AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Calculate the [OH] of
\( \left[\boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{H}_{3}\right]^{\oplus} \) and \( \left[\boldsymbol{H}_{3} \boldsymbol{N}-\right. \)
\( \left.C_{2} H_{4} N H_{3}\right]^{2+} \) in 0.15 M ethylene
diamine (aq) if
\( N H_{2} C_{2} H_{4} N H_{2}+H_{2} O \rightleftharpoons \)
\( N H_{2} C_{2} H_{4} \stackrel{\oplus}{N} H_{3}+\stackrel{\ominus}{O} H\left(K_{1}=8.5 \times\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{5}}\right) \)
\( N H_{2} C_{2} H_{4} \stackrel{\oplus}{N} H_{3}+H_{2} O \rightleftharpoons \)
\( \left[\boldsymbol{N} \boldsymbol{H}_{3} \boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{H}_{3}\right]^{2+}+\stackrel{\ominus}{\boldsymbol{O}} \boldsymbol{H}\left(\boldsymbol{K}_{2}=\right. \)
\( \left.2.7 \times 10^{-8}\right) \)
\( \begin{array}{lll}\text { A. Case } 1: 3.57 \times 10^{-3} M & \text { Case } \|: 2.7 \times 10^{-8} M=K_{b a}\end{array} \)
B. Casel: \( 4.57 \times 10^{-3} M \quad \) Case \( \|: 3.7 \times 10^{-8} M=K_{h} \)
C. Casel: \( 5.57 \times 10^{-3} M \quad \) Case \( \|: 4.7 \times 10^{-8} M=K_{h} \)
D. Case I: \( 6.57 \times 10^{-3} M \quad \) Case \( \|: 5.7 \times 10^{-8} M=K_{h} \)
Subject: Maths
Two adjacent sides of a parallelogram are \( 5 \mathrm{cm} \) and \( 3.5 \mathrm{cm} . \) One of its
diagonals is \( 6.5 \mathrm{cm} . \) Then the area of parallelogram is
A \( \cdot 5 \sqrt{3} \mathrm{cm}^{2} \)
в. \( 10 \sqrt{3} \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 15 \sqrt{3} \mathrm{cm}^{2} \)
D. \( 20 \sqrt{3} \mathrm{cm}^{2} \)
Subject: Maths
If in a \( G P \) the \( (p+q)^{t h} \) term is \( a \) and
the \( (p-q)^{t h} \) term is \( b, \) then \( p^{t h} \) term is
\( \mathbf{A} \cdot(a b)^{1 / 3} \)
B \( \cdot(a b)^{1 / 2} \)
\( \mathbf{c} \cdot(a b)^{1 / 4} \)
D. None of these
Subject: Physics
toppr
Q Type your question.
uniform magnetic field \( B \) with constant velocity \( \boldsymbol{v} \) at \( t=0 . \) The longest side of the frame is perpendicular to the direction of velocity If i is the instantaneous current through the frame then choose the alternative
showing the correct variation of i with time
\( A \)
\( (\mathrm{A}) \)
в.
\( (\mathrm{B}) \)
\( c \)
\( (\mathrm{C}) \)
\( D \)
\( (\mathrm{D}) \)
Subject: Physics
Equal net forces act on two different
blocks \( A \) and \( B \) of masses \( m \) and \( 4 m \)
respectively. For same displacement, identify the correct statement.
