AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
\( H_{2} O_{2} \) is decomposed to \( H_{2} O \) and \( O, \) in
the following sequence of reactions:
\( \mathbf{I} \boldsymbol{H}_{2} \boldsymbol{O}_{2(\boldsymbol{a q})}+\boldsymbol{I}_{(\boldsymbol{a} q)}^{-} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)}+\boldsymbol{I} \boldsymbol{O}_{(\boldsymbol{a} \boldsymbol{q})}^{-} \)
ii) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2(a q)}+\boldsymbol{I}_{(a q)}^{-} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)}+ \)
\( \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{I} \boldsymbol{O}_{(\boldsymbol{a} \boldsymbol{q})}^{-} \)
(a) Write the chemical equation for the overall reaction.
(b) Identify the species that acts as a
catalyst.
(c) Identify the intermediate.
Subject: Chemistry
Determine the standard emf of the cell
and standard free energy change of the cell reaction.
\( Z n / Z n^{2+} \| N i^{2+} / N \)
\( \boldsymbol{E}^{o} \boldsymbol{Z} \boldsymbol{n}^{2+} / \boldsymbol{Z} \boldsymbol{n}=-\mathbf{0 . 7 6} \boldsymbol{V} \)
\( \boldsymbol{E}^{o} \boldsymbol{N} \boldsymbol{i}^{2+} / \boldsymbol{N} \boldsymbol{i}=-\mathbf{0 . 2 5} \boldsymbol{V} \)
Subject: Physics
Which of the following statement(s)
is/are correct?
This question has multiple correct options
A. Conductors are materials that allow the flow of electric current, whereas dielectric (insulators) do not
B. The main difference between conductor and dielectric
behavior is the amount of available free electrons
C. Not all conductors have the same level of conductivity, just as not all insulators are resistant to electric
current.
D. Both A and B only
Subject: Physics
The dimensions of the ratio \( \frac{\text { force } \times \text { distance }}{\text { power }} \) are
\( \begin{array}{lll}\mathbf{A} \cdot M & L^{o} & T^{o}\end{array} \)
\( \begin{array}{lll}\text { В. } M^{o} & L & T^{o}\end{array} \)
\( \begin{array}{lll}\mathrm{c} \cdot M^{2} & L & T^{0}\end{array} \)
\( \begin{array}{lll}\text { D. } M^{o} & L^{o} & T\end{array} \)
Subject: Chemistry
The final acid obtained during the
manufacture of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) by contact
process is:
A \( \cdot H_{2} S O_{4} \) (conc.)
B . \( H_{2} S O_{4} \) (dil)
c. \( H C I \)
D. \( H_{2} S_{2} O_{7} \)
Subject: Physics
A body starts from rest with uniform acceleration. If its velocity after \( n \) second is \( v, \) then its displacement in
last two seconds is:
A \( \cdot \frac{2 v(n+1)}{n} \)
B. \( \frac{v(n+1)}{n} \)
c. \( \frac{v(n-1)}{n} \)
D. \( \frac{2 v(n-1)}{n} \)
Subject: Physics
A ball of mass \( \mathrm{m} \) and radius \( \mathrm{r} \) is
released in the viscous liquid. The value of its terminal velocity is proportional to
\( ^{A} \cdot\left(\frac{1}{r}\right) \) only
в. \( \frac{m}{r} \)
c. \( \left(\frac{m}{r}\right)^{1 / 2} \)
D. m only
Subject: Chemistry
Q Type your question-
with their correct arrangements.
List List - II
(i) Random Copolymer
1) \( (A- \)
\( A-A-A)-(B-B-B-B)-(A-A-A) \)
(ii) Block Copolymer
2) - A -
B-A-B-A.
