AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The bleaching action of \( H_{2} O_{2} \) is due to
which one of the following reactions?
A. \( P b S+4 H_{2} O_{2} \rightarrow P b S O_{4}+4 H_{2} O \)
в. \( H_{2} O_{2} \rightarrow H_{2} O+[O] \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2}+[\mathrm{O}] \rightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2} \)
D. \( H_{2} O_{2}+O_{3} \rightarrow H_{2} O+2 O \)
Subject: Physics
When the angle of incidence on a
material is \( 60^{\circ} \), the reflected light is
completely polarised. The velocity of the refracted ray inside the material is
A . \( 3 \times 10^{8} \)
B. \( \frac{3}{\sqrt{2}} \times 10^{8} \)
c. \( \sqrt{3} \times 10^{8} \)
D. \( 0.5 \times 10^{8} \)
Subject: Chemistry
The name of complex ion, \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\boldsymbol{6}}\right]^{\boldsymbol{3}-} \)
is:
A. Hexacyanoiron (III) ion
B. Hexacyanitoferrate (III) ion
c. Tricyanoferrate (III) ion
D. Hexacyanidoferrate (III) ion
Subject: Physics
A given resistor has the following colour code of the various strips on it : Brown,
black, green and silver. The value of its
resistance in ohm is
A \( \cdot 1.0 \times 10^{4} \pm 10 \% \)
B . \( 1.0 \times 10^{7} \pm 5 \% \)
C. \( 1.0 \times 10^{6} \pm 10 \% \)
D. \( 1.0 \times 10^{5} \pm 5 \% \)
E . \( 1.0 \times 10^{3} \pm 10 \% \)
Subject: Maths
The lines tangent to the curves \( y^{3}- \) \( x^{2} y+5 y-2 x=0 \) and \( x^{4}-x^{3} y^{2}+ \)
\( 5 x+2 y=0 \) at the origin intersect at
an angle \( \theta \) equal to
A \( \cdot \frac{\pi}{6} \)
B.
c.
D.
Subject: Chemistry
The standard reduction potentials \( \boldsymbol{E}^{\circ} \)
for \( \boldsymbol{O C l}^{-} / \boldsymbol{C l}^{-} \) and for \( \boldsymbol{C l}^{-} / \mathbf{1} / \mathbf{2 C l}_{2} \) are
\( 0.86 V \) and -1.10 volt respectively. The
\( \boldsymbol{E}^{\circ} \) value of \( \boldsymbol{O C l}^{-} / \mathbf{1} / \mathbf{2} \boldsymbol{C l}_{\mathbf{1}} \) will be \( \boldsymbol{?} \)
\( \mathbf{A} \cdot+1.96 V \)
B . \( -1.96 V \)
c. \( +0.24 V \)
D. \( -0.24 V \)
Subject: Biology
Match the item in column I with column
I and choose the correct answer.
\( \begin{array}{ll}\text { Column } 1 & \text { Column } 2 \\ \text { A. Microspermae } & \text { 1. Alismaceae } \\ \text { B. Epigynae } & \text { 2. Liliaceae } \\ \text { C. Calycinae } & \text { 3. Iridaceae } \\ \text { D. Apocarpae } & \text { 4. Orchidaceae } \\ \text { E. Coronarieae } & \text { 5. Palmae }\end{array} \)
\( \mathbf{A} \)
\( A-3, B-2, C-1, D-5, E-4 \)
B. \( A-2, B-4, C-3, D-5, E-1 \)
\( C \cdot A-4, B-3, C-5, D-1, E-2 \)
D. \( A-4, B-1, C-3, D-5, E-2 \)
Subject: Chemistry
A dust particle has mass equal to \( 10^{-11} g, \) diameter \( 10^{-4} c m \) and velocity \( 10^{-4} \mathrm{cm} / \mathrm{s} . \) The error in measurement of
velocity is \( 0.1 \% . \) What will be the uncertainty in its position?
A \( \cdot 0.527 \times 10^{10} \mathrm{cm} \)
B. \( 5.27 \times 10^{9} \mathrm{cm} \)
c. \( 0.527 \times 10^{-15} \mathrm{cm} \)
D. \( 0.527 \times 10^{-9} \mathrm{cm} \)
Subject: Physics
While doing an experiment with potentiometer (figure) it was found that the deflection is one sided and (i) the
deflection decreased while moving from
one end \( A \) of the wire, to the end \( R ;(\text { ii }) \)
the deflation increased, while the jockey
was removed towards the end D.