A ' their kinetic energies are in the ratio \( \frac{K_{A}}{K_{B}}=\frac{1}{4} \)
B. Their speeds are in the ratio \( \frac{v_{A}}{v_{B}}=\frac{1}{1} \)
c. work done on the blocks are in the ratio \( \frac{W_{A}}{W_{B}}=\frac{1}{1} \)
D. All of the above
Subject: Maths
The pressure \( P \) and volume \( V \) of a gas
are connected by the relation \( \boldsymbol{P} \boldsymbol{V}^{1 / 4}= \)
constant. The percentage increase in
the pressure corresponding to a deminition of \( \frac{1}{2} \% \) in the volume is
A \( \cdot \frac{1}{2} \% \)
B. \( \frac{1}{4} \% \)
c. \( \frac{1}{8} \% \)
D. none of these
Subject: Maths
The factors of \( \boldsymbol{x}^{\mathbf{4}}+\boldsymbol{y}^{\mathbf{4}}+\boldsymbol{x}^{\mathbf{2}} \boldsymbol{y}^{\mathbf{2}} \) are
\( \mathbf{A} \cdot\left(x^{2}+y^{2}\right)\left(x^{2}+y^{2}-x y\right) \)
\( \mathbf{B} \cdot\left(x^{2}+y^{2}\right)\left(x^{2}-y^{2}\right) \)
C \( \cdot\left(x^{2}+y^{2}+x y\right)\left(x^{2}+y^{2}-x y\right) \)
D. Factorization is not possible
Subject: Chemistry
Photochromic sunglasses, which darken when exposed to light, contain a
small amount of colourless \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}) \)
embedded in the glass. When irradiated with light, metallic silver atoms are produced and the glass darkens.
\[
\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}) \longrightarrow \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\boldsymbol{C l}
\]
Escape of chlorine atoms is prevented
by the rigid structure of the glass and the reaction therefore, reverses as soon
as the light is removed. If \( 310 k J / \) mol of
energy is required to make the reaction proceed, what wavelength of light is
necessary?
Subject: Physics
The dimension of stopping potential \( V_{0} \) in photoelectric effect in units of Planck's constant 'h', speed of light 'c'
and Gravitational constant 'G' and
ampere \( A \) is:
A \( \cdot h^{-2 / 3} c^{-1 / 3} G^{4 / 3} A^{-1} \)
B \( \cdot h^{2} G^{3 / 2} c^{1 / 3} A^{-1} \)
c. \( h^{0} c^{5} G^{-1} A^{-1} \)
D. \( h^{1 / 3} G^{2 / 3} c^{1 / 3} A^{-1} \)
Subject: Physics
\( 45 g \) of water at \( 50^{\circ} \mathrm{C} \) in a beaker is
cooled when \( 50 g \) of copper at \( 18^{\circ} \mathrm{C} \) is added to it. The contents are stirred till
a final constant temperature is reached Calculate this final temperature. The specific heat capacity of copper is
\( 40.39 J g^{-1} K^{-1} \) and that of water is \( 4.2 J g^{-1} K^{-1} \)
A \( \cdot 17^{\circ} \mathrm{C} \)
В. \( 27^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 47^{\circ} \mathrm{C} \)
D. none of the above
Subject: Biology
Which of the following statement/s is/are correct with regard to ozone depletion:
1. The ozone hole is measured in terms
of ozone concentrations, which is
expressed in Dobson units.
2. The major cause for ozone depletion is the presence of CFCs in the stratosphere - CFCs are entirely manmade and not found naturally.
A. only
B. Only 2
c. Both A and B
D. None of the above
Subject: Maths
The lines \( 2 x-3 y=5 \) and \( 3 x-4 y=7 \)
intersect at the center of the circle
whose area is 154 sq. units, then equation of circle is
A \( \cdot x^{2}+y^{2}-2 x+2 y=47 \)
B. \( x^{2}+y^{2}+2 x-2 y=31 \)
c. \( x^{2}+y^{2}-2 x-2 y=47 \)
D. \( x^{2}+y^{2}-2 x-2 y=31 \)
Subject: Chemistry
Choose the correct options:
This question has multiple correct options
\( \mathbf{A} \cdot \mathrm{PCl}_{5}(\text { solid }) \) dissociates into \( \mathrm{PCl}_{4}^{+} \) and \( \mathrm{PCl}_{6}^{-} \)
B. LiH reacts with AlH forming LiAlH \( _{4} \).
C \( . N H_{3} \) is protonated.
D. \( H_{3} P O_{2} \) on heated forms \( P H_{3} \) and \( H_{3} P O_{3} \)
Subject: Physics
A solenoid of inductance \( L \) carrying a certain current is linked with a total
magnetic flux \( \phi \). Now it is connected to a condenser with which it shares half of its initial energy. The total flux now linked with the solenoid is:
\( A \cdot \frac{\phi}{2} \)
в. \( \frac{\phi}{\sqrt{2}} \)
\( c \cdot \frac{\phi}{2 \sqrt{2}} \)
D.
