AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A thin spherical conduction shell of radius R has a charge q. another charge \( \mathrm{Q} \) is placed atthe centre of the shell. The electrostatic potential at a point \( \mathrm{P} \) at a distance \( \mathrm{R} / 2 \) from thecentre of the shell is
A \( \cdot \frac{2 Q}{4 \pi \varepsilon_{0} \mathrm{R}} \)
в. \( \frac{2 Q}{4 \pi \epsilon_{0} \mathrm{R}}-\frac{2 \mathrm{q}}{4 \pi \varepsilon_{0} \mathrm{R}} \)
c. \( \frac{2 \mathrm{Q}}{4 \pi \epsilon_{6} \mathrm{R}}+\frac{\mathrm{q}}{4 \pi \varepsilon_{0} \mathrm{R}} \)
D. \( \frac{(\mathrm{q}+\mathrm{Q})}{4 \pi \varepsilon_{0}} \frac{2}{\mathrm{R}} \)
Subject: Chemistry
A solution containing \( 30 g \) of a nonvolatile solute in exactly \( 90 g \) water has a vapour pressure of 21.85 mm \( H g \) at
\( 25^{\circ} \mathrm{C} . \) Further 18 gm of water is then added to the solution. The resulting solution has a vapour pressure of 22.18 \( \mathrm{mmHg} \) at \( 25^{\circ} \mathrm{C} \). Calculate
(a) molar mass of the solute, and (b) vapour
pressure of water at \( 25^{\circ} \mathrm{C} \)
В. \( (a) 61.21 g \) тод\( ^{-1} \),
(b) 23.99 \( \mathrm{mm} \) Н \( g \)
\( (b) 28.87 \mathrm{mm} \mathrm{Hg} \)
D. \( (a) 84.87 g \) mol \( ^{-1} \),
Subject: Maths
If \( S= \)
\( \left\{x \in N: 2+\log _{2} \sqrt{x+1}>1-\log _{1 / 2}\right. \)
then
\( \mathbf{A} \cdot S=1 \)
B. \( S=Z \)
c. \( S=N \)
D. none of these
Subject: Physics
A resistor and a capacitor are in series \( \operatorname{across} \) a \( 20 V \) ac source. Circuit
impedance is \( 4.33 k \Omega . \) Current flow in the circuit is
\( \mathbf{A} \cdot 9.2 m A \)
в. \( 92 m A \)
c. \( 4.6 m A \)
D. \( 460 m A \)
Subject: Biology
Assertion
Zoological parks are the places where wild animals are kept in protected environments under human care and
which enable use to learn about their
food habits and behaviour.
Reason
Adequate arrangements for the treatment, medication, regular check up and pathological investigations are absolutely necessary to be made for the health, care and upkeep of the animals.
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
A current of \( 1 \times 10^{-5} A \) is passed
through a solution of single atom thick
layer of \( A g N O_{3} \) for 16 min \( 5 s, \) using plantinum electrodes. A uniform single atom thick layer of Ag is deposited covering \( 90 \% \) of cathode surface. The
total surface area \( \left(\text { in } c m^{2}\right) \) of cathode if
each silver atom covers an area of
\( \mathbf{5 . 6} \times \mathbf{1 0}^{-\mathbf{1 6}} \mathbf{c m}^{\mathbf{2}} \mathbf{i s} \)
Subject: Physics
\( 50 g \) of copper is heated to increase its
temperature by \( 10^{\circ} \mathrm{C} . \) If the same
quantity of heat is given to \( 10 \mathrm{gm} \) of water, the rise in temperature is (specific heat of copper \( =420 \) J
\( k g^{-1} K^{-1}, \) specific heat of water \( =4200 \)
\( \left.k g^{-1} K^{-1}\right) \)
\( A \cdot 5^{\circ} \mathrm{C} \)
B . \( 6^{\circ} \mathrm{C} \)
\( c \cdot 7^{o} \)
D. \( 8^{\circ} \mathrm{C} \)
Subject: Chemistry
Assertion
Detergents can easily remove oil and
dirt from soiled garments.
Reason
Detergents increase the surface tension
of water.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
Assertion
Drift velocity of electrons is
independent of time.
Reason
Electrons are accelerated in the
presence 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
A tank of height \( 33.25 \mathrm{cm} \) is completely
filled with liquid \( (\mu=1.33) . \) An object
is placed at the bottom of tank on the
axis of concave mirror as shown in Fig.
