AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Draw a circle of radius \( 3 \mathrm{cm} \). Take a
point outside the circle at a distance of
\( 6 \mathrm{cm} \) from the centre of the circle.
Construct tangents from this point to the circle. Measure the angle between
the tangents and select the correct value from below.
\( \mathbf{A} \cdot 60 \)
B. 30
\( c \cdot 45 \)
D. \( 90^{\circ} \)
Subject: Physics
A thin wire is bent in the form of a ring
of diameter \( 3.0 \mathrm{cm} . \) The ring is placed
horizontally on the surface of soap solution and then raised up slowly. How much upward force is necessary to break the vertical film formed between
the ring and the solution?
A \( .5 .452 \times 10^{-3} \)
B. \( 4.452 \times 10^{-3} \)
c. \( 6.452 \times 10^{-3} \)
D. \( 9.452 \times 10^{-3} \)
Subject: Physics
A bi-convex lens is formed with two
plano-convex lenses as shown in the figure. Refractive index n of the first
lens is 1.5 and that of the second lens is
1.2. Both curved surfaces are of the
same radius of curvature \( \mathrm{R}=14 \mathrm{cm} . \) For
this bi-convex lens, for an object
distance of \( 40 \mathrm{cm}, \) the image distance will be
A. \( -280.0 \mathrm{cm} \)
B. \( 440.0 \mathrm{cm} \)
\( c .21 .5 \mathrm{cm} \)
D. \( 13.3 \mathrm{cm} \)
Subject: Chemistry
Hydrogen bonding originates from the dipole-interaction between H-atom and any of the other atom like \( F, O, N \) and in
some cases with Cl atom. There are two
types of H-bonding namely, intermolecular and intra-molecular H-
bonding. Which of the following molecule does not consist of intramolecular H-
bonding?
A. chloral
B. chloral hydrate
c. ortho-hydroxybenzaldehyde
D. ortho-chloropheno
Subject: Biology
Assertion
The columnar epithelium lining the intestinal mucosa appears to have a
brush like an appearance.
Reason
A large number of microvilli are present
on brush bordered columnar
epithelium.
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
\( \mathrm{C} \) is the centre of an equilateral triangle
PQR. \( f_{1}, f_{2} \) and \( f_{3} \) are the three forces acting along the sides as shown. For the
total torque about \( C \) to be zero,
\( ^{\mathrm{A}} \cdot f_{3}=\frac{\left(f_{1}+f_{2}\right)}{2} \)
3. \( f_{3}=\frac{\left(f_{1}+f_{2}\right)}{4} \)
\( \mathbf{c} \cdot f_{3}=f_{1}+f_{2} \)
D. \( f_{3}=f_{1}-f_{2} \)
Subject: Physics
Choose the correct options
This question has multiple correct options
A. Sl unit of magnetic flux is henry-ampere
B. SI unit of coefficient of self-inductance is \( J / A \)
C. Sl unit of coefficient of self inductance is
\( \frac{v o l t-s e c o n d}{a m p e r e} \)
D. Sl unit of magnetic induction is weber
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{3} \\ \mathbf{2} & -\mathbf{5}\end{array}\right] \)
\( \& \boldsymbol{K} \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{4} \boldsymbol{a} \\ -\mathbf{8} & \mathbf{5} \boldsymbol{b}\end{array}\right] \)
then find the value of a and
Subject: Physics
A uniform heavy disc of moment of
inertia \( I_{1} \) is rotating with constant
angular velocity \( \omega_{1} . \) Then, a second
nonrotating disc of moment of inertia \( I_{2} \)
is dropped on it. The two discs rotate together. The final angular velocity of the
system becomes
\( \mathbf{A} \cdot \frac{I_{1} \omega_{1}}{I_{2}} \)
B. \( \sqrt{\frac{I_{1}}{I_{2}} \omega_{1}} \)
C. \( \frac{I_{1} \omega_{1}}{I_{1}+I_{2}} \)
D. \( \frac{\left(I_{1}-I_{2}\right) \omega_{1}}{I_{1}+I_{2}} \)
Subject: Physics
A car of mass \( m \) is taking a circular
turn of radius ' \( r^{\prime} \) on a fictional level road
with a speed \( v . \) In order that the car
does not skid
A \( \cdot \frac{m v^{2}}{r} \geq \mu m g \)
B . \( \frac{m v^{2}}{r} \leq \mu m g \)
c. \( \frac{m v^{2}}{r}=\mu m g \)
D. \( \frac{v}{r}=\mu m g \)
Subject: Chemistry
Copper sulphate solution \( (250 \mathrm{ml}) \) was electrolysed using a platinum anode and a copper cathode. A constant current of \( 2 \mathrm{mA} \) was passed for 16 minutes. It was found that after
electrolysis, the absorbance of the solution was reduced to \( 50 \% \) of its
original value. Calculate the concentration of copper sulphate in the solution to begin with.