Subject: Maths
If \( A \) got \( 40 \% \) marks more than \( B \) in exam, by what \( \% \) is \( B s \) marks less than
\( A s ? \)
A . \( 28.57 \% \)
B. \( 7.14 \% \)
\( \mathrm{c} .9 .09 \% \)
D. \( 40 \% \)
Subject: Physics
A person is in front of a vertical
mountain fires a bullet and hears its
echo after a time 6 s. The person walks a
distance d towards mountain then fires
another bullet and hears its echo after a
time 2 s. If velocity of sound in air is 340
\( \mathrm{ms}^{-1} . \) The value of d is
A. 340 \( m \)
B. 170 \( m \)
c. \( 255 \mathrm{m} \)
D. \( 680 \mathrm{m} \)
Subject: Maths
A factory production line is manufacturing bolts using three machines, \( A, B \) and \( C . \) Of the total
output, machine A is responsible for 25 \( \%, \) machine \( \mathrm{B} \) for \( 35 \% \) and machine \( \mathrm{C} \) for the rest. It is known from previous
experience with the machines that \( 5 \% \)
of the output from machine \( A \) is defective, \( 4 \% \) from machine \( B \) and \( 2 \% \)
from machine C. A bolt is chosen at
random from the production line and found to be defective. What is the
probability that it came from machine c?
A. 0.232
в. 0.862
\( c \cdot 0.123 \)
D. 0.286
Subject: Physics
Assertion
The lowest attainable temperature is
absolute zero,i.e.,0 \( K=-273.15^{\circ} \mathrm{C} \)
Reason
Size of each degree on Kelvin scale is same as that on Celsius scale.
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: Biology
TLC of human blood is about?
\( \mathbf{A} \cdot 5000-6000 \) per \( \mathrm{ml} \) of blood
B. \( 5000-11000 \) per ml of blood
C \( .5000-11000 \) per cubic mm of blood
D. \( 2000-6000 \) per cubic mm of blood
Subject: Chemistry
Which of the following complex/ion has lowest C-O bond order?
\( \mathbf{A} \cdot\left[V(C O)_{6}\right]^{-} \)
в. \( F e(C O)_{5} \)
c. \( N i(C O)_{4} \)
D. \( \left[M n(C O)_{6}\right]^{+} \)
Subject: Physics
Choose the correct statements from the
following
This question has multiple correct options
A. The gravitational forces between two particles are an action and reaction pair
B. Gravitational constant \( (G) \) is scalar but acceleration due to gravity \( (g) \) is a vector
C. The values of \( G \) and \( g \) are to be determined
experimentally
D. \( G \) and \( g \) are constant everywhere
Subject: Chemistry
At \( 25^{\circ} \mathrm{C}, 1 \) mol of \( A \) having a vapour
pressure of 100 torr and 1 mol of \( B \) having a
vapour pressure of 300 torr were
mixed.
The vapour at equilibrium is removed, condensed and the condensate is
heated back to \( 25^{\circ} C \)

The vapour now formed are again removed, recondensed and analyzed.If the mole fraction of \( A \) in this
condensate is \( 1 \times 10^{-x} \), then what is the
value of \( \mathbf{x} ? \)
Subject: Physics
In a quark model of elemetary particles, a neutron is made of one up quark of charge \( \frac{2}{3} e \) and two down quark of charges \( \left(-\frac{1}{3} e\right) . \) If they have a triangle configuration with side length of the order of \( 10^{-15} \) m. The electrostatic
potential energy of neutron in \( M e V \) is
A. 7.68
B . -5.21
c. -.048
D. 9.34
Subject: Physics
According to Bohr's theory of hydrogen-
atom, for the electron in the \( n^{t h} \)
permissible orbit This question has multiple correct options
A \( \cdot \) Linear Momentum \( \propto \frac{1}{n} \)
B. Radius of orbit \( \propto n \)
c. Kinetic Energy \( \propto \frac{1}{n^{2}} \)
D. Angular Momentum \( \propto n \)
Subject: Chemistry
Consider the following statements and arrange in the order of true/false as
given in the codes.
\( S_{1}: \) Change in state function between
two states is a definite quantity and
does not depend on path.