(iii) Graft Copolymer
3) -A-
B-A-A-A-B-B-A-B-A-A-
B-B-B-B-
(iv) Alternating Copolymer
4)- \( A \)
\( \mathbf{A}-\mathbf{A}-\mathbf{A}-\mathbf{A}-\mathbf{A}-\mathbf{A}-\mathbf{A}-\mathbf{A}- \)
B-
A. (i)-1, (ii)-2, (iii)-3, (iv) -4
B. (i)-2, (ii)-4, (iii)-3, (iv)- -
c. (ii)-3, (ii)-1, (iii)-4, (iv)-2
D. (i)-4, (ii)-3, (iii)-1, (iv)-2
Subject: Physics
If \( C \) is the value of the capacitance of a capacitor filled with a given dielectric and \( a \) is the capacitance of an identical capacitor in a vacuum, the dielectric constant, symbolized by the Greek letter kappa,, is simply expressed as
A \( \cdot \frac{C}{a} \)
B. \( \frac{a}{C} \)
c. \( C \times a \)
D. None
Subject: Physics
Find out the increase in temperature of
\( 50 g \) block of solid marble (specific heat
\( =\mathbf{0 . 9 k J} / k g), \) originally at 20 if it
absorbs \( 100 \mathrm{J} \) of heat \( ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 4 \)
D. 10
E. 20
Subject: Biology
\( K_{m} \) value of enzyme is substrate
concentration at
\( A \cdot 10 \vee_{\max } \)
B. \( 0.5 / 1 \mathrm{V}_{\max } \)
c. \( 1 / 2 \mathrm{v}_{\max } \)
D. \( 4 / 5 \mathrm{V}_{\max } \)
Subject: Maths
If \( A \) is square matrix of order \( 3, \) then
\( \left|A d j\left(A d j A^{2}\right)\right|= \)
A \( \cdot|A|^{2} \)
B \( \cdot|A|^{4} \)
c. \( |A|^{8} \)
D・ \( |A|^{16} \)
Subject: Biology
The given figure shows diagrammatic
representation of exchange of gases at
the alveolus and the body tissues with
blood and transport of oxygen and
carbon dioxide. Identify the blood
vessels \( A \) to \( D \)
A. Systemic vein Pulmonary artery Pulmonary vein Systemic artery
B. Systemic artery Pulmonary artery Pulmonary vein Systemic vein
C. Pulmonary artery Systemic vein Pulmonary vein Systemic artery
D. Systemic vein Pulmonary vein Pulmonary artery Systemic artery
Subject: Maths
Consider \( \boldsymbol{f}:\{1,2,3\} \rightarrow\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} \) and
\( \boldsymbol{g}:\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} \rightarrow\{\text { apple,ball,cat }\} \) defined
as \( \boldsymbol{f}(\mathbf{1})=\boldsymbol{a}, \boldsymbol{f}(\mathbf{2})=\boldsymbol{b}, \boldsymbol{f}(\mathbf{3})=\boldsymbol{c}, \boldsymbol{g}(\boldsymbol{a})= \)
apple, \( g(b)= \) ball and \( g(c)= \) cat. Show
that \( f, g \) and \( g \circ f \) are invertible. Find
\( f^{-1}, g^{-1} \) and \( (g \circ f)^{-1} \) and show that \( (g \circ f)^{-1}=f^{-1} \circ g^{-1} \)
Subject: Chemistry
The heat of formation for \( C O_{2} \) is given
as \( \triangle \mathrm{H}=-94.2 \mathrm{kcal} / \mathrm{mole} . \) The negative
value of \( \triangle \mathrm{H} \) indicates that:
A. \( C O_{2} \) is formed form its elements by an endothermic reaction
B. The reaction of carbon with oxygen occurs rapidly at \( 25^{\circ} \mathrm{C} \)
C. The enthalpy of the product \( C O_{2} \) is less than that of the reactants, \( O_{2} \) and \( c \)
D. No heat is liberated when carbon is oxidized
E. \( 94.2 \mathrm{kcal} \) must be added to oxidize one mole of carbon
Subject: Maths
Vector equation of line \( \frac{\mathbf{3}-\boldsymbol{x}}{\mathbf{3}}= \)