A \( .0 .22 M \)
в. 2 М
c. \( 0.04 M \)
D. \( 0.13 M \)
Subject: Physics
A steel wire of length \( L \) and area of cross-section A shrinks by \( \Delta l \) during
night. Find the tension developed at
night if Young's modulus is \( Y \) and wire is clamped at both ends
A. \( \frac{A Y L}{\Delta l} \)
в. \( A Y L \)
c. \( A Y \Delta l \)
D. \( \frac{A Y \Delta l}{L} \)
Subject: Physics
Which of the following process
represents \( \gamma \) -decay?
A \( \cdot \frac{A}{Z} X+_{0}^{1} n \rightarrow_{Z-2}^{A-3} X+c \)
B . \( _{Z} X+_{-1} e \rightarrow_{Z-1}^{A} X+g \)
c. \( \frac{A}{Z} X+r \rightarrow_{Z-1}^{A} X+a+b \)
D. \( \frac{A}{Z} X \rightarrow \frac{A}{Z} X+\gamma \)
Subject: Physics
Two particles \( A \) and \( B \) are moving with constant velocities \( v_{1}=\hat{j} \) and \( v_{2}=2 \hat{i} \) respectively \( A \) is at \( c o \) -ordinates (0,0) and B is at (-4,0) . the angular velocity of B with respect to \( A \) at \( t=2 s \) is (all
physical quantities are in Sl units)
A \( \cdot \frac{1}{2} r a d / s \)
B. \( 2 r a d / s \)
c. \( 4 r a d / s \)
D. \( 1 r a d / s \)
Subject: Maths
The value of \( \int x(\operatorname{cosec} x \cot x) d x= \) is
A. \( x \operatorname{cosec} x-\log |\tan x / 2|+c \)
B. \( 2-x \operatorname{cosec} x+\log \left|\tan \frac{x}{2}\right|+c \)
c. \( x \operatorname{cosec} x-2 \log |\tan x / 2|+c \)
D. \( x \) cot \( x-\log \left|\tan \frac{x}{2}\right|+c \)
Subject: Physics
There are four concentric shells \( A, B, C \)
and D of radii a, \( 2 a, 3 a \) and \( 4 a \) respectively. Shells B and D are given charges \( +q \) and \( -q \) respectively. Shell \( C \) is now earthed. The potential difference \( V_{A}-V_{c} \) is \( k=\frac{1}{4 \pi \varepsilon_{0}} \)
A \( \cdot \frac{k q}{2 a} \)
в. \( \frac{k q}{3 a} \)
\( c \cdot \frac{k q}{4 a} \)
D. \( \frac{k q}{6 a} \)
Subject: Maths
If \( \boldsymbol{I}_{n}=\int_{\boldsymbol{\pi} / 4}^{\pi / 2}(\boldsymbol{T} \boldsymbol{a} \boldsymbol{n} \boldsymbol{\theta})^{-\boldsymbol{n}} \cdot \boldsymbol{d} \boldsymbol{\theta} \) for \( (\boldsymbol{n}>1) \)
then \( \boldsymbol{I}_{\boldsymbol{n}}+\boldsymbol{I}_{\boldsymbol{n}+\mathbf{2}}=? \)
A. \( \frac{1}{\mathrm{n}+1} \)
B. \( \frac{-1}{\mathrm{n}+1} \)
c. \( \frac{1}{\mathrm{n}-1} \)
D. \( \frac{-1}{\mathrm{n}-1} \)
Subject: Maths
Four parts of 24 are in A.P. such that the
product of extremes is to product of
means is 7: 15 then four parts are
A. \( \frac{3}{2}, \frac{9}{2}, \frac{15}{2}, \frac{21}{2} \)
B. \( \frac{11}{2}, \frac{13}{2}, 9 \)
C. \( \frac{5}{2}, \frac{15}{2}, \frac{9}{2}, \frac{21}{2} \)
D. \( \frac{21}{2}, \frac{9}{2}, \frac{15}{2}, \frac{5}{2} \)
Subject: Chemistry
Five moles of Hydrogen initially at STP is compressed adiabatically so that its temperature becomes 673 K. The
increase in internal energy of the gas, in
\( \boldsymbol{k} \boldsymbol{J} \) is:
\( [R=8.3 J / m o l e-K ; \gamma=1.4 \) for
diatomic gas
A . 80.5
B. 21.55
c. 41.50
D. 65.55
Subject: Maths
toppr
5
Q Type your question
first one is done for you.