\( S_{2}: \) Intensive properties cannot be
algebraically added or subtracted.
\( S_{3}: \) Ratio of two extensive properties
result in a parameter that depends on the amount of substance.
\( S_{4}: \) Molar heat capacity is a state
function.
The correct order to true/false of the
above statements is:
\( A \). FT FT
B. FF FT
c. TT FT
D. TTTF
Subject: Physics
The refractive indices of glass and water are \( 3 / 2 \) and \( 4 / 3 \) respectively. The refractive index of glass with respect to
water is :
\( A \cdot 2 \)
B. 8/9
\( c \cdot 9 / 8 \)
D. \( 5 / 3 \)
Subject: Maths
If \( 2 x+3 y=6 \sqrt{3} \) and \( 2 x-3 y=6, \) find
the value of \( x y ? \)
A. \( x y=3 \)
в. \( x y=2 \)
c. \( x y=1 \)
D. \( x y=7 \)
Subject: Physics
The \( \alpha \) -particles with initial kinetic
energy 4.8 mev are shot at gold atoms \( (z=79) . \) The potential of \( \alpha \) -particle at the closest distance to the gold nucleus
is
A \( .4 .8 M V \)
в. zero
\( \mathrm{c} .9 .6 \mathrm{MV} \)
D. 2.4MV
Subject: Maths
If \( \frac{\cos (\boldsymbol{A}-\boldsymbol{B})}{\cos (\boldsymbol{A}+\boldsymbol{B})}+\frac{\cos (\boldsymbol{C}+\boldsymbol{D})}{\cos (\boldsymbol{C}-\boldsymbol{D})}=\mathbf{0}, \) then
\( \tan A \tan B \tan C= \)
\( \mathbf{A} \cdot \tan D \)
B. \( \cot D \)
\( c .-\tan D \)
D. - cot \( D \)
Subject: Chemistry
A. \( C C l_{4} \) does not act as lewis acid.
B. Silanes are strong reducing agents.
C. Crystalline silica will have Diamond
like structure.

Which of the above statement(s) is/are
true?
\( A \cdot A \& B \)
B. only 'A'
c. only's'
D. \( A, B \& C \)
Subject: Physics
A cube has a side of length \( 1.2 \times \)
\( 10^{-2} m . \) Calculate its volume
A \( .1 .7 \times 10^{-6} m^{3} \)
В. \( 1.73 \times 10^{-6} m^{3} \)
C. \( 1.70 \times 10^{-6} m^{3} \)
D. \( 1.728 \times 10^{-6} \mathrm{m}^{3} \)
Subject: Chemistry
For the reaction \( 2 H g O(s) \rightarrow 2 H g(l)+ \)
\( \boldsymbol{O}_{2}(\boldsymbol{g}) \)
\( \mathbf{A} \cdot \Delta H>0 \) and \( \Delta S<0 \)
B. \( \Delta H>0 \) and \( \Delta S>0 \)
c. \( \Delta H<0 \) and \( \Delta S<0 \)
D. \( \Delta H<0 \) and \( \Delta S>0 \)
Subject: Physics
Speed \( v \) of a particle moving along a
straight line, when it is at a distance \( x \)
from a fixed point on the line is given by \( v^{2}=108-9 x^{2} \) (assuming mean
position to have zero phase constant)
(all quantities in are in \( c g s \) unit):
A. The motion is uniformly accelerated along the straight line
B. The magnitude of the acceleration at a distance \( 3 \mathrm{cm} \) from the fixed point is \( 27 \mathrm{cm} / \mathrm{s}^{2} \)
C. The motion is simple harmonic about \( x=\sqrt{12} \mathrm{m} \)
D. The maximum displacement from the fixed point is \( 4 \mathrm{cm} \)
Subject: Maths
Two triangles \( A B C \) and \( P Q R \) are \( \operatorname{similar}, \) if \( B C: C A: A B=1: 2: 3 \)
then \( \frac{Q R}{P R} \)
A \( \cdot \frac{3}{2} \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{2}{3} \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are defined by
\( f(x)=x^{2}, g(x)=\cos x \) then
\( (g o f)(x)= \)
\( \mathbf{A} \cdot \cos 2 x \)
B. \( x^{2} \cos x \)
\( \mathbf{c} \cdot \cos x^{2} \)
D. \( \cos ^{2} x^{2} \)
Subject: Chemistry
Choose the reactions which are not
feasible
I. Iron \( + \) Zinc sulphate \( \rightarrow \) Iron sulphate \( + \) zinc
II. Magnesium + Silver nitrate \( \rightarrow \) Magnesium nitrate + Silver
III. Copper + dil. sulphuric acid \( \rightarrow \)
Copper sulphate \( +\boldsymbol{H}_{2} \)
IV. Zinc \( + \) Ferrous sulphate \( \rightarrow \) Iron \( + \) Zinc sulphate
A. I, Il and III
B. III and IV only
c. I and III only
D. All of these
Subject: Maths
If the function \( f(x)=2 x^{2}+3 x+5 \)
satisfies LMVT at \( x=2 \) on the
closed interval \( [1, a] \) then the value of ' \( a^{\prime} \)
is equal to
A . 3
B. 4
\( c \cdot 6 \)
D.