Which terminal positive or negative of
the cell \( E_{1} \) is connected at \( X \) in case
(i) and how is \( E_{1} \) related to E?
(ii) Which terminal of the cell \( E_{1} \) is
connected at \( X \) in case (ii)?
Subject: Maths
Evaluate: \( \int_{0}^{\pi / 4} \sec ^{7} \theta \sin ^{3} \theta d \theta= \)
A \( \cdot \frac{1}{12} \)
в. \( \frac{3}{12} \)
c. \( \frac{5}{12} \)
D. \( \frac{7}{12} \)
Subject: Maths
ff \( x_{1}, x_{2}, x_{3} \) as well as \( y_{1}, y_{2}, y_{3} \) are in
G.P. with same common ratio, then the
points \( \boldsymbol{P}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}\right), \boldsymbol{Q}\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}\right) \) and
\( \boldsymbol{R}\left(\boldsymbol{x}_{3}, \boldsymbol{y}_{3}\right) \)
A. lies on a straight line
B. lie on an ellipse
c. lie on a circle
D. are vertices of a triangle
Subject: Chemistry
Assertion
The \( d_{c-o} \) in bridging carbonyl group is Ionger than that of terminal carbonyl group.
Reason
With an increase in the extent of
synergic bonding, the \( C-O \) bond
length increases.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-
B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation fo statement-
c. statement-1 is true, statement-2 is false
D. statement-1 is false, statement-2 is true
Subject: Chemistry
Consider the following statements with regard to chemical equilibria:
(1) Equilibrium constant is independent
of initial concentrations of reactants
and products.
(2) Equilibrium constant for the reverse reaction is equal to the inverse of the equilibrium constant for the forward
reaction.
(3) Equilibrium constant is independent of temperature. Which of the above statements are
correct?
A. 1 and 2 only
B. 2 and 3 only y
c. 1 and 3 only
D. 1,2 and 3
Subject: Chemistry
Assertion
All molecules of an ideal gas move with
the same speed.
Reason
There is no attraction between the
molecules in an ideal gas.
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
Calculate the cell potential \( \left(E_{c e l l}\right) \) of the
following cell at \( 298 K \)
\( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \mid \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{0} . \boldsymbol{0} \mathbf{1} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M} \)
Subject: Maths
If \( z_{1}=2+5 i, z_{2}=3-i \) find \( (a) z_{1} \cdot z_{2} \)
(b) \( z_{1} \times z_{2} \)
\( (c) z_{2} \cdot z_{1} \)
(d) \( z_{2} \times z_{1} \)
(e) acute angle between \( z_{1} \& z_{2} \)
Projection of \( z_{1} \) on \( z_{2} \)
A \( \cdot 1,17,1,17, \cos ^{-1} \frac{1}{\sqrt{290}}, \frac{1}{\sqrt{10}} \)
в. \( _{1,-17,1,17, \cos ^{-1}} \frac{1}{\sqrt{290}}, \frac{1}{\sqrt{10}} \)
c. \( _{1,17,1,-17, \cos ^{-1}} \frac{1}{\sqrt{290}}, \frac{1}{\sqrt{10}} \)
D. \( 1,-17,1,-17, \cos ^{-1} \frac{1}{\sqrt{290}}, \frac{1}{\sqrt{10}} \)
Subject: Chemistry
Calculate the molarity of a solution
containing \( 5 g \) of NaOH dissolved in the
product of a \( \boldsymbol{H}_{2}-\boldsymbol{O}_{2} \) fuel cell operated
at \( 1 A \) current for 595.1 hours.