This question has multiple correct options
\( \mathbf{A} \)
(i)
(1)
B.
(ii)
\( (\mathrm{i}) \)
\( c \)
(iii)
\( (\text { in }) \)
D.
(iv)
\( (\mathrm{iv}) \)
E .
\( (v) \)
Subject: Physics
An ice cube of size \( a=10 \mathrm{cm} \) is
floating in a tank (base \( =50 \mathrm{cm} \times \)
50cm ) partially filled with water. The
change in gravitational potential energy, when ice completely melts is [Density of ice is \( 900 k g m^{-3} \) and \( g=10 m s^{-2} \)
A. \( -0.0455 J \)
в. \( -0.016 J \)
c. \( -0.24 J \)
D. \( -0.072 J \)
Subject: Physics
The radius of a hydrogen atom is \( 0.5 \dot{A} \) Find the order of magnitude of volume
of 1 mole hydrogen in \( m^{3} . \) Given that 1
mole of hydrogen has \( 6.02 \times 10^{23} \)
hydrogen atoms.
A \( \cdot 2 \times 10^{-4} m^{3} \)
B. \( 10^{-3} m^{3} \)
\( \mathbf{c} \cdot 10^{-7} m^{3} \)
D. \( 10^{-2} m^{3} \)
Subject: Chemistry
Assertion
Reduction of \( Z n O \) with carbon is done
at \( 1100^{0} C \)
Reason
\( \triangle G^{0} \) is negative at this temperature
thus, process is spontaneous.
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 and Reason is correct
Subject: Physics
A source of \( 220 \mathrm{V} \) is applied in an \( \mathrm{A} . \mathrm{C} \) circuit. The value of resistance is \( 220 \Omega \)
Frequency \( \& \) inductance are \( 50 \mathrm{Hz} \) and
0.7 H, then wattless current is
A . \( 0.5 a m p \)
в. \( 0.7 a m p \)
c. \( 1.0 a m p \)
\( D \cdot \) none
Subject: Chemistry
When water is cooled it contracts until
it reaches and then it
starts expanding.
A \( \cdot 37^{\circ} \mathrm{C} \)
B. \( 40^{\circ} \mathrm{C} \)
\( c \cdot 0^{\circ} \mathrm{C} \)
D. \( 4^{\circ} \mathrm{C} \)
Subject: Chemistry
The bromination involves so called
bromonium ions.Among the given statements identify the one which does
not appply:
A. bromonium ions are 3-membered rings
B. bromonium ions are intermediates in the formation of halohydrins
c. bromonium ions are intermediate in the formation of vicinal dibromides by addition of bromides to alkenes
D. bromonium ions of asymmetrical alkenes are attacked by nucleophiles at the least subtituted alkene c-atom
Subject: Physics
For a particle executing SHM the displacement \( x \) is \( \operatorname{given} \) by \( x=A \operatorname{cost} \) Identify the graph which represents the variation of potential energy (PE) as a function of time \( t \) and displacement \( x \)
A . ।, ॥ I
в. ॥, Iv
c. ॥, ॥
D. I, IV
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ccc}1 & -2 & 3 \\ -4 & 2 & 5\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{cc}1 & 3 \\ -1 & 0 \\ 2 & 4\end{array}\right] . \) Show that \( (A B)^{\prime}=? \)
A \( \cdot B^{\prime} A^{\prime} \)
в. \( A^{\prime} B^{\prime} \)
c. \( A B^{\prime} \)
D. \( A^{\prime} B \)
Subject: Chemistry
Assertion
f more and more solute is added to a
solvent, the freezing point of the solution keeps on becoming higher and
higher.