\( \frac{2 y-3}{5}=\frac{z}{2} \) is \( _{--}-------k \in R \)
A \( \cdot \bar{r}=(3,5,2)+k(3,3,0) \)
B \( \cdot \quad \bar{r}=\left(3, \frac{3}{2}, 0\right)+k(-6,5,4) \)
c. \( \bar{r}=(3,3,0)+k(3,5,2) \)
D \( \cdot_{\bar{r}}=(-6,5,4)+k\left(3, \frac{3}{2}, 0\right) \)
Subject: Maths
If \( \sum_{i=1}^{9}\left(x_{i}-5\right)=9 \) and \( \sum_{i=1}^{9}\left(x_{i}-5\right)^{2}= \)
\( 45, \) then the standard deviation of the 9
\( \operatorname{times} x_{1}, x_{2}, \dots, x_{9} \) is
A . 9
B. 4
\( c \cdot 3 \)
\( D \cdot 2 \)
\( E \)
Subject: Maths
Evaluate the following limits. \( \lim _{x \rightarrow 0} \frac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a^{2}+a x}} \)
A \( \cdot \frac{1}{2 \sqrt{a}} \)
B. \( \frac{1}{2 a \sqrt{a}} \)
c. \( \frac{1}{2 a} \)
D. None of these
Subject: Chemistry
In the equation \( \boldsymbol{h} \boldsymbol{v}=\boldsymbol{h} \boldsymbol{v}_{0}+\frac{1}{2} \boldsymbol{m}_{e} \boldsymbol{v}^{2}, \boldsymbol{v}_{0} \)
is known as:
A. work function
B. velocity of ejected electron
c. threshold frequency
D. frequency of photon
Subject: Maths
If \( \vec{A} \times \vec{B}=\vec{C}, \) which of the following
options is wrong?
\( A \cdot \vec{C} \) is \( \perp \) to \( \vec{A} \)
B \cdot \( \vec{C} \) is \( \perp \) to \( \vec{B} \)
c. \( \vec{C} \) is \( \perp(\vec{A}+\vec{B}) \)
D \( \cdot \vec{C} \) is \( \perp \) to \( (\vec{A} \times \vec{B}) \)
Subject: Physics
The force of attraction between two
masses each of \( 1 k g \) kept at a
separation of \( 1 m \) is:
\( \mathbf{A} \cdot 9.8 N \)
B. \( 6.7 N \)
c. \( 980 N \)
D. \( 6.7 \times 10^{-11} N \)
Subject: Physics
A boy sitting on the top most berth in the compartment of a train which is
just going to stop on the railway station, drops an apple aiming at the open hand of his brother situated vertically below his hands at a distance of about \( 2 \mathrm{m} \)
The apple will fall
A. In the hand of his brother
B. Slightly away from the hand of his brother in the direction of the motion of the train
c. Slightly away from the hands of his brother in the direction opposite to the direction of the motion of the train
D. None of these
Subject: Physics
In a certain oscillatory system, the amplitude of motion is \( 5 \mathrm{m} \) and the time
period is 4 s. The time taken by the particle for passing between points which are at distance of \( 4 \mathrm{m} \) and \( 2 \mathrm{m} \)
from the centre and on the same side of
it will be
A. 0.30 s
B. 0.32
c. 0.33
D. 0.35
Subject: Chemistry
Arrange the following in order of decreasing acidic strength. nitrophenol
(1), p-cresol (II), m-cresol phenol (IV) :
A \( . I>I V>I I>I I I \)
\( I \)
B. \( I V>I I I>I I>I \)
c. \( I>I I>I I I>I V \)
\( . I I I>I I>I>I V \)
\( V \)
Subject: Maths
In a right triangle the square of the hypotenuse is equal to twice the product of the legs. One of the acute angles of the triangle is:
A \( \cdot 15^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
\( E \cdot 75^{\circ} \)
Subject: Physics
A 60 -kg person on a merry-go round is travelling in a circle with a radius of \( 3 m \) at a speed of \( 6 m / s . \) What is the magnitude of the net force experienced by this person?