Image of the object is formed at \( 25 \mathrm{cm} \)
below the surface of the liquid. Focal length of the mirror is
\( A \cdot 10 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
\( c \cdot 20 \mathrm{cm} \)
D. 25 cm
Subject: Physics
A double convex lens, made of a
material of refractive index \( \mu_{1}, \) is
placed inside two liquids of refractive
indices \( \mu_{2} \) and \( \mu_{3} \) as shown. \( \mu_{2}>\mu_{1}>\mu_{3} \)
A wide, parallel beam of light is incident
on the lens from the left. The lens will
give rise to
A. a single convergent beam
B. two different convergent beams
c. two different divergent beams
D. a convergent and a divergent beam
Subject: Physics
Two particles of equal mass go around a circle of radius \( R \) under the action of
their mutual gravitational attraction. The speech of each particle is
\( ^{\mathbf{A}} \cdot_{v}=\frac{1}{2 R} \sqrt{\left(\frac{1}{G M}\right)} \)
в. \( v=\sqrt{\left(\frac{G M}{2 R}\right)} \)
\( ^{\mathrm{c}} \cdot_{v}=\frac{1}{2} \sqrt{\left(\frac{G M}{R}\right)} \)
D. \( v=\sqrt{\left(\frac{4 G M}{R}\right)} \)
Subject: Maths
The number of solutions of equations \( \left|\begin{array}{ccc}\sin 3 \theta & -1 & 1 \\ \cos 2 \theta & 4 & 3 \\ 2 & 7 & 7\end{array}\right|=0 \) in \( [0,2 \pi] \) is
A .2
B. 3
\( c \cdot 4 \)
D. 5
Subject: Maths
Factorise:
\( 6 x y\left(a^{2}+b^{2}\right)+8 y z\left(a^{2}+b^{2}\right)- \)
\( \mathbf{1 0 x z}\left(\mathbf{a}^{2}+\mathbf{b}^{\mathbf{2}}\right) \)
Subject: Physics
The displacement of a particle is
represented by the equation \( y= \) \( 3 \cos \left[\frac{\pi}{4}-2 \omega t\right] \)
The motion is:
A. non- periodic
B. periodic but not simple harmonic
c. simple harmonic with period 2 piw
D. simple harmonic with period \( \left(\frac{\pi}{\omega}\right) \)
Subject: Physics
\( n^{\prime} \) identical bulbs, each designed to draw a power \( P \) from a certain voltage supply are joined in series across the supply. The total power which they will draw is :-
A. \( P \)
в. \( n P \)
c. \( \frac{P}{n^{2}} \)
D. \( \frac{P}{n} \)
Subject: Maths
Find the Quotient and the Remainder when the first polynomial is divided by the second.
\( \left(6 x^{2}-31 x+47\right) \) by \( (2 x-5) \)
A. Quotient \( =3 x-8, \) Remainder \( =7 \)
B. Quotient = 3x + 8, Remainder = 7
c. Quotient \( =-3 x-8, \) Remainder \( =7 \)
D. Quotient \( =-3 x+8, \) Remainder \( =7 \)
Subject: Physics
A swimmer wants to cross a \( 200 m \) wide
river which is flowing at a speed of \( 2 m / s . \) The velocity of the swimmer with respect to river is \( 1 \mathrm{m} / \mathrm{s} \). How far from
the point directly opposite to the starting point does the swimmer reach
the opposite bank?
