AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Define specific latent heat of fusion, \( L_{f} \)
A. The specific heat of fusion of a substance is the quantity of heat required to convert a unit mass of the substance from liquid to gaseous state at its boiling point.
B. The specific heat of fusion of a substance is the quantity of heat required to convert a unit mass of the substance from solid to liquid state at its melting point.
C. The specific heat of fusion of a substance is the quantity of heat required to raise the temperature of unit mass of the substance by \( 1^{\circ} \mathrm{C} \)
D. The specific heat of fusion of a substance is the quantity of heat required to lower the temperature of unit mass of the substance by \( 1^{\circ} \mathrm{C} \)
Subject: Physics
A convex lens of focal length \( 5 \mathrm{cm} \) is
placed at a distance of \( 6 \mathrm{cm} \) from a wall. How far from the lens should an object be placed so as to form its real image on the wall?
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. \( -30 c m \)
\( \mathrm{c} \cdot 1.2 \mathrm{cm} \)
D. -1.2cm
Subject: Physics
Consider 3 identical charges of charge
q placed at the vertices of an equilatera triangle, as shown in the figure. What is the force on one of the charges due to
the others?
\( ^{\mathbf{A}} \cdot \frac{1}{4 \pi \epsilon_{0}} \frac{q^{2}}{l^{2}} \)
B. \( \frac{\sqrt{2}}{4 \pi \epsilon_{0}} \frac{q^{2}}{l^{2}} \)
C. \( \frac{\sqrt{3}}{4 \pi \epsilon_{0}} \frac{q^{2}}{l^{2}} \)
D \( \cdot \frac{2 \sqrt{3}}{4 \pi \epsilon_{0}} \frac{q^{2}}{l^{2}} \)
Subject: Maths
If the magnitudes of two vectors \( \vec{a} \) and \( \vec{b} \) are equal then which one of the following is correct?
A \( \cdot(\vec{a}+\vec{b}) \) is parallel to \( (\vec{a}-\vec{b}) \)
в. \( (\vec{a}+\vec{b}) \bullet \vec{a}-\vec{b} \)
C . \( (\vec{a}+\vec{b}) \) is perpendicular to \( (\vec{a}-\vec{b}) \)
D. None of the above
Subject: Maths
Using substitution method find the value of \( x \) and \( y: \)
\( 4 x+9 y=5 \) and \( -5 x+3 y=8 \)
A. -1 and \( \frac{-2}{5} \)
B. -1 and \( \frac{2}{5} \)
c. -1 and 1
D. 1 and \( \frac{2}{5} \)
Subject: Physics
The electric flux over the surface of a
sphere if it is charged with \( 10 \mu C \) is
A \( \cdot 36 \pi \times 10^{4} \quad N m^{2} / C \)
B . \( 36 \pi \times 10^{-4} \quad N m^{2} / C \)
\( \begin{array}{ll}\text { C. } 36 \pi \times 10^{6} & \text { N } m^{2} / C\end{array} \)
D. \( 36 \pi \times 10^{-6} \quad \mathrm{Nm}^{2} / \mathrm{C} \)
Subject: Physics
A spark is produced between two insulated surfaces maintained at a
potential difference of \( 5 \times 10^{6} V . \) If the
energy output is \( 10^{-5} J \), the charge
transferred during the spark is :
A \( \cdot 5 \times 10^{11} C \)
В. \( 5 \times 10^{-11} C \)
C \( \cdot 2 \times 10^{12} C \)
D. \( 2 \times 10^{-12} C \)
Subject: Physics
A body initially at rest is moving with uniform acceleration a. Its velocity after
n seconds is v. The displacement of the body in last 2 s is :
A \( \cdot \frac{2 v(n-1)}{u} \)
B. \( \frac{v(n-1)}{n} \)
c. \( \frac{v(n+1)}{n} \)
D. \( \frac{2 v(n+1)}{n} \)
Subject: Physics
The coefficient of self induction of two
inductor coils are \( 20 m H \) and \( 40 m H \)
respectively. If the coils are connected
in series so as to support each other and the resultant inductance is \( 80 m H \)
then the value of mutual inductance
between the coils will be
\( \mathbf{A} \cdot 5 m H \)
в. \( 10 m H \)
c. \( 20 m H \)
D. \( 40 m H \)
Subject: Biology
Fermentation is represented by the
equation
\( \mathbf{A} \cdot C_{6} H_{12} O_{6}+6 O_{2} \rightarrow 6 C O_{2}+6 H_{2} O+673 \mathrm{k} \) cal
B \( \cdot C_{6} H_{12} O_{6} \rightarrow 2 C_{2} H_{5} O H+2 C O_{2}+18 k \) cal
\( \mathbf{c} \cdot 6 C O_{2}+12 H_{2} O \rightarrow C_{6} H_{12} O_{6}+6 H_{2} O+6 O_{2} \)
\( \mathbf{D} \cdot 6 C O_{2}+6 H_{2} O \rightarrow C_{6} H_{12} O_{6}+6 O_{2} \)
Subject: Physics
A copper wire with a cross-section area
of \( 2 \times 10^{-6} m^{2} \) has a free electon
density equal to \( 5 \times 10^{22} / c m^{2} . \) If this
wire carries a current of \( 16 A \), the drift
velocity of the electron is?