A . zero
B. \( 60 N \)
c. \( 180 N \)
D. \( 600 N \)
E. \( 720 N \)
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}\}, \boldsymbol{B}=\{\boldsymbol{x}, \boldsymbol{y}\}, \) find
\( \boldsymbol{A} \boldsymbol{X} \boldsymbol{B}, \boldsymbol{B} \boldsymbol{X} \boldsymbol{A}, \boldsymbol{A} \boldsymbol{X} \boldsymbol{A}, \boldsymbol{B} \boldsymbol{X} \boldsymbol{B} \)
Subject: Chemistry
What is the normality of aqueous
solution of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) having \( \boldsymbol{p} \boldsymbol{H}=\mathbf{1} ? \)
A. \( 1 N \)
B. \( 0.05 N \)
\( c \cdot 0.1 N \)
D. \( 0.5 N \)
Subject: Chemistry
Choose the correct answer among the alternatives given :
Classify the following compounds as primary, secondary and tertiary halides.
(i) 1-Bromobut-2-ene
(ii) \( 4- \) Bromopent.2-ene
(iii) 2-Bromo-2-methylpropane
A. (i)-secondary, (ii)-tertiary, (iii)-primary
B. (i)-secondary, (ii)-primary, (iii)-tertiary
c. (i)-primary,
(ii)-tertiary, (iii)-secondary
D. (i)-primary, (ii)-secondary, (iii)-tertiary
Subject: Maths
The side of an equilateral triangle is \( 20 \sqrt{3} \mathrm{cm} . \) The numerical value of the
radius of the circle circumscribing the triangle is:
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
в. \( 20 \sqrt{3} \mathrm{cm} \)
c. \( 20 \pi c m \)
D. \( \frac{20}{\pi} \)
Subject: Physics
The energy of the electron of hydrogen
atom in its nth orbit is given by \( \boldsymbol{E}_{\boldsymbol{n}}= \) \( -\frac{13.6}{n^{2}} \) electron volt(eV). Based on this
formula
(i) Draw different energy levels corresponding to \( n=1,2,3,4,5,6 \) and
\( \infty \)
(ii) Show Lyman and Baler series of
emission spectrum of hydrogen atom by drawing various electronic transitions.
(iii) Find the ionisation energy of
hydrogen atom.
Subject: Physics
A hydraulic press has a ram of \( 15 \mathrm{cm} \) diameter and plunger is \( 1.5 \mathrm{cm} . \) It is required to lift a weight of 1 tonne. The force required on plunger is
A. \( 10 \mathrm{kg} \)
B. \( 100 \mathrm{kg} \)
c. \( 1000 \mathrm{kg} \)
\( D \cdot 1 \mathrm{kg} \)
Subject: Maths
The area bounded by the curves \( y= \)
\( \sqrt{5-x^{2}} \) and \( y=|x-1| \) is
\( ^{\mathbf{A}} \cdot\left(\frac{5 \pi}{4}-2\right) \) square unit
B. \( \frac{(5 \pi-2)}{4} \) square units
c. \( \frac{(5 \pi-2)}{2} \) square units
D \( \cdot\left(\frac{5 \pi}{2}-2\right) \) square unit
Subject: Chemistry
Which of the following oxide has the maximum basicity?
A. \( \operatorname{Pr}_{2} \) O \( _{3} \)
в. \( L a_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{Sm}_{2} \mathrm{O}_{3} \)
D. \( G d_{2} O_{3} \)
Subject: Maths
Factors of \( \boldsymbol{x}^{\boldsymbol{4}}-(\boldsymbol{y}+\boldsymbol{z})^{\boldsymbol{4}} \) are
This question has multiple correct options
\( \mathbf{A} \cdot(x-y-z) \)
B.