\( \mathbf{A} \cdot 200 m \)
B. \( 400 m \)
\( c .600 m \)
D. \( 800 m \)
Subject: Maths
If \( \int \frac{4 e^{x}+6 e^{-x}}{9 e^{x}-4 e^{-x}} d x=A x+b \ln \left(9 e^{2 x}-\right. \)
4) \( +C ; \) then; value of \( A, B, \& C \) are
A \( \cdot A=-\frac{3}{2}, B=\frac{35}{36}, C \varepsilon R \)
в. \( A=\frac{3}{2}, B=\frac{-35}{36}, C \varepsilon R \)
c. \( A=-\frac{3}{2}, B=\frac{35}{36}, C>0 \)
D. None of these
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}^{2}+\mathbf{2}}, \boldsymbol{x} \in \boldsymbol{R} \).Find \( \boldsymbol{f}(\mathbf{0}) \)
Subject: Physics
An object is placed at a distance of
\( 15 \mathrm{cm} \) from a convex lens of focal length
10cm. On the other side of the lens, a
convex mirror is placed at its focus
such that the image formed by the
combination coincides with the object
itself. The focal length of the convex
mirror is :
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( c .15 \mathrm{cm} \)
D. \( 30 \mathrm{cm} \)
Subject: Chemistry
For the process Dry ice \( \rightarrow C O_{2}(g) \)
A. \( \Delta H \) is positive and \( \Delta S \) is negative
B. Both \( \Delta H \) and \( \Delta S \) are negative
c. Both \( \Delta H \) and \( \Delta S \) are positive
D. \( \Delta H \) is negative and \( \Delta S \) is positive
Subject: Chemistry
The IUPAC name of the compound is:
\[
\begin{array}{cc}
0 & 0 \\
C H_{3}-C H_{2}-C-C H_{2}-C-C H_{3}
\end{array}
\]
A. Hexane-2,4-dione
B. hexane-2,4-diol
c. pentane- 2,4 -dione
D. heptane-2,4-dione
Subject: Chemistry
An alkali is titrated against an acid
with methyl orange as indicator, which of the following is a correct combination
\( ? \)
A. Base - Weak, Acid - Strong, End point- Yellow to pinkish red
B. Base - Strong, Acid - Strong, End point - Pink to colourless
c. Base - weak, Acid - Strong, End point- - Colourless to pink
D. Base - strong, Acid- Strong, End point - Pinkish red to yellow
Subject: Chemistry
STATEMENT-1: Heat of neutralization of
\( \mathrm{HCl} \) and \( \mathrm{NaOH} \) is same as that of
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) with \( \mathrm{NaOH} \)
STATEMENT-2: HCI, \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and \( \mathrm{NaOH} \)
are all strong electrolyte.
A. Statement-1 is True, Statement-2 is True; Statementis a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Chemistry
Which one of the following is not a redox reaction?
A. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
В. \( 2 H_{2}+O_{2} \longrightarrow 2 H_{2} O \)
\( ^{\mathrm{c}} \cdot_{N a+H_{2} O} \rightarrow N a O H+\frac{1}{2} H_{2} \)
D. \( _{M n C l_{3}} \rightarrow M n C l_{2}+\frac{1}{2} C l_{2} \)
Subject: Maths
A square and a rectangular plot of land have same perimeter. If the square is of side \( 40 m \) and rectangle is of length 5 decameter. Then area of rectangle is
A \( \cdot 1500 m^{2} \)
В. \( 1600 m^{2} \)
c. \( 200 m^{2} \)
D. \( 150 m^{2} \)
Subject: Maths
\( \mathbf{A} \)
\& B are sharp shooters whose probabilities of hitting a target are \( \frac{\mathbf{9}}{\mathbf{1 0}} \)
\( \& \frac{14}{15} \) respectively. If it is knownthat exactly one of them has hit the target, then the probability that it was hit by \( A \) is equal to
A \( \cdot \frac{24}{55} \)
в. \( \frac{27}{55} \)
c. \( \frac{9}{23} \)
D. \( \frac{10}{23} \)
Subject: Physics
\( _{6}^{14} C \) in upper atmosphere is generated by the nucleus reaction:
A \( \cdot \frac{14}{7} N+_{1}^{1} H \longrightarrow_{6}^{14} C+_{1}^{0} e+_{1}^{1} H \)
B . \( \frac{14}{7} N \longrightarrow_{6}^{14} C+_{1}^{0} e \)
C \( \cdot \frac{14}{7} N+_{0}^{1} n \longrightarrow_{6}^{14} C+_{1}^{1} H \)
D \( \cdot \frac{14}{7} N+\frac{1}{1} H \rightarrow \frac{11}{6} C+_{2}^{4} H e \)
Subject: Physics
In a series LCR circuit connected to an
a.c. source of voltage \( \boldsymbol{v}=\boldsymbol{v}_{m} \sin \omega \boldsymbol{t} \)
use phasor diagram to derive an expression for the current in the circuit. Hence, obtain the expression for the power dissipated in the circuit. Show that power dissipated at resonance is maximum.
Subject: Chemistry
Two closed bulbs of equal volume (v) containing an ideal gas initially at
pressure \( P_{4} \) and temperature \( T_{1} \) are connected through a narrow tube of negligible volume as shown in the
figure below. The temperature of one of
the bulbs is then raised to \( T_{2} \). What is
the final pressure \( \boldsymbol{P}_{f} ? \)
Subject: Physics
Consider three waves represented by
\( \boldsymbol{y}_{1}=\boldsymbol{3} \sin (\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}) \)
\( \boldsymbol{y}_{2}=\boldsymbol{3} \sin \left(\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}+\frac{2 \pi}{3}\right) \)
\( \boldsymbol{y}_{3}=\boldsymbol{3} \sin \left(\boldsymbol{k} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}+\frac{4 \pi}{3}\right) \)
What is the amplitude or resultant of
waves at \( x=0 ? \)
\( A \cdot O \)
B. 9
\( c \cdot 6 \)
\( D \)
Subject: Chemistry
Which of the following statement(s) is/are correct?