\( \mathbf{A} \cdot 1 m / s \)
в. \( 0.1 m / s \)
c. \( 0.01 m / s \)
D. \( 0.001 m / s \)
E. \( 0.00001 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Identify the balanced chemical reaction
of chlorine with respect to reactant \( D \)
A \( \cdot F e+C l_{2} \rightarrow F e C l_{3} \)
в. \( 2 F e+3 C l_{2} \rightarrow 2 F e C l_{3} \)
\( \mathrm{c} \cdot 2 \mathrm{Fe}+6 \mathrm{Cl}_{2} \rightarrow 2 \mathrm{FeCl} \)
D. \( F e+C l_{2} \longrightarrow F e C l_{3}+F e C l_{2} \)
Subject: Physics
Two point charges \( (+e) \) and \( (-e) \) are
kept inside a large metallic cube without touching its sides. Electric flux emerging out of the cube is?
A \( \cdot e / \varepsilon_{0} \)
В. - \( -e / \varepsilon_{0} \)
c. zero
D. \( 2 e / \varepsilon_{0} \)
Subject: Physics
Consider two children riding on the merry-go-round Child 1 sits near the edge, child 2 sits closer to the centre.
Let \( v_{1} \) and \( v_{2} \) denote the linear speed of
child 1 and child \( 2, \) respectively. Which of the following is true?
\( A \cdot v_{1}>v_{2} \)
В . \( v_{1}=v_{2} \)
\( \mathrm{c} \cdot v_{1}<v_{2} \)
D. (4) we cannot determine which is true, without mo nformatio
Subject: Maths
Let \( \boldsymbol{E}=\left\{\boldsymbol{x}: \boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}-\boldsymbol{6}=\boldsymbol{0}\right\} \) and
\( \boldsymbol{F}=\{-\mathbf{6}, \mathbf{1}\} . \) Then
A \( . E=F \)
в. \( E \neq F \)
c. \( E \subset F \)
D. \( F \subset E \)
Subject: Physics
Find the magnitude of force acting on
the conductor carrying current \( \boldsymbol{I} \) as
shown in the diagram. The magnitude of
magnetic field is \( B \) and direction is into
the plane of paper:
\( \mathbf{A} \cdot I(2 L+\mu R) B \)
\( \mathbf{B} \cdot I(2 L+R) B \)
\( \mathbf{c} \cdot I(2 L+2 R) B \)
D. none of these
Subject: Physics
In the circuit shown, what will be the
current through the \( 6 V \) zener?