\( \mathbf{c} \cdot(x+y+z) \)
D. \( \left(x^{2}+y^{2}+z^{2}+2 y z\right) \)
Subject: Maths
If \( \vec{r}=3 \hat{i}+2 \hat{j}-5 \hat{k}, \vec{a}=2 \hat{i}-\hat{j}+\hat{k} \)
\( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\boldsymbol{2} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=-\boldsymbol{2} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}-\boldsymbol{3} \hat{\boldsymbol{k}} \)
such that \( \vec{r}=\lambda \vec{a}+\mu \vec{b}+v \vec{c}, \) then \( \mu, \frac{\lambda}{2} \)
\( \boldsymbol{v} \) are in
A. \( H . P \)
в. \( G . P \)
c. \( A . G . P \)
D. A.P
Subject: Maths
The differential equation representing the family of curves given by \( \boldsymbol{y}= \)
\( \boldsymbol{a} e^{-\boldsymbol{3} x}+\boldsymbol{b}, \) where \( \boldsymbol{a} \) and \( \boldsymbol{b} \) are arbitrary
constants, is :
\( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{3} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-\boldsymbol{2} \boldsymbol{y}=\mathbf{0} \)
A \( \cdot \frac{d^{2} y}{d x^{2}}+3 \frac{d y}{d x}-2 y=0 \)
B. \( \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}=0 \)
c. \( \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}-2 y=0 \)
D \( \cdot \frac{d^{2} y}{d x^{2}}+3 \frac{d y}{d x}+2 y=0 \)
E \( \cdot \frac{d^{2} y}{d x^{2}}+3 \frac{d y}{d x}=0 \)
Subject: Maths
Let \( \mathbf{y}(\mathbf{x}) \) be the solution of the
differential equation \( (\mathbf{x} \log \mathbf{x}) \frac{\mathbf{d y}}{\mathbf{d x}}+\mathbf{y}=2 \mathbf{x} \log \mathbf{x},(\mathbf{x} \geqslant 1) \)
Then \( \mathbf{y}(\mathbf{e}) \) is equal to :
A.
B. 2
\( c \cdot z \)
D.
Subject: Chemistry
From Bohr's model radius of the orbit
and energy of the hydrogen atom are
calculated as:
This question has multiple correct options
A. radius of the 1st orbit is \( 0.529 A^{\circ} \)
B. energy of the 1st orbit is \( -13.6 e V \)
C. energy of the 1st orbit is \( -21.72 \times 10^{-19} \mathrm{J} \)
D. radius of the 1st orbit is \( 1.06 A^{\circ} \)
Subject: Physics
toppr
Q Type your question
aimed towards \( Q \) and velocity \( \vec{u} \) of \( Q \) is
perpendicular to \( \vec{v} \). The two projectiles
meet at time \( \boldsymbol{T}= \)
\( A \)
B.
\[
\frac{(v+u) d}{v^{2}}
\]
\( c \)
\[
\frac{v(v-u)}{d}
\]
D.
\[
\frac{v d}{\left(v^{2}-u^{2}\right)}
\]
Subject: Maths
In the given figure, \( O \) is the centre of the
circle, \( \angle A C B=54^{\circ} \) and \( B C E \) is a
straight line. Find \( \boldsymbol{x} \)
\( A \cdot 126 \)
B. 54
\( c \cdot 108 \)
D. 90
Subject: Maths
If \( \boldsymbol{A}+\boldsymbol{B}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{3}\end{array}\right] \)
then matrix \( B \) is
\( \mathbf{A} \cdot\left[\begin{array}{ll}1 & 1 \\ 4 & 2\end{array}\right] \)
в. \( \left[\begin{array}{ll}1 & 4 \\ 1 & 2\end{array}\right] \)
c. \( \left[\begin{array}{ll}2 & 4 \\ 1 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ll}4 & 2 \\ 1 & 1\end{array}\right] \)
Subject: Maths
A polynomial function \( f(x) \) satisfies the condition \( \boldsymbol{f}(\boldsymbol{x}+\mathbf{1})=\boldsymbol{f}(\boldsymbol{x})+\mathbf{2} \boldsymbol{x}+\mathbf{1} \)
Find \( \boldsymbol{f}(\boldsymbol{x}) \) if \( \boldsymbol{f}(\mathbf{0})=1 . \) Find also the
equations of the pair of tangents from
the origin on the curve \( y=f(x) \) and
compute the area enclosed by the curve
and the pair of tangents.