I. Starch is almost insoluble in cold
water but relatively more soluble in boiling water.
II. Starch solution gives blue colour with
\( I_{2} \) solution in cold.
III. Starch is a reducing sugar.
IV. Starch forms osazone.
A. III and IV
B. I and II
c. ॥ and III
D. I and IV
Subject: Physics
If the specific heat of lead is \( 0.03 \frac{c a l}{g^{o} C} \)
thermal capacity of \( 500 \mathrm{g} \) of lead is.
A . \( 5 \mathrm{cal}^{\circ} C^{-1} \)
B . \( 10 \mathrm{cal}^{\circ} \mathrm{C}^{-1} \)
C . \( 15 \mathrm{cal}^{\circ} \mathrm{C}^{-1} \)
D. 20cal \( ^{\circ} C^{-1} \)
Subject: Maths
A cylindrical tennis ball container can
contain maximum three ball stacked on
one another. The top and bottom balls
also touch the lid and the base of the
base of the container respectively. If the
volume of a tennis ball is \( 240 \mathrm{cm}^{3} \), then
what is the volume of the container?
A \( \cdot 1080 \mathrm{cm}^{3} \)
B. \( 840 \mathrm{cm}^{3} \)
c. \( 1440 \mathrm{cm}^{3} \)
D. \( 720 \mathrm{cm}^{3} \)
Subject: Maths
If \( 2 \sin ^{-1} x=\sin ^{-1}(2 x \sqrt{1-x^{2}}), \) then
\( \boldsymbol{x} \in \)
A \( .[-1,1] \)
B. \( \left[-\frac{1}{\sqrt{2}}, 1\right] \)
\( c \cdot\left[-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right] \)
D. none of these
Subject: Physics
A converging lens of focal length \( f_{1} \) is placed in front of and coaxially with a
convex mirror of focal length \( f_{2} \). Their separation is d and whole arrangement is in air. A parallel beam of light incident on the lens returns as a
parallel beam from the arrangement. This question has multiple correct options
A. The diameter of incident and emergent beam is the same
B. the distance d can be \( f_{1} \)
c. the distance d can be \( f_{2} \)
D. the distance d can be \( f_{1}-2 f_{2} \)
Subject: Chemistry
Assertion
\( H C l \) diffuses faster than ammonia.
Reason

Rate of diffusion of a gas is inversely proportional to the square root of its
density
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Physics
Assuming that shear stress at the base of a mountain is equal to the force per
unit area due to its weight. Calculate the maximum possible height of a mountain on the earth if breaking stress of a typical rock is \( 3 \times 10^{8} N m^{-2} \)
and its density is then \( 3 \times 10^{3} k g \quad m^{-3} \)
(Take \( \left.g=10 m s^{-2}\right) \)
\( A .4 k m \)
в. \( 8 k m \)
c. \( 10 k m \)
D. \( 16 k m \)
Subject: Maths
The tangent at any point \( P(a \cos \theta, b \sin \theta) \) on the ellipse \( \frac{x^{2}}{a^{2}}+ \)
\( \frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}=1 \) meets the auxiliary circle at two
point which subtend a right angle at the centre, then eccentricity is
A \( \cdot \frac{1}{\sqrt{1+\sin ^{2} \theta}} \)
в. \( \frac{1}{\sqrt{2-\cos ^{2} \theta}} \)
c. \( \frac{1}{\sqrt{1+\tan 2 \theta}} \)
D. noneofthese
Subject: Physics
A satellite is revolving around a planet
in a circuit orbit of radius. ' \( r^{\prime} \) and has
angular momentum \( L \). If it is taken into
a higher orbit of radius \( ^{\prime} \mathbf{4} r^{\prime}, \) the charge
in its angulatr momentum is
A. \( L / 4 \)
B. \( L / 2 \)
c. \( 3 L / 4 \)
D. \( L \)
Subject: Chemistry
Assertion
To overcome electrostatic force of
attraction between electrons and
nucleus, they revolve around the
nucleus.