\( \mathbf{A} \cdot 6 m A, \) from \( A \) to \( B \)
B. \( 2 m A \), from A to \( B \)
\( \mathrm{c} .2 \mathrm{mA}, \) from \( \mathrm{B} \) to \( A \)
D. Zero
Subject: Physics
Two rigid boxes containing different ideal gases are placed on a table. Box \( \boldsymbol{A} \) contains one mole of nitrogen at
temperature \( T_{o}, \) while box \( B \) contains one mole of helium 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 (Ignore the heat capacity of boxes).Then, the final temperature of
\( \operatorname{gases}, \boldsymbol{T}_{f}, \) in the terms of \( \boldsymbol{T}_{\boldsymbol{o}} \) is:
\( ^{\mathbf{A}} \cdot T_{f}=\frac{3}{7} T_{0} \)
\( ^{\mathrm{B}} \cdot_{T_{f}}=\frac{7}{3} T_{0} \)
\( ^{\mathbf{C}} \cdot_{T_{f}}=\frac{3}{2} T_{0} \)
\( ^{\mathrm{D}} \cdot_{T_{f}}=\frac{5}{2} T_{0} \)
Subject: Maths
Let \( r \) be the range of \( n(\forall n \geq 1) \)
observations \( \boldsymbol{x}_{1} \boldsymbol{x}_{2} \ldots, \boldsymbol{x}_{\boldsymbol{n}} \) if \( \boldsymbol{S}= \)
\( \sqrt{\frac{\sum_{t=1}^{n}\left(x_{i}-\bar{x}\right)^{2}}{n-1}}, \) then
\( ^{\mathbf{A}} \cdot_{S}<r \sqrt{\frac{n^{2}+1}{n-1}} \)
в. \( s \geq r \sqrt{\frac{n}{n-1}} \)
c. \( s=r \sqrt{\frac{n}{n-1}} \)
D. \( s<r \sqrt{\frac{n}{n-1}} \)
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}-\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{5} & \mathbf{7} & \mathbf{9} \\ -\mathbf{2} & \mathbf{1} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{array}\right], \) then verify that
\( (i)(A+B)^{T}=A^{T}+B^{T} \)
\( (i i)(A-B)^{T}=A^{T}-B^{T} \)
Subject: Chemistry
The correct set the quantum unpaired electron of chlorine atom is:
A \( \cdot n=2,1=1, m_{1}=0 \)
B . \( n=2,1=1, m_{1}=1 \)
c. \( n=3,1=1, m_{1}=1 \)
D. \( n=3,1=0, m_{1}=0 \)
Subject: Physics
A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is 'a' and it
is rolling without slipping then the
value of 'F' is:
\( A \cdot 2 \mathrm{ma} \)
B \cdot \( \frac{3}{2} \mathrm{ma} \)
\( c . \) ma
D・言ma
Subject: Biology
Select the correct option:
Match column I with column II and
select the correct option from the codes
given below:
Column I (Parts of alimentary canal of earthworm)
(A) Buccal cavity
(i) \( 1-3 \)
(B) Pharynx
(ii) \( 3-4 \)
(C) Oesophagus
(iii) 5-7
(D) Gizzard
(iv) \( 8-9 \)
(E) Stomach
\( (v) 9-14 \)
(F) Intestine
(vi) 15 to last
(G) Typhlosole
(vii) \( 26-35 \)
A \( \cdot \) A- (i); B- (ii); C- (iii);
D- (iv); E- (v); F- (vi); G- (vii)
B. \( A-(i) ; B-(i i) ; C-(i i i) ; D-(v) ; E-(i v) ; F-(v i) ; G-(v i i) \)
C. \( A-(i) ; B-(i i i) ; C-(i i) ; D-(i v) ; E-(v) ; F-(v i i) ; G-(v i) \)
D. A- (i); B- (iii); C\( (v) ; E-(i v) ; F-(v i i) ; G-(v i) \)
Subject: Maths
If \( x^{2}-(a+b) x+a b=0, \) then the
value of \( (x-a)^{2}+(x-b)^{2} \) is
\( \mathbf{A} \cdot a^{2}+b^{2} \)
B. \( (a+b)^{2} \)
c. \( (a-b)^{2} \)
D. \( a^{2}-b^{2} \)
Subject: Physics
The relation between time \( t \) and
distance \( x \) is \( t=a x^{2}+b x, \) where \( a \) and
\( b \) are constants. The acceleration is:
A \( --2 a v^{3} \)
3 \( ^{-2 a v} \)
B . \( 2 a v^{2} \)
c. \( -2 a v^{2} \)
D. \( 2 b v^{2} \)
Subject: Maths
A body, initially at rest, is acted upon by four forces \( \boldsymbol{F}_{\mathbf{1}}=\hat{\boldsymbol{i}}+\widehat{\boldsymbol{k}}, \boldsymbol{F}_{2}=\mathbf{2} \hat{\boldsymbol{j}}+ \)
\( \mathbf{3} \widehat{k}, \boldsymbol{F}_{3}=\mathbf{3} \hat{\mathbf{i}} \) and \( \boldsymbol{F}_{4}=\mathbf{3} \hat{\mathbf{j}}-\mathbf{4} \hat{\mathbf{i}} . \) In which
plane will the body move?