\( f(x)=x^{2}+1 ; y=\pm 2 x ;, A=\frac{2}{3} \) sq.units
B. \( f(x)=x^{2}-1 ; y=\pm 2 x ; A=\frac{2}{3} \) sq.units
c. \( f(x)=x^{2}+1 ; y=\pm 2 x ; \), \( A=\frac{3}{2} \) sq.units
D. \( f(x)=x^{2}-1 ; y=\pm 2 x ; A=\frac{3}{2} \) sq.units
Subject: Chemistry
Liquid chlorine boils at:
\( \mathbf{A} \cdot-24.6^{\circ} \mathrm{C} \)
B. \( -44.6^{\circ} \mathrm{C} \)
c. \( -14.6^{\circ} \mathrm{C} \)
D. \( -34.6^{\circ} \mathrm{C} \)
Subject: Physics
A long wire carries a current of \( 20 A \)
long the axis of a solenoid, the field due to the solenoid is 4 mT. The resultant
field at a point 3 mm from the solenoid
axis is :
A. \( 1.33 \mathrm{mT} \)
в. \( 4.2 \mathrm{mT} \)
c. \( 2.1 m T \)
D. \( 8.4 \mathrm{mT} \)
Subject: Biology
n the given figure, what are the
substances labelled as \( P, Q, R \) and \( S ? \)
A . P-PGA, Q-Glyoxylate, \( R-N H_{3} \), S-serine
3. P-Glycolate, Q-Glyoxylate, \( R-N H_{3} \), S-serin
c. P-Glycolate, Q-Glyoxylate, \( R-C O_{2} \), S-serin
'. P-RuBP, Q-Glycerate, \( R-C O_{2} \), S-Serine
Subject: Physics
Certain substance emits only the
wavelengths, \( \lambda_{1}, \lambda_{2}, \lambda_{3} \) and \( \lambda_{4} \) when it is at a high temperature. When this substance is at a colder temperature, it will absorb only the following wavelengths:
\( A \cdot \lambda_{1} \)
B. \( \lambda_{2} \)
\( c \cdot \lambda_{1} \) and \( \lambda_{2} \)
D. \( \lambda_{1}, \lambda_{2}, \lambda_{3} \) and \( \lambda_{4} \)
Subject: Chemistry
Which combinations of quantum number \( n, 1, m, s \) for the electron in an
atom does not provide a permissible solution of the wave equation?
A. \( 3,2,-2,1 / 2 \)
B. 3, 3, 1,-1/2
c. \( 3,2,1,1 / 2 \)
D. 3, 1, 1, -1/2
Subject: Physics
How much pressure should be applied on a litre of water if it is to be
compressed by \( 0.1 \% ? \) (Bulk moduls of water \( =2100 M P a) \)
A \( .2100 k P a \)
в. \( 210 k P a \)
c. \( 2100 M P a \)
D. \( 210 M P a \)
Subject: Physics
Which of the following processes
described below is irreversible?
A. The increase in temperature of an iron rod by hammering it.
B. A gas in a small container at a temperature \( T_{1} \) is brought in contact with a big reservoir at a higher temperature \( T_{2} \) which increases the temperature of the gas.
C. An ideal gas is enclosed in a piston cylinder arrangement with adiabatic walls.A weight \( \mathrm{W} \) is added to the piston resulting in compression of gas.
D. All of above
Subject: Maths
Find the equation of the line passing through (1,2,-4) and perpendicular to both the lines \( \frac{x-1}{2}=\frac{y+2}{-3}=\frac{z-4}{4} \)
and \( \frac{\boldsymbol{x}-\mathbf{3}}{\mathbf{5}}=\frac{\boldsymbol{y}+\mathbf{6}}{\mathbf{1}}=\frac{\boldsymbol{z}+\mathbf{1 0}}{\mathbf{2}} \)
Subject: Physics
Relation between current in a conductor
and time is shown in Figure. If the
resistance of the conductor is \( R \), then
the total heat dissipated across
resistance \( \boldsymbol{R} \) is :
A \( \cdot \frac{i_{0}^{2} R t_{0}}{2} \)
B. \( \frac{i_{0}^{2} R t_{0}}{4} \)
c. \( \frac{i_{0}^{2} R t_{0}}{3} \)
D \( \cdot i^{2}_{0} R t_{0} \)
Subject: Chemistry
Maximum frequency of emission is obtained for the transition:
\( \mathbf{A} \cdot n=2 \) to \( n=1 \)
B. \( n=6 \) to \( n=2 \)
c. \( n=1 \) to \( n=2 \)
D. \( n=2 \) to \( n=6 \)
6
Subject: Physics
Two points charges \( 4 \mu C \) and \( -2 \mu C \) are separated by a distance of \( 1 \mathrm{m} \) in air. \( \mathrm{At} \) what point in between the charges and on the line joining the charges, is the electric potential zero?