Reason
Presence of large amount of the solid
solute does not allow the solution to
freeze.
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
Mendeleev's periodic table have some demerits.
Reason
There was no place for all isotopes of the elements and some heavy elements
were placed before lighter elements.
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
Calculate the wavelength of a wave if it travels with speed \( 2 \mathrm{cm} / \mathrm{s} \) and period is
2 s.
A. \( 0.25 \mathrm{cm} \)
B. \( 0.5 \mathrm{cm} \)
\( c \cdot 1 \mathrm{cm} \)
D. \( 2 \mathrm{cm} \)
E. \( 4 \mathrm{cm} \)
Subject: Chemistry
Equilibrium constant for the reaction,
\( A_{2}+B_{2} \rightleftharpoons 2 A B, \) at a given
temperature is 2 while is the degree of
dissociation for \( \boldsymbol{A}_{2} \) is:
A . 0.2
B. 0.5
c. \( \frac{1}{1+\sqrt{2}} \)
D. \( \frac{\sqrt{2}}{1+\sqrt{2}} \)
Subject: Maths
Calculate the numbers of times \( \boldsymbol{f}(|\boldsymbol{x}|) \) \( \operatorname{crosses} \boldsymbol{x}-\boldsymbol{a x i s} \) where \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-1 \)
\( A \cdot 2 \)
B.
\( c .3 \)
D. None of these
Subject: Maths
If \( \boldsymbol{A} \) is \( (2,4,5), \) and \( B \) is (-7,-2,8) then which of the following is collinear with \( A \) and \( B \) is
A \( .(1,2,6) \)
В. (2,-1,6)
c. (-1,2,6)
D. (2,6,-1)
Subject: Maths
The degree of the differential equation \( \left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\left(\frac{d y}{d x}\right)^{2}=x \sin \left(\frac{d^{2} y}{d x^{2}}\right) \)
\( A \cdot 1 \)
B. 2
\( c .3 \)
D. None of these
Subject: Physics
semıcırcle block trom alr is shown
below. Consider the given figure and select the correct option which correctly
identifies the true (T) and false (F)?
(i) There is no change in the direction of
ray at \( P \) because light ray incident on
semicircular block at \( 90^{\circ} \)
(ii) As light rays enters the semicircular block, its frequency remains the same.
(iii) Wavelength of light rays as it enters the block decreases.
(iv) Speed of light as it enters the block
increases.
A . T F FT
B. FTTF
c. न T T \( F \)
\( D \cdot F F F \)
Subject: Physics
A millivoltmeter is connected in parallel to an axle of the train running with a speed of \( 180 \mathrm{km} / \) hour. If the vertical component of earth's magnetic field is \( 0.2 \times 10^{-4} W b / m^{2} \) and the distance
between the rails is \( 1 \mathrm{m} \), then the
reading of voltmeter will be :
A \( \cdot 10^{-2} \) volt
B. \( 10^{-4} \) volt
c. \( 10^{-3} \) volt
D. 1 volt
Subject: Chemistry
\( \boldsymbol{C N}^{-} \longrightarrow \boldsymbol{C N O}^{-} \)
The number of electrons that must be
added in balancing the half reaction is:
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1 on the right
c. 1 on the left
D. 2 on the right
Subject: Physics
Two blocks of masses \( 6 \mathrm{kg} \) and \( 4 \mathrm{kg} \) are attached to the two ends of a massless
string passing over a smooth fixed pulley. If the system is released, the acceleration of the centre of mass of the
system will be :
A . g, vertical downwards
B. g/5, vertical downwards
c. g/25, vertical downwards
D. zero
Subject: Maths
Let \( *: \boldsymbol{R} \times \boldsymbol{R} \rightarrow \boldsymbol{R} \) given by \( (\boldsymbol{a}, \boldsymbol{b}) \rightarrow \)
\( a+4 b^{2} \) is a binary operation, compute
(-5)\( *(2 * 0) \)
Subject: Physics
Assertion
The magnetic field at the ends of a very long current carrying solenoid is half of that at the centre.