(Assume \( 1 F=96500 \mathrm{C} / \mathrm{mol} \) of
electrons and molecular weight of NaOH as \( 40 \mathrm{g} \) mol \( ^{-1} \) )
A . 0.05 M
B. 0.025 м
\( c .0 .1 \mathrm{m} \)
D. 0.075 м
E. 1 M
Subject: Maths
Let \( \boldsymbol{f}:[\boldsymbol{a}, \boldsymbol{b}] \rightarrow[\mathbf{1}, \infty) \) be a continuous
function and let \( g: R \rightarrow R \) be defined
\( \operatorname{as} g(x)=\left\{\begin{array}{ccc}0 & \text { if } & x<a \\ \int_{a}^{x} f(t) d t & \text { if } & a \leq x \leq b \\ \int_{a}^{b} f(t) d t & \text { if } & x>b\end{array}\right. \)
Then
This question has multiple correct options
\( \mathbf{A} \cdot g(x) \) is continuous but not differentiable at \( a \)
B. \( g(x) \) is differentiable on \( R \)
C \( \cdot g(x) \) is continuous but not differentiable at \( b \)
D. \( g(x) \) is continuous and differentiable at either \( a \) or \( b \) but not both
Subject: Chemistry
Balance the following chemical equation and identify the type of chemical reaction? \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{O}(\boldsymbol{s}) \stackrel{\boldsymbol{H} e a t}{\longrightarrow} \boldsymbol{H} \boldsymbol{g}(\boldsymbol{l})+\boldsymbol{O}_{2}(\boldsymbol{g}) \)
Subject: Physics
A \( 50 H z \) a.c. source of \( 20 V \) is
connected across \( \mathrm{R} \) and \( \mathrm{C} \) as shown in
figure below. The voltage across \( \mathrm{R} \) is
\( 12 \mathrm{V} \). The voltage across \( \mathrm{C} \) is:
\( \mathbf{A} \cdot 8 V \)
B. \( 16 V \)
\( c \cdot 10 V \)
D. not possible to determine unless values of \( \mathrm{R} \) and \( \mathrm{C} \) are given
Subject: Chemistry
Arrange the following alcohols in order of increasing reactivity towards sodium metal.
(i) \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{O H} \) (ii) \( \left(\boldsymbol{C H}_{3}\right) \mathbf{2 C H}- \)
\( O H \) (iii) \( C H_{3} C H_{2} O H \)
A. (iii) < (ii) < (i)
B. (ii) < (i) < (iii)
c. (i) < (ii) < (iii)
D. (iii) < (i) < (ii)
Subject: Chemistry
If \( I \) is the intensity of absorbed light
and 'C' is the concentration of AB for the
photochemical process, \( A B+h v \rightarrow \)
\( A B, \) the rate of the formation of \( A B \) is
directly proportional to:
A.
B. \( I \)
c. \( I^{2} \)
D. \( C, I \)
Subject: Physics
Which of the following statement is
correct regarding induced electric field (symbols have their usual meanings)? This question has multiple correct options
A. Work done in moving a test charge in an induced electric field can be zero
B. Induced electric field is non-conservative is nature
C. Induced electric lines of force form closed loops
D. Induced e.m.f. in the loop in \( \varepsilon=\oint \vec{E} . \overline{d \iota}=-\frac{d \phi}{d t} \)
Subject: Biology
toppr
Q Type your question
Glucose
Glyceraldehyde
Lactic
\( +\mathrm{CO}_{2} \)
\( \mathbf{A} \cdot \mathbf{A}-N A D H+H^{+} \rightarrow N A D^{+} ; \mathrm{B}-N A D^{+} \rightarrow N A D H+ \)
\( H^{+} ; \mathrm{C}-N A D^{+} \rightarrow N A D H+H^{+} \)
B. A-NADH \( +H^{+} \rightarrow N A D^{+} ; \) B-N \( A D H+H^{+} \rightarrow \)
