{array} \)
\( \mathbf{A} \)
\( A-4, B-3, C-2, D-1 \)
B. \( A-3, B-4, C-2, D-1 \)
C. \( A-2, B-4, C-1, D-3 \)
D. \( A-2, B-1, C-3, D-4 \)
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{\sqrt{1+\boldsymbol{p} \boldsymbol{x}}-\sqrt{\mathbf{1}-\boldsymbol{p} \boldsymbol{x}}}{\boldsymbol{x}} \\ \frac{\mathbf{2} \boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}-\mathbf{2}}, \quad \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{1}\end{array} \quad, \quad-\mathbf{1} \leq \boldsymbol{x}<\right. \)
0 is continuous in the interval [-1,1]
then \( p \) equals-
A . -1
B. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{2} \)
\( D \)
Subject: Maths
If the plane \( 3 x+2 y+6 z=6 \)
intersects the coordinate axes at
\( A, B, C \) then the area of the \( \Delta A B C \) is
\( \mathbf{A} \cdot 49 \)
B. 7
\( c \cdot \frac{7}{2} \)
D. \( \frac{11}{2} \)
Subject: Chemistry
An electron make transition from orbit
number \( N \) to \( P^{t h} \) orbit in \( H- \) atom and
emit the photon of wavelength \( (\lambda) . \) In
orbit \( \boldsymbol{P}, \) velocity of electron in \( \boldsymbol{H}- \) atom is maximum. Which of the following wavelength \( (\lambda) \) is not possible?
(Where \( 1 / R=912 A) \)
\( \mathbf{A} \cdot 1216 \stackrel{\circ}{A} \)
B . 972.8 A
\( c \cdot 1026^{\circ} \)
D. 3973 h