Reason
If the solenoid is sufficiently long, the field within it is uniform.
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
Statement-1: When a travelling wave is sent along a particular string by
oscillating one end, the speed of the
wave will increase if we increase the
frequency of oscillations. Statement-2: If a travelling wave sent
along a particular string by oscillating
its one end, it is the wavelength of the
wave that decreases.
A. If both the statements are true and statement- 2 is the correct explanation of statement-
B. If both the statements are true but statement-2 is not the correct explanation of statement-
C. If statement-1 is true and statement-2 is false
D. If statement-1 is false and statement-2 is true
Subject: Maths
The value of an estate in January 1905 started gradually declining in such a way that at the end of each year it was worth only \( x \) times its value at the beginning of the year. What was its worth in end December \( 1910 ? \)
(1) It was worth Rs. 10109 in the end of
December 1906
(2) It was worth Rs. 12345 in the
beginning of January 1905
Subject: Chemistry
Cold solution of barium nitrite on
mixing with sulphuric acid produces
A \( \cdot \) BaSO \( _{4}+H N O_{2} \)
в. \( B a S O_{4}+H N O_{3} \)
c. \( B a S O_{4}+N O_{2} \)
D. \( B a S O_{4+} N_{2}+O_{2} \)
Subject: Maths
Find the value of \( p \) if following function \( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\left\{\begin{array}{ll}
\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & \text { if }-1 \leq x< \\
\frac{2 x+2}{x-2}, & \text { if } 0 \leq x<1
\end{array}\right.
\]
is continuous at \( x=0 \)
Subject: Physics
At the Earth, a block of mass \( m \) which
rest on the frictionless table, let \( \boldsymbol{F} \) be
the force required to produce acceleration \( a \). Calculate the force at
the Moon to produce same acceleration
if \( g_{m o o n} \) is one sixth of \( g_{e a r t h} \)
A \( \cdot \frac{F}{12} \)
в. \( \frac{F}{6} \)
c. \( \frac{F}{3} \)
D. \( F \)
E . \( 6 F \)
Subject: Chemistry
Which of the following is the CORRECT
electron configuration for the
potassium ion \( \left(\boldsymbol{K}^{+1}\right) \) ?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} \)
B . \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} \)
Subject: Chemistry
Calculate the amount (in milligrams)
of \( S e O_{3}^{2-} \) in solution on the basis of following data:
\( 20 \mathrm{mL} \) of \( \frac{M}{60} \) solution of \( K B r O_{3} \) was added to a definite volume of \( S e O_{3}^{2-} \) solution. The bromine evolved was
removed by boiling and excess of
\( K B r O_{3} \) was back titrated with 5 mL of
\( M \) solution of \( N a A s O_{2} . \) The reactions \( \overline{\mathbf{2 5}} \)
are given below.