\( N A D^{+} ; \mathrm{C}-N A D^{+} \rightarrow N A D H+H^{+} \)
C \( \cdot \mathrm{A}-N A D^{+} \rightarrow N A D H+H^{+} ; \mathrm{B}-N A D H+H^{+} \rightarrow \)
\( N A D^{+} ; \mathrm{C}-N A D H+H^{+} \rightarrow N A D^{+} \)
D. \( A-N A D^{+} \rightarrow+H^{+} ; B-N A D H+H^{+} \rightarrow N A D^{+} ; C- \)
\( N A D^{+} \rightarrow N A D H+H^{+} \)
Subject: Physics
An object is dropped from a height \( h \) from the ground. Every time it his the ground it looses \( 50 \% \) of its kinetic energy. The total distance covered as
\( \rightarrow \infty \) is:
\( \mathbf{A} \cdot 2 h \)
B . \( \infty \)
c. \( \frac{5}{3} h \)
D. \( \frac{8}{3} h \)
Subject: Maths
Find the middle term(s) in the
expansion of :
\( \left(3 x-\frac{x^{3}}{6}\right)^{9} \)
A \( \cdot \frac{189}{8} x^{15},-\frac{21}{16} x^{17} \)
В \( \cdot \frac{189}{8} x^{17},-\frac{21}{16} x^{19} \)
C. \( \frac{189}{7} x^{15},-\frac{23}{13} x^{19} \)
D. None of thes
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{r}\frac{\boldsymbol{K} \cos \boldsymbol{x}}{\boldsymbol{\pi}-\mathbf{2} \boldsymbol{x}} ; \boldsymbol{x} \neq \frac{\boldsymbol{\pi}}{\mathbf{2}} \\ \boldsymbol{5} ; \boldsymbol{x}=\frac{\boldsymbol{\pi}}{2}\end{array}\right. \)
Find the value of \( K \) so that the function is continuous at the point \( \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\mathbf{2}} \)
Subject: Physics
(a) Using Bohr's second postulate of
quantization of orbital angular
momentum show that the
circumference of the electron in the \( n^{t h} \)
orbital state in hydrogen atom is \( n \) times the de Broglie wavelength
associated with it.
(b) The electron in hydrogen atom in initially in the third excited state.What is the maximum number of spectral lines which can be emitted.When it
finally moves to the ground state?
Subject: Maths
The value of \( x \) where \( x>0 \)
\( \tan \left(\sec ^{-1} \frac{1}{x}\right)=\sin \left(\tan ^{-1} 2\right) \) is
A \( \cdot \sqrt{5} \)
в. \( \frac{\sqrt{5}}{3} \)
c.
D.
Subject: Chemistry
Which is the correct IUPAC name for
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{B} \boldsymbol{r}: \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \)
A. 1-Bromo-2-ethylpropane.
B. 1-Bromo-2-ethyl-2-methylethane.
c. 1 -Bromo-2-methylbutane
D. 2-Methyl-1-bromobutane
Subject: Chemistry
Assertion
Kinetic energy of photoelectrons increases with increase in the
frequency of incident radiation.
Reason
The number of photoelectrons ejected increases with increase in intensity of incident radiation.
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
\( \ln N, e, \tau \) and \( m \) are representing electron density, charge, relaxation time and mass of an electron
respectively, then the resistance of wire of length \( l \) and cross-sectional area \( \boldsymbol{A} \) is given by
A \( \cdot \frac{2 m l}{N e^{2} A \tau} \)
в. \( \frac{2 m \tau A}{N e^{2} l} \)
c. \( \frac{N e^{2} \tau A}{2 m l} \)
D. \( \frac{N e^{2} A}{2 m \tau l} \)
Subject: Physics
A circuit consists of a battery, a resistor
\( \mathrm{R} \) and two light bulbs \( \mathrm{A} \) and \( \mathrm{B} \) as shown.