Reason
Mass of the atom is almost due to its
nucleus.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
Subject: Physics
In the relation \( \boldsymbol{F}=\boldsymbol{a} \sin \boldsymbol{k}_{1} \boldsymbol{x}+ \)
\( \boldsymbol{b} \sin \boldsymbol{k}_{2} \boldsymbol{t}, \) the units \( (\mathrm{Sl}) \) of \( \frac{\boldsymbol{k}_{1}}{\boldsymbol{k}_{2}} \) is
\( (F, x \& t \) have usual meanings)
\( \mathbf{A} \cdot s / m \)
B. sm
\( c \cdot s t \)
D. s/t
Subject: Chemistry
Silver metal is recovered industrially by using the chemistry shown below. Which of the following statements is/are not true?
\( \boldsymbol{2} \boldsymbol{K}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right]+\boldsymbol{Z} \boldsymbol{n} \rightarrow \)
\( \mathbf{4} \boldsymbol{K}_{\mathbf{2}}\left[\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{C} \boldsymbol{N})_{4}\right]+\mathbf{2} \boldsymbol{A} \boldsymbol{g} \)
This question has multiple correct options
A. Ag has been oxidised and Zn reduced
B. Ag has been reduced and Zn oxidised
c. Both \( \mathrm{Ag} \) and \( \mathrm{Zn} \) have been oxidised
D. Both Ag and Zn have been reduced
Subject: Physics
A body rotating with uniform angular acceleration covers \( 100 \pi(\text {radian}) \) in
the first \( 5 s \) after the start. Its angular
speed at the end of \( 5 s( \) in radian/s) is
then
A . \( 40 \pi \)
B. \( 30 \pi \)
\( c \cdot 20 \pi \)
D. \( 10 \pi \)
Subject: Chemistry
Assertion
Concentrated \( H_{2} S O_{4} \) reacts with \( K C l \)
to give \( C l_{2} \) gas
Reason
\( H C l \) cannot be oxidised by
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Chemistry
Assertion
In adiabatic process work is
independent of path.
Reason
In adiabatic process work done is equal to negative of change in internal energy.
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
Potassium alum, \( K A l\left(S O_{4}\right)_{2} \cdot 12 H_{2} O \)
is obtained in the form of octahedral
crystals when a solution of \( K_{2} S O_{4} \) and
\( A l_{2}\left(S O_{4}\right)_{3} \) is concentrated by
evaporation. Suggest specific experiments to specify whether it is a complex or double salt.
A. One can determine conductance
B. One can determine freezing points
c. one can detect \( A l^{3+}, S O_{4}^{2-}, K^{+} \)
D. All of these
Subject: Biology
\( \mathbf{2} C_{51} \boldsymbol{H}_{98} \boldsymbol{O}_{6}+\mathbf{1 4 6} \boldsymbol{O}_{2} \rightarrow \mathbf{1 0 2} \boldsymbol{C O}_{2}+\mathbf{9 8} \boldsymbol{H} \)
the R.Q for the above reaction is
A. 0.7
в.
c. \( 1-45 \)
D. 1-62
Subject: Chemistry
At \( 25^{\circ} \mathrm{C} \), the molar conductances at
infinite dilution for the strong
electrolytes \( N a O H, N a C l \) and \( B a C l_{2} \)
\( \operatorname{are} 248 \times 10^{-4}, 126 \times 10^{-4} \) and \( 280 \times \)
\( 10^{-4} S m^{2} m o l^{-1} \) respectively
\( \lambda_{m}^{\circ} B a(O H)_{2} \) in \( S m^{2} m o l^{-1} \) is
\( \mathbf{A} \cdot 52.4 \times 10^{4} \)
B \( .524 \times 10^{4} \)
c. \( 4.2 \times 10^{4} \)
D \( .262 \times 10^{4} \)
Subject: Biology
Assertion
Failure of secretion of somatotropin from an early age causes dwarfism in the patient.
Reason
Somatotropin hormone stimulates the body growth and elongation of long
bones
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
When the temperature of a straight rigid rod increases from \( t \) to \( t+\Delta t \), its
moment of inertia changes from I to
\( I+\Delta I . \) If \( \alpha \) be the coefficient of linear
expansion, then \( 2 \alpha \Delta t \) will be equal to.
\( ^{A} \cdot \frac{I}{\Delta I} \)
B. \( I \times \Delta I \)
c. \( \frac{\Delta I}{I} \)
D. \( 2 I \Delta I \)
Subject: Chemistry
Ammonia forms a complex ion \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} \) with copper ions in
alkaline solutions but not in acidic
solutions. What is the reason for it?
