AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If the total surface area of a solid
hemisphere is \( 462 \mathrm{cm}^{2} \), find its volume. Note: Take \( \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}} \)
\( \mathbf{A} \cdot 716 \)
B. 718.67
c. 720.87
D. 840
Subject: Chemistry
Calculate the amount of \( C a C l_{2} \) (van't
Hoff factor \( i=2.47 \) ) dissolved in \( 2.5 L \)
solution so that its osmotic pressure at
\( 300 K \) is 0.75 atmosphere
Given: Molar mass of \( C a C l_{2} \) is
\( 111 g \cdot m o l^{-1} \)
\( \boldsymbol{R}=\mathbf{0 . 0 8 2} \boldsymbol{L} . \boldsymbol{a t m} . \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)
Subject: Physics
The resistances in left and right gap of a meter bridge are \( 20 \Omega \) and \( 30 \Omega \) respectively. When the resistance in the
left gap is reduced to half its value, the balance point shifts by
A. \( 15 \mathrm{cm} \) to the right
B. \( 15 \mathrm{cm} \) to the left
c. \( 20 \mathrm{cm} \) to the right
D. \( 20 \mathrm{cm} \) to the left
Subject: Chemistry
\( \mathrm{K} \) for the reaction \( 2 \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons 2 \boldsymbol{C} \) is
\( 1.5 \times 10^{12} . \) This indicates that in
equilibrium the concentration of would be maximum.
\( A \cdot A \)
B. B
\( c \cdot c \)
D. none
Subject: Physics
A battery of emf \( E_{0}=12 \mathrm{V} \) is connected across a \( 4 \mathrm{m} \) long uniform wire having
resistance \( \frac{4 \Omega}{m} . \) The cells of small emfs \( \varepsilon_{1} \)
\( =2 V \) and \( \varepsilon_{2}=4 V \) having internal
resistance \( 2 \Omega \) and \( 6 \Omega \) respectively, are connected as shown in the figure. If
galvanometer shows no deflection at the point \( \mathrm{N} \), find the distance of point \( \mathrm{N} \)
from the point \( \mathbf{A} \)
Subject: Physics
How should the mass of a rotating body
of radius r be distributed so as to
maximize its angular velocity?
A. The mass should be concentrated at the outer edge of the body
B. The mass should be evenly distributed throughout the body
C. The mass should be concentrated at the axis of
rotation
D. The mass should be concentrated at a point midway between the axis of rotation and the outer edge of the body
E. Mass distribution has no impact on angular velocity
Subject: Chemistry
Assertion: The value of \( \boldsymbol{K}_{\boldsymbol{w}} \) increases
with increase in temperature.

Reason: Water dissociates more as
temperature increases.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Physics
A ball is dropped from a height h on the ground. If the coefficient of restitution is e, the height to which the ball goes up after it rebounds for the nth time is
\( A \cdot h e^{2 n} \)
В. \( h e^{n} \)
c. \( \frac{2^{e n}}{h} \)
D. \( \frac{h}{2^{e n}} \)
Subject: Physics
Potential energy of a bar magnet of magnetic moment \( M \) placed in a magnetic field of induction \( B \) Such that
it makes an angle \( \theta \) with the direction
of \( B \) is \( \left(\operatorname{take} \theta=90^{\circ} \) as datum) \right.
\( \mathbf{A} \cdot-M B \sin \theta \)
B. \( -M B \cos \theta \)
c. \( M B(1-\cos \theta) \)
D. \( M B(1+\cos \theta) \)
Subject: Chemistry
\( \ldots B r O_{3}^{-}(a q)+\ldots B r^{-}(a q)+ \)
\( \ldots \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \ldots \boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{l})+\ldots \boldsymbol{H}_{2} \boldsymbol{O} \)
After balancing the above equation.
What is the ratio of coefficient \( B r O_{3}^{-} \) to
\( B r^{-} ? \)
A .1: 5
B. 1: 3
\( c \cdot 1: 2 \)
D. 1:
E. 2: 3
Subject: Chemistry
Assertion
Hydrolysis of ethyl acetate in the
presence of acid is a reaction of first
order whereas in presence of alkali, it is
reaction of second order.
Reason
Acid only acts as a catalyst whereas
alkali acts as one of the reactants.
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 marks of a student in 6 tests are
41,45,54,57,43 and \( x \). If the mean marks of these tests is \( 48, \) then
standard deviation of these tests is?
A \( \cdot \frac{10}{\sqrt{3}} \)
B. \( \frac{10}{\sqrt{2}} \)
c. \( \frac{10}{3} \)
D. \( \frac{20}{3} \)
Subject: Chemistry
Assertion
Plastic is not responsible for utilising a major share of the world's oil or hydrocarbon resources
Reason
plastics use less than \( 4 \% \) of the world's hydrocarbon resources. Approximately
\( 90 \% \) is consumed for transportation,
power generation and heating.