If the filaments in light A burns out,
then the following is true for light bulb
A. It is turned off
B. Its brightness does not change
c. It gets dimmer
D. It gets brighter
Subject: Physics
A point near the equator has:
\( \mathbf{A} \cdot B_{V}>>B_{H} \)
\( \mathbf{B} \cdot B_{H}>>B_{V} \)
\( \mathbf{c} \cdot B_{V}=B_{H} \)
D \( . B_{V}=B_{H}=0 \)
Subject: Maths
If the line \( 2 x+3 y+12=0 \) cuts the
axes at \( A \) and \( B \), then the equation of
the perpendicular bisector of \( A B \) is
A. \( 3 x-2 y+5=0 \)
B. \( 3 x-2 y+7=0 \)
c. \( 3 x-2 y+9=0 \)
D. \( 3 x-2 y+8=0 \)
Subject: Maths
The differential equation of the family of circles with fixed radius 5 units and
centre on the line \( y=2 \) is
A \( \cdot(x-2)\left(y^{1}\right)^{2}=25-(y-2)^{2} \)
B . \( (y-2)\left(y^{1}\right)^{2}=25+(y-2)^{2} \)
C \( \cdot(y-2)^{2}\left(y^{1}\right)^{2}=25-(y-2)^{2} \)
D. \( (x-2)^{2}\left(y^{1}\right)^{2}=25-(y-2)^{2} \)
Subject: Maths
If \( A \) is \( 2 \times 3 \) matrix and \( A B \) is a \( 2 \times 5 \)
matrix, then \( B \) must be a
A. \( 3 \times 5 \) matrix
B. \( 5 \times 3 \) matrix
c. \( 3 \times 2 \) matrix
D. \( 5 \times 2 \) matrix
Subject: Physics
The change in potential energy, when a body of mass \( m \) is raised to a height \( n R \) from the earth's surface is \( (R= \) radius of earth)
A \( \cdot \operatorname{mg} R\left(\frac{n}{n-1}\right) \)
в. \( n m g R \)
\( ^{\mathbf{c}} \cdot \operatorname{mg} R\left(\frac{n^{2}}{n^{2}+1}\right) \)
D. \( \operatorname{mg} R\left(\frac{n}{n+1}\right) \)
Subject: Biology
Assertion
Histamine is related with allergic and
inflammatory reactions
Reason
Histamine is a vasodilator
A. If both the assertion and the reson are true and the
reason
is correct explanation of the assertion.
B. If both the assertion and the reson are true but the
reason
is not correct explanation of the assertion.
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Chemistry
Hardness in water is expressed in
terms of ppm of \( C a C O_{3} . \) If hardness is
200 ppm \( C a C O_{3}, \) then in terms of molarity, it is:
A. \( 0.004 \mathrm{M} \)
B. \( 0.002 M \)
c. \( 0.001 M \)
D. \( 0.0005 M \)
Subject: Chemistry
One atom of an element X weighs \( 6.644 \times 10^{-23} . \) Calculate the number of
gram atoms in \( 40 \mathrm{kg} \) of it.
A \( \cdot 10^{2} \)
B . \( 10^{3} \)
\( c \cdot 10^{-2} \)
D. \( 10^{4} \)
Subject: Chemistry
An alloy weighing 1.05 g of \( P b-A g \) was dissolved in desired amount of
\( H N O_{3} \) and the volume was made 350
\( \mathrm{mL} . \) An \( \mathrm{Ag} \) electrode was dipped in
solution and \( E_{\text {cell}} \) of the cell
K. The percentage of lead in alloy is (divide answer by 25 ) :
Given: \( \boldsymbol{E}_{A \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}}^{o}=\mathbf{0 . 8 0} \boldsymbol{V} \)
Subject: Maths
The total revenue in Rupees received
from the sale of \( x \) units of a product
is given by \( \boldsymbol{R}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}^{2}+\mathbf{3 6} \boldsymbol{x}+\mathbf{5} . \) The
marginal revenue, when \( \boldsymbol{x}=\mathbf{1 5} \) is.
A . 116
B. 96
\( c \cdot 90 \)
D. 126
Subject: Maths
If \( [A] \neq 0 \) then which of the following is
not true?
A \( \cdot\left(A^{2}\right)^{-1}=\left(A^{-1}\right)^{2} \)
B. \( \left(A^{\prime}\right)^{-1}=\left(A^{-1}\right)^{\prime} \)
\( \mathbf{c} \cdot A^{-1}=|A|^{-1} \)
D. None of these
Subject: Chemistry