Subject: Physics
A charge \( Q \) is placed at each of two
opposite corners of a square. A charge \( q \)
is laced at each of the two opposite corners of the square. If the resultant electric field on \( Q \) is zero, then
\( ^{\mathbf{A}} \cdot Q=-\frac{q}{2 \sqrt{2}} \)
в. \( Q=-2 \sqrt{2} q \)
c. \( Q=-2 q \)
Subject: Maths
If the projection of the line segment \( A B \) on the coordinate axes are 2,3,6 then
the square of the sines of the angles made by \( A B \) with \( O Y \) axis is
A \( \cdot \frac{3}{7} \)
B. \( \frac{3}{49} \)
\( c \cdot \frac{4}{7} \)
D. \( \frac{40}{49} \)
Subject: Physics
A ladder of mass \( M \) and length \( L \) is
supported in equilibrium against a smooth vertical wall and a rough horizontal surface, as shown in figure. If \( \theta \) be the angle of inclination of the rod
with the horizontal, then calculate
(a) normal reaction of the wall on the
ladder
(b) normal reaction of the ground on the
ladder
(c) net force applied by the ground on
the ladder
Subject: Chemistry
The primary and secondary valency of Co in the octahedral complex
\( \boldsymbol{C o C l}_{3} \cdot \boldsymbol{5} \boldsymbol{N} \boldsymbol{H}_{3} \) are
A. 6 and 3
B. 3 and 6
\( c \cdot 4 \) and 3
D. 3 and
Subject: Maths
\( \operatorname{Let} f(x)=(x+1) 2^{-\left(\frac{1}{[x]}+\frac{1}{x}\right)} \) and
\( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \)
A. \( f \) is continuous at \( x=0 \)
B. \( \lim _{x \rightarrow 0^{+}} f(x) \) exists
C. \( \lim _{x \rightarrow 0^{+}} f(x) \) does not exist
D. \( \lim _{x \rightarrow 0} f(x) \neq \lim _{x \rightarrow 0^{-}} f(x) \)
Subject: Physics
Two small bar magnets are placed in a line at certain distance \( d \) part. If the
length of each magnet is negligible compared to \( d \), the force between them will be inversely proportional to:
\( \mathbf{A} \cdot d^{2} \)
B. \( d \)
\( c \cdot d^{3} \)
D. \( d^{4} \)
Subject: Physics
A capacitance of \( \left(\frac{10^{-3}}{2 \pi}\right) F \) and an inductance of \( \left[\frac{100}{\pi}\right] m H \) and \( a \) resistance of \( 10 \Omega \) are connected in
series with an AC voltage source of \( 220 V, 50 H z . \) The phase angle of the circuit is
A . \( 60^{\circ} \)
B. \( 30^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ} \)
D. \( 90^{\circ} \)
Subject: Physics
The velocity of a body is given by the equation \( v=6-0.02 t, \) where \( t \) is the time taken.What does the body
undergo?