A. x-y plane
B. x-z plane
c. \( y \) -z plane
D. none of these
Subject: Chemistry
Calculate the longest wavelength in \( \boldsymbol{A} \) \( \left(1 \dot{A}=10^{-10} m\right) \) in the Balmer series of singly ionized helium \( H e^{+} . \) Select the
correct answer. lgnore the nuclear
motion in your calculation.
в. \( 1641.1 \dot{A} \)
\( c .6569 \hat{A} \)
D. \( 3249 \dot{h} \)
Subject: Physics
Assertion
A cricket player while catching a bal lowers his hands to save himself from
getting hurt.
Reason
The impulsive force on hands is reduced by increasing the time of action.
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: Maths
The function \( x(x-1)(x-2) \) attains its
maximum value when \( x \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( 1+\frac{1}{\sqrt{3}} \)
c. \( _{1-} \frac{1}{\sqrt{3}} \)
D. \( 1 \pm \sqrt{3} \)
Subject: Physics
If the relative permeability of a medium
is \( \mu_{r} \) and its dielectric constant is \( \varepsilon_{r} \)
then the velocity of light in that medium will be
A \( \cdot \sqrt{\frac{\mu_{r}}{\varepsilon_{r}}} \)
в. \( \frac{1}{\sqrt{\mu_{r} \varepsilon_{r}}} \)
C \( \cdot \sqrt{\mu_{r} \varepsilon_{r} / \mu_{\varepsilon_{0}}} \)
D. \( \sqrt{\mu_{e} \varepsilon_{0} / \mu_{x} \varepsilon_{r}} \)
Subject: Maths
If the lines \( 3 x+2 y-5=0,2 x-5 y+ \)
\( \mathbf{3}=\mathbf{0}, \mathbf{5 x}+\mathbf{b y}+\mathbf{c}=\mathbf{0} \) are concurrent
then \( \mathbf{b}+\mathbf{c}= \)
A. 7
B. - -
\( c \cdot 6 \)
D.
Subject: Chemistry
What are the products obtained upon the ozonolysis of 2 -pentene? This question has multiple correct options
A. \( C H_{3} C H_{2} C H O \)
в. \( C H_{3} C H O \)
c. \( C H_{3} \) COCH\( _{3} \)
D. \( C H_{3} C O C H_{2} C H_{3} \)
Subject: Chemistry
For a particular reaction \( \triangle \boldsymbol{H}^{0}= \)
\( -76.6 K J \) and \( \Delta S^{0}=226 J K^{-1} . \) This
reaction is:
A. spontaneous at all temperatures
B. non-spontaneous at all temperatures
C. spontaneous at temperature below \( 66^{\circ} \mathrm{C} \)
D. spontaneous at temperature above \( 66^{\circ} \mathrm{C} \)
Subject: Maths
Assertion
If \( \boldsymbol{x}<\mathbf{0}, \tan ^{-1} \boldsymbol{x}+\tan ^{-1} \frac{\mathbf{1}}{\boldsymbol{x}}=\frac{\boldsymbol{\pi}}{\mathbf{2}} \)
Reason \( \tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2} \forall x \in R \)
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
A \( 12 k g \) bomb at rest explodes into two
pieces of \( 4 k g \) and \( 8 k g . \) If the momentum
of \( 4 k g \) piece is \( 20 N s, \) the kinetic energy
of the \( 8 k g \) piece is:
A \( .25 J \)
B. \( 20 J \)
c. \( 50 J \)
D. \( 40 J \)
Subject: Maths
Let \( m \) be a positive integer. Then al pairs of integers \( (x, y) \) such that \( x^{2}\left(x^{2}+y^{2}\right)=y^{m+1} \) is \( x=t^{5}+t^{3}, y= \)
\( t^{4}+t^{2} \)
If true then enter 1 and if false then
enter 0
A. True
B. False
Subject: Physics
A \( 1000 \Omega \) resistance and a capacitor of
100 \( \Omega \) resistance are connected in
series a \( 220 V \) source. when the
capacitor is \( 50 \% \) charged, the value of the displacement current is.