A \( 5 \% \) solution of cane sugar \( (\text { mol. } \boldsymbol{w} \boldsymbol{t}= \)
342) is isotonic with \( 1 \% \) solution of
substance \( X . \) The molecular weight of
\( \boldsymbol{X} \) is:
A . 34.2
B. 171.2
\( c .68 .4 \)
D. 136.8
Subject: Chemistry
A solution is made of \( 0.1 ~ M C l^{-} \) and
\( \mathbf{1 0}^{-4} \mathbf{M} \mathbf{C r} \mathbf{O}_{\mathbf{4}}^{\mathbf{2 -}} . \) If solid \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} \) is
gradually added to this solution,
then what will be the concentration of
\( C l^{-} \) when \( A g_{2} C r O_{4} \) begins to
precipitate? \( \left[\boldsymbol{K}_{s p}(\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l})=\right. \)
\( \mathbf{1 0}^{-\mathbf{1 0}} \boldsymbol{M}^{\mathbf{2}} ; \boldsymbol{K}_{\boldsymbol{s p}}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}\right)= \)
\( \left.\mathbf{1 0}^{-\mathbf{1 2}} \mathbf{M}^{\mathbf{3}}\right] \)
В. \( 10^{-4} \) М
\( \mathbf{c} \cdot 10^{-5} M \)
D. \( 10^{-9} M \)
Subject: Physics
A moving block having mass \( m \), collides with another stationary block having mass \( 4 m . \) The lighter block comes to
rest after collision. When the initial
velocity of the lighter block is \( v \), then the value of coefficient of restitution \( (e) \) will
be:
A . 0.5
B. 0.25
c. 0.4
D. 0.8
Subject: Chemistry
Primary and secondary valency of Pt in
\( \left[\boldsymbol{P t}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right] \boldsymbol{C l}_{2} \) are:
\( A \cdot 4,4 \)
B. 2,6
\( c \cdot 6, \)
D. None of these
Subject: Chemistry
If the molar conductance values of
\( C a^{2+} \) and \( C l^{-} \) at infinite dilution are
respectively \( 118.88 \times \) \( 10^{-4} m^{2} \) mho mol \( ^{-1} \) and \( 77.33 \times \)
\( 10^{-4} m^{2} \) mho mho \( ^{-1} \) then that of \( C a C l_{2} \)
is:
A . \( 118.88 \times 10^{-4} \)
B . \( 154.66 \times 10^{-4} \)
c. \( 273.54 \times 10^{-4} \)
D. \( 196.21 \times 10^{-4} \)
Subject: Physics
The differential equation for a particle of mass \( 2 \mathrm{kg} \) executing \( \mathrm{SHM} \) is \( 2 \frac{d^{2} x}{d t^{2}}+ \)
\( x=0 . \) If amplitude of oscillation is 3
\( \mathrm{cm}, \) then maximum velocity of the particle will be
A. \( 3 \sqrt{0.5} \mathrm{cm} / \mathrm{s} \)
B. \( \sqrt{0.5} \mathrm{cm} / \mathrm{s} \)
c. \( \sqrt{0.5} / 3 \mathrm{cm} / \mathrm{s} \)
D. \( 2 \sqrt{0.5} \mathrm{cm} / \mathrm{s} \)
Subject: Maths
If \( \alpha+\beta=\frac{\pi}{2} \) and \( \sin \alpha=\frac{1}{3}, \) then \( \sin \beta \)
is equal to
A. \( \frac{\sqrt{2}}{3} \)
B. \( \frac{2 \sqrt{2}}{3} \)
\( c \cdot \frac{2}{3} \)
D. 3
Subject: Maths
A line passes through the points whose position vectors \( \hat{\mathbf{i}}+\hat{\mathbf{j}}-\mathbf{2} \hat{\boldsymbol{k}} \) and \( \hat{\mathbf{i}}- \)
\( 3 \hat{j}+\hat{k} . \) Then the position vector of a
point on it at a unit distance from the first point is
A \( \cdot \frac{1}{5}(5 \hat{i}+\hat{j}-7 \hat{k}) \)
B \( \cdot \frac{1}{5}(5 \hat{i}+9 \hat{j}-13 \hat{k}) \)
c. \( (\hat{i}-4 \hat{j}+3 \hat{k}) \)
D. \( (\hat{i}+4 \hat{j}+3 \hat{k}) \)
Subject: Maths
Two players \( A \) and \( B \) are competing at a trivia quiz game involving a series of questions. On any individual question,
the probabilities that \( A \) and \( B \) give the correct answer are \( \alpha \) and \( \beta \) respectively,
for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins if B answers the first question.