A. In the middle of the two charges
B. \( 1 / 3 m \) from \( 4 \mu C \)
c. \( 1 / 3 m \) from \( -2 \mu C \)
D. Nowhere the potential is zero
Subject: Maths
Choose the correct answer from the
alternatives given.
Directions for questions 71 to 75 : Study
the following bar-graph and answer the
questions What is the ratio of highest
consumption in the year 2012 and 2013
respectively?
A . 7: 6
B. 6: 7
\( c \cdot 7: 2 \)
D. 14: 1
Subject: Maths
In the tetrahedron \( \boldsymbol{A B C D}, \boldsymbol{A}= \)
(1,2,-3) and \( G(-3,4,5) \) is the
centroid of the tetrahedron. If \( P \) is the
centroid of the \( \Delta B C D, \) then \( A P= \)
A \( \cdot \frac{8 \sqrt{21}}{3} \)
B. \( \frac{4 \sqrt{21}}{3} \)
c. \( 4 \sqrt{21} \)
D. \( \frac{\sqrt{21}}{3} \)
Subject: Physics
The correct relation relating the potential energy U and \( r \) between two atoms is
A \( \cdot U_{(r)}=\frac{A}{r^{12}}+\frac{B}{r^{6}} \)
B. \( U_{(r)}=\frac{A}{r^{12}}-\frac{B}{r^{6}} \)
c. \( U_{(r)}=\frac{A}{r^{6}}-\frac{B}{r^{12}} \)
D. \( -U_{(r)}=\frac{K}{r^{2}} \)
Subject: Physics
A jar filled with two non mixing liquids
1 and 2 having densities \( \rho_{1} \) and \( \rho_{2} \) respectively. A solid ball, made of a
material of density \( \rho_{3}, \) is dropped in the jar. It comes to equilibrium in the
position shown in the figure
A \( \cdot \rho_{3}<\rho_{1}<\rho_{2} \)
B . \( \rho_{1}<\rho_{3}<\rho_{2} \)
\( \mathbf{c} \cdot \rho_{1}<\rho_{2}<\rho_{3} \)
D. \( \rho_{3}<\rho_{2}<\rho_{1} \)
Subject: Physics
The reverse breakdown voltage of a
Zener diode is \( 5.6 \mathrm{V} \) in the given circuit
The current \( I_{Z} \) through the Zener is
\( \mathbf{A} \cdot 7 m A \)
В. 17 тА
\( c .10 m A \)
D. \( 15 \mathrm{mA} \)
Subject: Maths
\( \int \frac{x^{4}}{(x-1)\left(x^{2}+1\right)} d x \) (Assuming all
conditions for the domain to be met)
A \( x^{2}+x+\frac{1}{2} \log (x-1)-\frac{1}{4} \log \left(x^{2}+1\right)-\frac{1}{2} \tan ^{-1} x+c \)
B \( \cdot \frac{1}{2} x^{2}+x+\frac{1}{2} \log (x-1)-\frac{1}{4} \log \left(x^{2}+1\right)-\frac{1}{2} \tan ^{-1} x+c \)
C \( \cdot \frac{1}{2} x^{2}+x-\frac{1}{2} \log (x-1)-\frac{1}{4} \log \left(x^{2}+1\right)-\frac{1}{2} \tan ^{-1} x+c \)
D \( \cdot \frac{1}{2} x^{2}-x+\frac{1}{2} \log (x-1)-\frac{1}{4} \log \left(x^{2}+1\right)+\frac{1}{2} \tan ^{-1} x+c \)
Subject: Chemistry
At \( 60^{\circ} C \), pure water has \( \left[\boldsymbol{H}_{3} \boldsymbol{O}^{+}\right]= \)
\( 10^{-6.7} \) mol / lit.What is the value of \( K_{W} \)
\( a t 60^{\circ} C:- \)
A \( \cdot 10^{-6} \)
B. \( 10^{-12} \)