A \( .11 . \sqrt{2} A \)
в. \( 2.2 A \)
\( c .11 A \)
D. \( 4.4 A \)
Subject: Chemistry
What is the IUPAC name of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\left(\boldsymbol{O} \boldsymbol{H}_{2}\right) \boldsymbol{I}\right] \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. Tetraammineaquaiodocobalt(III) sulphate
B. Tetraammineaquaiodocobalt(II) sulphate
C. Tetraammineaquaiodocobaltate(III) sulphate
D. None of these
Subject: Physics
A particle is constrained to move along
a straight line. The graph in the
adjoining figure shows the distance \( s \)
moved by the particle in time \( t \)
measured from the starting time. The
shape of the curve indicates that
A. Acceleration of the particle is increasing at \( X \)
B. The speed of the particle is maximum at the point \( Z \)
C. The speed of the particle \( X \) is greater than that \( Z \)
D. The particle is at rest at the point \( Y \)
Subject: Physics
Textbooks on science may give you a wrong impression that studying science is dry and all too serious and
that scientists are absent-minded
introverts who never laugh or grin. This image of science and scientists is patently false. Scientists, like anyother group of humans, have their share of humorists, and many have led their
lives with a great sense of fun and adventure, even as they seriously pursued their scientific work. Two great physicists of this genre are Gamow and
Feynman. You will enjoy reading their books listed in the Bibliography.
Subject: Chemistry
A compound which is having hydrogen and carbon is called hydrocarbon. A hydrocarbon is heated in an excess of oxygen to produce 58.67 g of \( C O_{2} \) and 27 g of \( H_{2} O . \) What is the empirical formula of the hydrocarbon?
A. \( C_{3} H_{9} \)
в. \( C_{4} H_{12} \)
\( \mathbf{c} \cdot C_{8} H_{18} \)
D. \( C_{4} H_{9} \)
Subject: Maths
If the dr's the line are \( (1+\lambda, 1-\lambda, 2) \)
and it makes an angle \( 60^{\circ} \) with the \( Y \) -
axis then \( \lambda \) is
A \( .1 \pm \sqrt{3} \)
B. \( 4 \pm \sqrt{5} \)
c. \( 2 \pm 2 \sqrt{3} \)
D. \( 2 \pm \sqrt{5} \)
Subject: Maths
If \( \boldsymbol{x}=\cos ^{n} \boldsymbol{\theta}, \boldsymbol{y}=\sin ^{n} \boldsymbol{\theta} \operatorname{then} \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}= \)
A \( \cdot \frac{n}{n-1} \cdot \frac{\cos ^{2 n-1} \theta}{\sin ^{n-3} \theta} \)
B. \( \frac{n-2}{n} \cdot \frac{\tan ^{n-3} \theta}{\cos ^{n+1} \theta \sin \theta} \)
c. \( n-1 . \tan ^{n-2} \theta \cdot \sec ^{2} \theta \)
D. \( \quad n \frac{\sin ^{n-1} \theta}{\cos ^{n-2} \theta} \)
Subject: Maths
The possible value(s) of ' \( \boldsymbol{\theta} \) ' satisfying
the equation \( \sin ^{2} \theta \tan \theta+ \)
\( \cos ^{2} \theta \cot \theta-\sin 2 \theta=1+\tan \theta+ \)
\( \cot \theta, \) where \( \theta \in[0, \pi] \) is/are
A.
в. \( \pi \)
c. \( \frac{7 \pi}{12} \)
D. None of these
Subject: Chemistry
A compound (A) when reacted with ammonia gave (B),(B) when treated with bromine and caustic powder produced (C), (C) on treatment with
\( N a N O_{2} \) and \( H C l \) at \( 0^{\circ} \mathrm{C} \) and then
produce ortho-cresol. Compound (A) is:
A. o-chlorotoluene
B. o-toluic acid
c. m-toluic acid
D. n-bromotoluene
Subject: Biology
Bryophytes are the first land plants but incompletely adapted to land conditions as
(i) Plant body is parenchymatous.
(ii) Protonema is present.
(iii) Male gametes are mobile.
(iv) Stomata are absent in liverworts.
Which of the above-mentioned
statement(s) is/are correct?