A. Uniform retardation of 0.02 \( \mathrm{m} s^{-2} \)
B. Uniform acceleration of 0.02 \( \mathrm{m} \) s \( ^{-2} \)
c. Uniform retardation of \( -0.04 \mathrm{m} s^{-2} \)
D. Uniform acceleration of - 0.04 \( \mathrm{m} \) s \( ^{-2} \)
Subject: Chemistry
Assertion
Hydrides of group-16 elements show
volatility in the order \( : \boldsymbol{H}_{2} \boldsymbol{O}>\boldsymbol{H}_{2} \boldsymbol{S}> \)
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{e}>\boldsymbol{H}_{2} \boldsymbol{T} \boldsymbol{e} \)
Reason
Electronegativity of group-16 elements increases down the group from oxygen to tellurium.
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
How much electricity in terms of Faraday is required to produce:
(i) \( 20 g \) of \( C a \) from molten \( C a C l_{2} \)
(ii) \( 40 g \) of \( A l \) from molten \( A l_{2} O_{3} \)
[Given : Molar mass of calcium \&
Aluminium are 40 g \( m o l^{-1} \& 27 g \) mol \( \left.^{-1} \text {respectively }\right] \)
Subject: Chemistry
After balancing and reducing the coefficients to lowest whole number
terms, What is the coefficient of \( \boldsymbol{H}_{2} \boldsymbol{O} \) ?
\( \boldsymbol{H} \boldsymbol{C l}+\boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{K} \boldsymbol{C l}+ \)
\( M n C l_{2}+C l_{2} \)
\( A \cdot 1 \)
B. 2
\( c .5 \)
D. 8
E . 16
Subject: Maths
Left hand derivative and right hand derivative of a function \( f(x) \) at a point \( \boldsymbol{x}=\boldsymbol{a} \) are defined as
\( f^{\prime}\left(a^{-}\right)=\lim _{h \rightarrow 0^{+}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{h \rightarrow 0^{-}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{x \rightarrow a^{+}} \frac{f(a)-f(x)}{a-x} \) respectively
Let \( f \) be a twice differentiable function.
We also know that derivative of an even
function is odd function and derivative
of an odd function is even function
The statement
\( \lim _{h \rightarrow 0} \frac{f(-x)-f(-x-h)}{h}= \)
\( \lim _{h \rightarrow 0} \frac{f(x)-f(x-h)}{-h} \) implies that for all
\( \mathbf{x} \boldsymbol{\epsilon} \boldsymbol{R} \)
\( A . f \) is odd
B. \( f \) is even
c. \( f \) is neither odd nor ever
D. nothing can be concluded
Subject: Physics
A 2-ampere current flows in a conductor which has \( 1 \times 10^{24} \) free electrons per
meter. What is their average drift velocity?
A \( .1 .25 \mathrm{m} / \mathrm{s} \)
в. \( 125000 \mathrm{m} / \mathrm{s} \)
c. \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. \( 1.25 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
Subject: Physics
The total angular momentum of a rigid
body can be written as
A. \( I \times \omega \); where I: moment of inertia of body, : angular velocity
B. \( I^{2} \times \omega ; \) where I: moment of inertia of body, : angular velocity
C \( \cdot I^{2} \times \omega^{2} ; \) where I: moment of inertia of body, : angular
velocity
D. \( I \times \omega^{2} \); where I: moment of inertia of body, : angular
velocity
Subject: Chemistry
The first ionization potential of \( N a \) is 5.1 \( e V \). The value of electron gain
enthalpy of \( N a^{+} \) will be :
A. \( -5.1 \mathrm{eV} \)
B. \( -10.2 \mathrm{eV} \)
\( \mathbf{c} .+2.55 \mathrm{eV} \)
D. -2.55 eV
Subject: Physics
In a sample of semi conductor
mobilities of electrons and holes are
\( 24 \times 10^{3} c m^{2} V^{-1} S^{-2} \) and \( 0.2 \times \)
\( 10^{3} \mathrm{cm}^{2} V^{-1} S^{-1} \) respectively. If the
density electrons is \( 0.8 \times 10^{14} \mathrm{cm}^{-3} \)
and that of holes is \( 0.4 \times 10^{14} \mathrm{cm}^{-3} \)
Find the nature of semi conductor and
its conductivity
Subject: Maths
Given \( A=\{2,3,4\}, B=\{2,5,6,7\} \)
Construct an example of each of the following
(i) an injective mapping from \( A \) to \( B \)
(ii) a mapping from \( A \) to \( B \) which is not injective.