1) \( S e O_{3}^{2-}+B r O_{3}^{-}+H^{-} \rightarrow \)
\( \boldsymbol{S} \boldsymbol{e} \boldsymbol{O}_{\boldsymbol{4}}^{2-}+\boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
2) \( B r O_{3}^{-}+A s O_{2}+H_{2} O \rightarrow B r^{-}+ \)
\( \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}^{3-}+\boldsymbol{H}^{+} \)
(Atomic mass of \( \boldsymbol{K}=\mathbf{3 9}, \boldsymbol{B r}= \)
\( \mathbf{8 0}, \boldsymbol{A s}=\mathbf{7 5}, \boldsymbol{N a}=\mathbf{2 3}, \boldsymbol{O}=\mathbf{1 6}, \boldsymbol{S e}= \)
\( \mathbf{7} 9 \)
A .84
в. 95
\( c \cdot 42 \)
D. None of the above
Subject: Maths
\( \mathbf{f} \mathbf{f}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{- 1} \\ \mathbf{3} & -\mathbf{2}\end{array}\right] \) then \( \mathbf{A}^{\mathbf{5}}= \)
\( A \cdot I \)
в. \( A \)
\( c .-A \)
D. \( A^{2} \)
Subject: Physics
A block of mass \( m \) is pushed against a
spring of spring constant \( k, \) fixed to one
end of the wall. The natural length of the
spring is / and it is compressed to half
its natural length when the block is
released. The velocity of the block as a
function of its distance \( x \) from the wall
is
\( \sqrt[A \cdot]{\frac{k}{m}\left(\frac{l^{2}}{4}-(l-x)^{2}\right)} \)
B. \( \sqrt{\frac{k}{m}(l-x)^{2}} \)
c. \( \sqrt{\frac{k}{m}\left(\frac{l^{2}}{4}+(l+2 x)^{2}\right.}) \)
D. \( \sqrt{\frac{k}{m}(l+x)^{2}} \)
Subject: Maths
Let \( f \) be a function defined for every \( x \)
such that \( f^{\prime \prime}=-f, f(0)=0, f^{\prime}(0)=1, \) then \( f(x) \)
is equal to
A. \( \tan x \)
B \( \cdot e^{x}-1 \)
\( c \cdot \sin x \)
\( D \cdot 2 \sin x \)
Subject: Maths
If \( I \) is the centre of a circle inscribed in
a triangle \( A B C, \) then \( |\overline{B C}| \overline{I A}+ \) \( |\overline{C A}| \overline{I B}+|\overline{A B}| \overline{I C} \) is
A. \( \overline{0} \)
в. \( \overline{I A}+\overline{I B}+\overline{I C} \)
c. \( \frac{\overline{I A}+\overline{I B}+\overline{I C}}{3} \)
D. \( \frac{\overline{I A}+\overline{I B}+\overline{I C}}{2} \)
Subject: Maths
An urn contains one black ball and one
green ball. A second urn contains one
white and one green ball. One ball is drawn at random from each urn. What is
the probability that both balls are of
same colour?
A . \( 1 / 2 \)
B. \( 1 / 3 \)
c. \( 1 / 4 \)
D. \( 2 / 3 \)
Subject: Physics
A long slender rod of mass \( 2 \mathrm{kg} \) and
length 4 m is placed on a smooth
horizontal table. Two particles of
masses \( 2 k g \) and \( 1 k g \) strike the rod
simultaneously and stick to the rod
after collision as shown in Figure. Velocity of the centre of mass of the rod
after collision is
A \( .12 \mathrm{m} / \mathrm{s} \)
B. \( 9 \mathrm{m} / \mathrm{s} \)
c. \( 6 m / s \)
D. \( 3 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
An stoichiometric mixture of hydrogen
gas and the air at \( 25^{\circ} \mathrm{C} \) and a total
pressure of 1 atm, is exploded in a
closed rigid vessel. If the process occurs under adiabatic condition then using
the given data answer the questions
that follow:
Given:(i) \( C_{p}=8.3 \mathrm{cal} \) deg \( ^{-1} \) mol \( ^{-1} \)
\( (\mathrm{ii}) C_{p}=11.3 \mathrm{cal} \mathrm{deg}^{-1} \mathrm{mol}^{-1} \)
\( \Delta \boldsymbol{H}_{f}\left[\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})\right]=-\mathbf{5 7 . 8} \boldsymbol{k} \boldsymbol{c} \boldsymbol{a l} \boldsymbol{l} \)
[Take air as 80 per \( N_{2}, 20 \) per \( O_{2} \) by volume \( ] \)
The value of \( C_{p} \) of \( N_{2} \& H_{2} O \) will be:
(in cal deg. \( ^{-1} \)mol\( ^{-1} \) )
A. 8.3,8.3
B. 8.3, 11.3
c. 11.3,11.3
D. 11.3,8.3
Subject: Chemistry
(i) Which allotrope of phosphorus is more reactive and why?