A. only (i)
B. Only (iii)
c. (i), (ii) and (iii)
D. (i), (ii), (iii) and (iv)
Subject: Physics
\( 2 \mathrm{kg} \) of ice at \( -20^{\circ} \mathrm{C} \) is mixed with \( 5 \mathrm{kg} \)
of water at \( 20^{\circ} C \) in an insulating vessel having a negligible heat capacity

Calculate the final mass of water in the
vessel. It is given that the specific heats of water and ice are \( 1 k c a l k g^{-1} o C^{-1} \) and \( 0.5 k \) calk \( g^{-1} o C^{-1} \) respectively and the latent heat of fusion of ice is 80
kcal/kg.
\( A \cdot 5 \mathrm{kg} \)
B. \( 6 \mathrm{kg} \)
\( c \cdot 7 k g \)
D. 8 kg
Subject: Chemistry
Which of the following is wrong
statement?
A. Larger the \( T_{c} / P_{C} \) for a gas, larger would be excluded volume
B. Critical temperature, \( T_{C}> \) Boyle's temperature, \( T_{B} \) for any gas.
\( \mathbf{C} \cdot\left[\frac{\partial T}{\partial P}\right]_{T_{i}}=0 \) for a van der Waal's gas.
D \( \cdot\left[\frac{\partial P}{\partial V}\right]_{T_{C}}=0 \) for a van der Waal's gas.
Subject: Physics
\( \ln \operatorname{an} A C \) circuit \( V \) and \( I \) are given \( V= \)
\( 100 \sin (100 t) V \) and \( I= \)
\( \mathbf{1 0 0} \sin (\mathbf{1 0 0} t+\boldsymbol{\pi} / \mathbf{3}) \boldsymbol{m m} . \) The power
dissipated in the circuit is:
A \( \cdot 10^{4} \) watt
B. 10 watt
c. 2.5 watt
D. 5 watt
Subject: Physics
A solld sphere of radıus \( r \) Is tloating at
the interfare of two immiscible liquids
of densities \( p_{1} \) and \( p_{2}\left(p_{2}>p_{1}\right), \) half of
its volume lying in each. The height of
the upper liquid column from the
interfare of the two liquids is \( h . \) The
force exerted on the upper liquid is
(atmosphere pressure \( =p_{o} \) and
acceleration due to gravity is \( g \) ):
\( ^{\mathbf{A}} \cdot p_{0} \pi r^{2}+\left(h-\frac{2}{3 r}\right) \pi r^{2} p_{1} g \)
B. \( \left(h-\frac{2}{3 r}\right) \pi r^{2} p_{1} g \)
c. \( \frac{2}{3} \pi r^{3} p_{1} g \)
\( \mathbf{D} \cdot P_{0} \times \pi r^{2} \)
Subject: Physics
To measure
This question has multiple correct options
A. you will measure the potential drop across resistor till it is minimum on varying frequency
B. you will measure the voltage across \( L \) and \( C \) at various frequencies until \( V_{L}=V_{D} \)
C. you will measure the voltage across L and C at various frequencies until \( V_{L}=V_{C} \)
D. you will measure voltage across L until is minimum at a particular frequency
Subject: Physics
The vector \( \vec{c} \) is perpendicular to the vectors \( \overrightarrow{\boldsymbol{a}}=(\mathbf{2},-\mathbf{3}, \mathbf{1}), \overrightarrow{\boldsymbol{b}}=(\mathbf{1},-\mathbf{2}, \mathbf{3}) \)
and satisfies the condition \( \vec{c} .(\hat{i}+2 \hat{j}- \) \( \mathbf{7} \hat{k})=10 . \) Then the vector \( \hat{c}= \)
\( A \cdot(7,5,1) \)
B. (-7,-5,-1)
\( c \cdot(1,1,-1) \)
\( c \)
\( D . \) none
Subject: Chemistry
Assertion
In the Contact process, vanadium
pentoxide is preferred to platinum during the catalytic oxidation of sulphur dioxide.
Reason
Vanadium pentoxide is cheaper and
easily available as compared to platinum
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
During lactic acid fermentation,
\( A \cdot O_{2} \) is used, \( C O_{2} \) is not liberated.
B. \( O_{2} \) is not used, \( C O_{2} \) is liberated.
\( \mathrm{C} \cdot \mathrm{O}_{2} \) is used, \( \mathrm{CO}_{2} \) is liberated.