c. \( 10^{-67} \)
D. \( 10^{-13.4} \)
Subject: Physics
State the approximate value of the critical angle for (a) glass-air surface,
(b) water-air surface (Given \( \mu_{\text {glass}}= \)
\( \left.\mathbf{1 . 5}, \boldsymbol{\mu}_{\boldsymbol{w} \boldsymbol{a} \boldsymbol{t} e r}=\mathbf{1 . 3 3}\right) \)
A \( \cdot \) (a) \( 49^{\circ},(b) 49^{\circ} \)
B . (a) \( 42^{\circ},(b) 42^{\circ} \)
\( \mathbf{c} \cdot(\mathbf{a}) 42^{o},(\mathbf{b}) 49^{\circ} \)
D \( \cdot \) (a) \( 49^{\circ},(b) 42^{\circ} \)
Subject: Biology
All are true about bacterial endospores
except
A. Sporulation in bacteria is a method of reproduction.
B. The spores of all the medically important bacteria are killed by autoclaving at \( 121^{\circ} \mathrm{C} \) for 15 minutes.
C. Spores can be stained by modified Ziehl-Neelsen technique.
D. Bacterial spores helps them to survive under unfavourable conditions.
Subject: Chemistry
Coal gas is mixture of:
\( \mathbf{A} \cdot C H_{4}+H_{2}+C O_{2}+H_{2} S \)
\( \mathbf{B} \cdot C H_{4}+H_{2}+C O+H_{2} S \)
\( \mathbf{c} \cdot C H_{4}+H_{2}+C O \)
D. ethane, propane, butane
Subject: Physics
Two point charges \( 2 C \) and \( -1 C \) are
placed at \( \boldsymbol{x}=\mathbf{0} \) and \( \boldsymbol{x}=\boldsymbol{6} \) respectively.
The potential will be zero at points:
A. \( x=2,-2 \)
в. \( x=1,5 \)
c. \( x=4,12 \)
D. \( x=2,9 \)
Subject: Chemistry
Compound 'A' on chlorination gives compound 'B', compound 'B' reacts with alc. KOH gives gas 'C', which decolourizes Baeyer's reagent and ozonolysis of compound 'C' gives only HCHO compound. Then compound 'A' is:
A. \( C_{2} H_{6} \)
в. \( C_{2} H_{4} \)
c. \( C_{4} H_{10} \)
D. \( C_{2} H_{5} C l \)
Subject: Physics
Three infinite planes have a uniform
surface charge density \( \sigma \) on is surface.
All charges are fixed.On each of the
three infinite planes parallel to the \( y- \)
\( z \) plane placed at \( x=-a, x=0 \) and
\( \boldsymbol{x}=\boldsymbol{a} . \) The potential difference between
\( A \) and \( C \) is:
\( A \)
в. \( \frac{\sigma}{\varepsilon_{0}} \)
c. \( \frac{\sigma a}{2 \varepsilon_{0}} \)
D.
Subject: Chemistry
3 mol of a mixture of \( F e S O_{4} \) and
\( \boldsymbol{F} \boldsymbol{e}_{2}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{3} \) required \( \mathbf{1 0 0 m} \boldsymbol{L} \) of \( \boldsymbol{2} \boldsymbol{M} \)
\( K M n O_{4} \) solution in acidic medium.
Hence, mole fraction of \( F e S O_{4} \) in the
mixture is:
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
c. \( \frac{2}{5} \)
D. \( \frac{3}{5} \)