(ii) How the supersonic jet aeroplanes are responsible for the depletion of ozone layers?
(iii) \( F_{2} \) has lower bond dissociation
enthalpy than \( C l_{2} \). Why?
(iv) Which noble gas is used in filling balloons for meteorological observations?
(v) Complete the equation: \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2}+ \)
\( \boldsymbol{P} \boldsymbol{F}_{5} \longrightarrow \)
Subject: Physics
The work done in rotating the magnet from the direction of uniform field to the
opposite direction to the field is \( W \). The
work done in rotating the magnet from the field direction to half the maximum
couple position is :
A \( .2 ~ W \)
B. \( \frac{\sqrt{3} W}{2} \)
c. \( \frac{W}{4}(2-\sqrt{3}) \)
D. \( \frac{W}{4}(1-\sqrt{3}) \)
Subject: Physics
Kirchhoff's first law is given by \( \sum \boldsymbol{I}=\mathbf{0} \) and Kirchhoff's second law is given by \( \sum I R=0, \) where the symbols have their
usual meanings. Choose the correct option.
A. Kirchhoff's first law is based on conservation of energy and second law is based on conservation of charge
B. Kirchhoff's second law is based on the conservation of energy and first law is based on conservation of charge
c. Both the laws based on the conservation of momentum
D. First law based on the conservation of momentumm and second law on the conservation of charge
Subject: Chemistry
The specific conductance of a saturated solution of \( A g C l \) at \( 298 \mathrm{K} \) is found to be
\( 1.386 \times 10^{-6} \mathrm{Scm}^{-1} . \) Calculate its
solubility. \( \left(\lambda_{A g^{+}}^{\circ}=62.0 S c m^{2} m o l^{-1} \text {and } \lambda_{C l^{-}}^{\circ}=7\right. \)
Subject: Physics
An electrically heating coil is placed in a calorimeter containing 360 g of \( \mathrm{H}_{2} \mathrm{O} \) at \( 10^{\circ} \mathrm{C} . \) The coil consumes energy at the
rate of \( 90 \mathrm{W} \). The water equivalent of calorimeter and the coil is 40 g. The temperature of water after 10 minutes
will be
A \( \cdot 42.15^{0} \mathrm{C} \)
в. \( 32.14^{\circ} \mathrm{C} \)
c. \( 22.14^{\circ} \mathrm{C} \)
D. \( 52.14^{\circ} \mathrm{C} \)
Subject: Chemistry
Proteins give a red precipitate with
Millon's reagent. The reagent is :
A. mercurous and mercuric nitrate and nitrites in \( H N O_{3} \)
B. mercurous and mercuric chloride in \( H C l \)
c. mercurous and mercuric chloride in \( H N O_{3} \)
D. none of the above
Subject: Maths
If \( f(x)= \) \( \left|\begin{array}{ccc}(\mathbf{1}+\mathbf{3} \boldsymbol{x})^{2 \boldsymbol{a}} & (\mathbf{1}+\mathbf{2} \boldsymbol{x})^{\boldsymbol{3} \boldsymbol{b}} & \mathbf{1} \\ \mathbf{1} & (\mathbf{1}+\mathbf{3} \boldsymbol{x})^{2 \boldsymbol{a}} & (\mathbf{1}+\mathbf{2} \boldsymbol{x})^{\boldsymbol{3} \boldsymbol{b}} \\ (\mathbf{1}+\mathbf{2} \boldsymbol{x})^{\boldsymbol{3} \boldsymbol{b}} & \mathbf{1} & (\mathbf{1}+\mathbf{3} \boldsymbol{x})^{\mathbf{2} \boldsymbol{a}}\end{array}\right| \)
then
A. \( f(x) \) has constant term 1
B. constant term is \( 2 a-3 b \)
c. coefficient of \( x \) in \( f(x) \) is zero
D. constant term is \( 2 a+3 b \)