D. Neither \( O_{2} \) is used, nor \( C O_{2} \) is liberated.
Subject: Physics
Two equally charged identical metal spheres \( A \) and \( B \) repel each other with a force F. Another identical uncharged sphere \( C \) is touched to \( A \) and then placed midway between \( A \) and \( B \). The net force on
\( \mathrm{C} \) is in the direction:
A. \( F \) towards \( A \)
B. \( F \) towards
\( \mathrm{c} .2 F \) towards \( \mathrm{A} \)
D. \( 2 F \) towards \( B \)
Subject: Physics
A sphere ' \( A \) ' is placed at frictionless table. another sphere ' \( B \) ' is suspended
as shown in fig. both the spheres are identical in all respects.equal quantity of heat is supplied to both sphere all kind of heat loses are neglected the
final temperature of \( \boldsymbol{A} \) and \( \boldsymbol{B} \) are \( \boldsymbol{T}_{\boldsymbol{A}} \)
and \( T_{B} \) respectively then :
A \( \cdot T_{A}=T_{B} \)
В . \( T_{A}<T_{B} \)
\( c \cdot T_{A}>T_{B} \)
D. data is insufficient
Subject: Physics
A hydrogen-like atom (atomic number
\( Z \) ) is in a higher excited state of
quantum number ' \( n \) '. This excited atom can make a transition to the first
excited state by successively emitting two photons of energies \( 10.2 e V \) and
17.0 \( e V \), respectively. Alternatively, the
atom from the same excited state can
make a transition to the second excited
state by successively emitting two photons of energies \( 4.25 e V \) and \( 5.95 e V \)
respectively. The values of \( n \) and \( Z \) are,
respectively
A. 6 and 6
B. 3 and 3
c. 6 and 3
D. 3 and 6
Subject: Physics
The slope of a velocity-time graph for the free fall of a body under gravity, starting from rest is (Take \( \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2} \)
.)
A \( \cdot 10 m / s^{2} \)
В. \( -10 m / s^{2} \)
c. \( 0 m / s^{2} \)
D. \( 1 m / s^{2} \)
Subject: Physics
A \( 7.2 V \) zener diode \( \left(7.2 V \text { at } 20^{\circ} C\right) \) has a positive temperature coefficient of
\( 0.0007 /^{o} C . \) What is the zener voltage at
\( 45^{\circ} \mathrm{C} ? \)
A \( .7 .20 V \)
B. \( 7.33 V \)
c. \( 7.13 V \)
D. \( 6.36 V \)
Subject: Physics
Two concentric spheres kept in air have radii 'R' and 'r'. They have similar charge
and equal surface charge density' \( \sigma^{\prime} \) The electric potential at their common
centre is. \( \left(\epsilon_{0}= \) permittivity of free \right. space \( ) \)
A \( \cdot \frac{\sigma(R+r)}{\epsilon_{0}} \)
в. \( \frac{\sigma(R-r)}{\epsilon_{0}} \)
c. \( \frac{\sigma(R+r)}{2 \epsilon_{0}} \)
D. \( \frac{\sigma(R+r)}{4 \epsilon_{0}} \)
Subject: Chemistry
The mechanism of the reaction:
\( N u^{-}+R-X \rightarrow R-N u+X^{-} \) is:
\( N u^{-}+R-X \rightarrow[\text { Transition state }] \)
(slow) [Transition state] \( \rightarrow N u-R+ \)
\( X^{-}(\text {fast }) \) The rate of reaction can be
increased by:
A. increasing the cone, of \( N u^{-} \) only
B. increasing the core, of \( R-X \) only
c. increasing the cone, of both \( N u^{-} \) and \( R-X \)
D. decreasing the cone, of both \( N u^{-} \) and \( R-X \)
Subject: Maths
If \( \boldsymbol{y}=|\cos \boldsymbol{x}|+|\sin \boldsymbol{x}|, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}= \)
\( \frac{2 \pi}{3} \) is
A \( \cdot \frac{1-\sqrt{3}}{2} \)
в. 0
c. \( \frac{\sqrt{3}-1}{2} \)
D. \( \frac{\sqrt{3}+1}{2} \)
Subject: Physics
A man of mass \( 60 k g \) climbs up a \( 20 m \) long staircase on the top of a building
10 \( m \) high. What is the work done by
him? \( \left(\text { Takeg }=10 m s^{-2}\right) \)
A. \( 12 k J \) J 5 J. 12 .
в. \( 6 k J \)
c. \( 3 k J \)
D. \( 18 k J \)