(iii) a mapping from \( \mathrm{B} \) to \( \mathrm{A} \)
Subject: Physics
Two open pipes of length \( 50 \mathrm{cm} \) and 51
cm produce 6 beats when sounded together, find the speed of sound:
A \( \cdot 330 m s^{-1} \)
B. \( 316 \mathrm{ms}^{-1} \)
c. \( 306 m s^{-1} \)
D. \( 360 \mathrm{ms}^{-1} \)
Subject: Chemistry
Which of the following changes
represents a disproportional
reaction(s)?
\( \mathbf{A} \cdot C l_{2}+2 O H^{-} \rightarrow C l O^{-}+C l^{-}+H_{2} O \)
B. \( C u_{2} O+2 H^{+} \rightarrow C u+C u^{2+}+H_{2} O \)
\( \mathbf{C} \cdot 2 H C u C l_{2} \frac{\text {dilution with}}{\text {water}} C u+C u^{2+}+4 C l^{-}+2 H^{+} \)
D. All of the above
Subject: Physics
Two thin lenses, when in contact,
produce a combined power +10 dioptre When they are \( 0.25 \mathrm{m} \) apart, the power reduce to +6 dioptre. The power of the lenses in dioptre, are:
A . 1 and 9
B. 2 and 8
\( c \cdot 4 \) and 6
D. 5 each
Subject: Physics
Billy jogs \( 2.5 k m \) east in 45 minutes,
takes a water break for 12 minutes, and
then walks west at a rate of \( 0.65 k m / h \) for 30 min. What is Billy's average
velocity? (Answer units: km/hr)
A . 1.52
B. 1.96
\( c \cdot 2 \)
D. 1.45
Subject: Physics
A conducting body 1 has some initial charge \( Q, \) and its capacitance is \( C . \) There are two other conducting bodies, 2 and \( 3, \) having capacitances: \( C_{2}=2 C \)
and \( C_{3} \rightarrow \infty . \) Bodies 2 and 3 are
initially uncharged. "Body 2 is touched with body \( 1 . \) Then, body 2 is removed from body 1 and touched with body 3 and then removed". This process is
repeated \( N \) times. Then, the charge on
body 1 at the end must be :
A \( \cdot Q / 3^{N} \)
B . \( Q / 3^{N-1} \)
c. \( Q / N^{3} \)
D. None
Subject: Physics
Liquid is filled in a vessel which is kept
in a room with temperature \( 20^{\circ} \mathrm{C} \). When
the temperature of the liquid is \( 80^{\circ} C \) then it losses heat at the rate of 60
cal/sec.What will be the rate of loss of
heat when the temperature of the liquid
is \( 40^{\circ} \mathrm{C} \)
A . 180 cal / sec
B . 40 cal/sec
c. 30 cal/sec
D. 20 cal/sec
Subject: Maths
The line \( x+y=a \) meets the axis of \( x \)
and \( y \) at \( A \) and \( B \) respectively. \( A \)
triangle \( \triangle A M N \) is inscribed in the \( \triangle O A B, O \) being the origin, with right
angle at \( N . M \) and \( N \) lie respectively on
\( O B \) and \( A B . \) If the area of the triangle \( \triangle A M N \) is \( \frac{3}{8} \) of the area of the \( \triangle O A B \) then \( \frac{A N}{B N} \) is equal to
A.
B. 2
\( c .3 \)
\( D \)
Subject: Chemistry
Assertion
In the electrolytic reduction of \( A l_{2} O_{3} \)
cryolite is used.
Reason
Cryolite is an ore of aluminium.
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: Chemistry
A reaction takes place in three steps.
The rate constants are \( k_{1}, k_{2} \) and \( k_{3} \)
The over all rate constant \( \boldsymbol{k}=\frac{\boldsymbol{k}_{1} \boldsymbol{k}_{3}}{\boldsymbol{k}_{2}} . \) If
(energy of activation) \( E_{1}, E_{2} \) and \( E_{3} \)
The overall energy of activation is:
A. 40
B. 30
c. 400
D. 60