A. Copper hydroxide is an amphoteric substance.
B. In acidic solutions, hydration protects copper ions.
C. In acidic solutions, protons coordinate with ammonia molecules forming \( N H_{4}^{+} \) ions and \( N H_{3} \) molecules are no longer available for co-ordination to metal ions.
D. In alkaline solutions, insoluble \( C u(O H)_{2} \) is precipitated out which is soluble in excess of any alkali
Subject: Maths
A ladder of length \( 20 m \) is resting
against a wall \( 10 m \) high such that the
top of the ladder touches the top edge of the wall. Find the distance of the foot of the ladder from the foot of the wall?
A \( \cdot \frac{10}{\sqrt{3}} m \)
в. \( 10 m \)
c. \( 10 \sqrt{3} \mathrm{m} \)
.
D. 30 \( m \)
Subject: Maths
If \( c_{0}, c_{1}, c_{2}, \ldots \ldots c_{n} \) are the coefficients in
the expansion of \( (1+x)^{n}, \) when \( n \) is a
positive integer, prove that
(1) \( c_{0}-c_{1}+c_{2}-c_{3}+\dots \dots+ \)
\( (-1)^{r} c_{r}=(-1)^{r} \frac{\mid n-1}{|\underline{r}| n-r-1} \)
(2) \( c_{0}-2 c_{1}+3 c_{2}-4 c_{3}+\dots \dots+ \)
\( (-1)^{n}(n+1) c_{n}=0 \)
(3) \( c_{0}^{2}-c_{1}^{2}+c_{2}^{2}-c_{3}^{2}+\dots \dots+ \)
\( (-1)^{n} c_{n}^{2}=0, \) or \( (-1)^{\frac{n}{2}} c_{\frac{n}{2}} \)
according as \( n \) is odd or even.
Subject: Maths
Find the area of the shaded region in
figure ,if \( \mathrm{PQ}=24 \mathrm{cm}, \mathrm{PR}=7 \mathrm{cm} \) and \( \mathrm{O} \) is
the centre of the circle.
A \( \cdot 100.98 \mathrm{cm}^{2} \)
B \( \cdot 161.54 \mathrm{cm}^{2} \)
c. \( 101.54 \mathrm{cm}^{2} \)
D. None of these
Subject: Chemistry
Einstein's photo-electric equation
states that \( \boldsymbol{E}_{\boldsymbol{k}}=\boldsymbol{h v}-\boldsymbol{W} . \) In this
equation, \( \boldsymbol{E}_{\boldsymbol{k}} \) refers to:
A. kinetic energy of all ejected electrons
B. mean kinetic energy of emitted electrons
c. minimum kinetic energy of emitted electrons
D. maximum kinetic energy of emitted electrons
Subject: Maths
\begin{tabular}{llllll} 
C.I. & \( 0- \) 4 & 4 8 & \( 8- \) 12 & \( 12- \) 16 & 16 20 \\
\hline
\end{tabular}
19
Find the mode of the following data
A. 10.6
B. 12
c. 12.6
D. 8
Subject: Maths
In an examination \( 70 \% \) students
passed both in Mathematics and Physics \( 85 \% \) passed in Mathematics
and \( 80 \% \) passed in Physics If 30 students have failed in both the
subjects then the total number of students who appeared in the examination is equal to:
A . 900
в. 600
\( c .150 \)
D. 100
Subject: Chemistry
Select the correct statements about
galvanic cells.
This question has multiple correct options
A. Electrons are fed into anode by the oxidation reaction that takes place at the electrode.
B. The anode pushes these electrons into the external circuit and thus, acts as a source of negative charge.
C. The cathode acts as an electron sink and thus, called positive electrode.
D. The algebraic sum of E \( _{O P} \) of anode and E \( _{O P} \) of cathode gives the +ve value for spontaneous process.
Subject: Physics
Match the columns:
\( \begin{array}{ll}\text { i. convex lens } & \text { a. presbyopia } \\ \text { ii. concave lens } & \text { b. cataract } \\ \text { iii. Artificial lens } & \text { c. myopia } \\ \text { iv. focal lens } & \text { d. hypermetropia }\end{array} \)
\( A \cdot \) i-c,ii-d,iii-a,iv-b
B. i-d,ii-c,iii-b,iv-a
C. i-b,ii-c,iii-a,iv-d
D. i-a,ii-b-iii-d,iv-c