A \( \cdot \frac{\alpha}{1-(1-\alpha)(1-\beta)} \)
в. \( \frac{(1-\beta)}{1-(\alpha)(\beta)} \)
c. \( \frac{(1-\beta) \alpha}{1-(1-\alpha)(1-\beta)} \)
D. none of these
Subject: Physics
A car of mass \( \mathrm{m} \) is moving on a level
circular track of radius R. If \( \mu_{s} \)
represents the static friction between
the road and tyres of the car, the maximum speed of the car in circular motion is given by:
A \( \cdot \sqrt{R g / \mu_{s}} \)
B . \( \sqrt{m R g / \mu_{s}} \)
\( \mathrm{c} \cdot \sqrt{\mu_{s} R g} \)
D. \( \sqrt{\mu_{s} m R g} \)
Subject: Maths
The side of a rhombus is \( 10 \mathrm{cm} \) and one
diagonal is \( 16 \mathrm{cm} . \) The area of the
rhombus is
\( \mathbf{A} \cdot 96 c m^{2} \)
B. \( 95 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 94 c m^{2} \)
D. \( 93 c m^{2} \)
Subject: Maths
Line \( \overrightarrow{\boldsymbol{r}}=(\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}})+\boldsymbol{t}(\boldsymbol{2} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \)
contained in a plane to which vector \( \vec{n}=3 \hat{i}-2 \hat{j}+\lambda \hat{k} \) is normal. Find the
value of \( \lambda \). Also find the vector equation
of the plane.
Subject: Chemistry
The solubility product of \( M g F_{2} \) is \( 7.4 x \)
\( 10^{-11} . \) Calculate the solubility of \( M g F_{2} \) in \( 0.1 \mathrm{M} \) NaF solution.
A \( .7 .4 \times 10^{-9} \)
В. \( 3.7 \times 10^{-9} \)
c. \( 3.7 \times 10^{-11} \)
D. \( 7.4 \times 10^{-11} \)
Subject: Maths
Solve the given differential equation:
\( \boldsymbol{y}^{2} \boldsymbol{d} \boldsymbol{x}+\left(\boldsymbol{x}^{2}-\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
Subject: Chemistry
Consider the two gaseous equilibrium
involving \( S O_{2} \) and the corresponding equilibrium constants at \( 299 \mathrm{K} \)
\( \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\mathbf{1} / \boldsymbol{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) ; \boldsymbol{K}_{1} \)
\( \mathbf{4} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{4} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{2} \)
The value of the equilibrium constant are related by :-
A \( \cdot_{K_{2}}=\frac{1}{\left(K_{1}\right)^{4}} \)
B. \( K_{2}=K_{1}^{4} \)
c. \( _{K_{2}}=\left(\frac{1}{K_{1}}\right)^{1 / 4} \)
D. \( _{K_{2}}=\frac{1}{K_{1}} \)
Subject: Chemistry
The Henry's law constant for the
solubility of \( N_{2} \) gas in water at \( 298 K \) is \( 1 \times 10^{5} \) atm. The mole fraction of \( N_{2} \) in
air is \( 0.8 . \) Calculate the number of
moles of \( N_{2} \) dissolved in 10 moles of
water at \( 298 K \) and 5 atm.
A \( \cdot 5 \times 10^{-4} \)
В. \( 3 \times 10^{-5} \)
c. \( 4 \times 10^{-4} \)
D. \( 4 \times 10^{-5} \)
Subject: Maths
If \( a+b+c=2 s, \) then the value of \( (s- \)
\( a)^{2}+(s-b)^{2}+(s-c)^{2} \) will be
A \( \cdot s^{2}+a^{2}+b^{2}+c^{2} \)
B. \( a^{2}+b^{2}+c^{2}-s^{2} \)
c. \( s^{2}-a^{2}-b^{2}-c^{2} \)
D. \( 4 s^{2}-a^{2}-b^{2}-c^{2} \)
Subject: Physics
A uniform ring of mass \( m, \) with the
outside radius \( r_{2}, \) is fitted tightly on a
shaft of radius \( r_{1} . \) The shaft is rotated
about its axis with a constant angular
acceleration \( \beta . \) Find the moment
of elastic forces in the ring as a
function of the distance \( r \) from the
rotation axis.
A \( \cdot N=\frac{1}{2} \frac{m \beta}{\left(r_{2}^{2}-r_{1}^{2}\right)}\left(r_{2}^{4}-r^{4}\right) \)
B. \( N=\frac{1}{2} \frac{m \beta}{\left(r_{2}^{2}+r_{1}^{2}\right)}\left(r_{2}^{4}-r^{4}\right) \)
C \( \quad N=\frac{1}{2} \frac{m \beta}{\left(r_{2}^{2}+r_{1}^{2}\right)}\left(r_{2}^{4}+r^{4}\right) \)
D. None of these