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
For a reaction \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightarrow \) products
when \( \mathrm{B} \) is taken in excess, then the rate
law expression can be written as:
\( \mathbf{A} \cdot \operatorname{Rate}=K[A]^{1}[B]^{0} \)
B . Rate \( =K[A]^{1}[B]^{2} \)
\( \mathbf{c} . \) Rate \( =K[A][B] \)
D. Rate\( =K[A]^{2}[B]^{1} \)
Subject: Maths
The value of \( \left|\begin{array}{lllll}\mathbf{1} & \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} \\ \mathbf{2} & \mathbf{2} & \mathbf{0} & \mathbf{0} & \mathbf{0} \\ \mathbf{4} & \mathbf{4} & \mathbf{3} & \mathbf{0} & \mathbf{0} \\ \mathbf{5} & \mathbf{5} & \mathbf{5} & \mathbf{4} & \mathbf{0} \\ \mathbf{6} & \mathbf{6} & \mathbf{6} & \mathbf{6} & \mathbf{5}\end{array}\right| \)
\( A \cdot 6 \)
B. 5
c. \( 1.2^{2} .3 .4^{3} .5^{4} .6^{4} \)
D. None of these
Subject: Physics
The potential difference between the
wire and the cylinder produces an
electric field of \( 2 \times 10^{4} V m^{-1} \) at a
distance of \( 1.2 \mathrm{cm} \) from the wire
\( \mathbf{A} \cdot 360 V \)
B. \( 180 V \)
\( c \cdot 200 V \)
D. \( 240 V \)
Subject: Physics
What is the conductivity of a semiconductor sample having electron concentration of \( 5 \times 10^{18} \quad m^{-3}, \) hole
concentration of \( 5 \times 10^{19} \quad m^{-3} \)
electron mobility of \( 2.0 m^{2} v^{-1} s^{-1} \) and
hole mobility of \( 0.01 m^{2} v^{-1} s^{-1} ? \)
(Take charge of electron as \( 1.6 \times \)
\( \left.10^{-19} C\right) \)
A \( \cdot 1.68(\Omega-m)^{-1} \)
в. \( 0.59(\Omega-m)^{-1} \)
c. \( 1.83(\Omega-m)^{-1} \)
D. \( 1.20(\Omega-m)^{-1} \)
Subject: Maths
Let \( \mathbf{f}:(-\mathbf{1}, \mathbf{1}) \rightarrow \mathbf{R} \) be a differentiable
function with \( \mathbf{f}(\mathbf{0})=-\mathbf{1} \) and \( \mathbf{f}^{\prime}(\mathbf{0})=\mathbf{1} \)
Let \( \mathbf{g}(\mathbf{x})=[\mathbf{f}(\mathbf{2 f}(\mathbf{x})+\mathbf{2})]^{2} . \) Then \( \mathbf{g}^{\prime}(\mathbf{0})= \)
A . -4
B.
\( c \cdot-2 \)
D. 4
Subject: Maths
If \( \boldsymbol{A}_{1}, \boldsymbol{A}_{3}, \dots \dots A_{2 n-1} \) are \( \boldsymbol{n} \) skew
symmetric matrices of same order, then \( \boldsymbol{B}=\sum_{r=1}^{n}(2 r-1)\left(A_{2 r-1}\right)^{2 r-1} \) will be
A. symmetric
B. skew-symmetricç
c. neither symmetric nor skew-symmetric
D. data not adequate
Subject: Physics
If the first minima in Young's double-slit experiment occurs directly in front of the slits (distance between slit and
\( \operatorname{screen} D=12 c m \) and distance
between slits \( d=5 c m \) ), then the
wavelength of the radiation used can be
\( A \cdot 2 c m \)
в. 4 ст
c. \( _{\overline{3}^{c m}} \)
\( \stackrel{-4}{3}^{c m} \)
Subject: Chemistry
Identify the process to which the
following reaction belongs:
\( A l_{2} O_{3} \cdot 2 H_{2} O+N a_{2} C O_{3} \longrightarrow \)
\( \mathbf{2} N \boldsymbol{a} \boldsymbol{A} \boldsymbol{l} \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C} \boldsymbol{O}_{2} \)
\( \mathbf{2} N \boldsymbol{a} \boldsymbol{A} \boldsymbol{l} \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( C O_{2} 50-60^{\circ} C A l_{2} O_{3} .2 H_{2} O+ \)
\( N a_{2} C O_{3} \)
A. Hall's process
B. Baeyer's process
C. Serpeck's process
D. None of these
Subject: Chemistry
The correct decreasing order of basic strength of the following species is:
\( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{O} \boldsymbol{H}^{-}, \boldsymbol{N} \boldsymbol{H}_{2} \)
\( \mathbf{A} \cdot N H_{2}^{-}>O H^{-}>N H_{3}>H_{2} O \)
в. \( O H^{-}>N H_{2}^{-}>H_{2} O>N H_{3} \)
C. \( N H_{3}>H_{2} O>N H_{2}^{-}>O H^{-} \)
D. \( H_{2} O>N H_{3}>O H^{-}>N H_{2}^{-} \)
Subject: Chemistry
During the electrolysis of carnallite,
\( M g C l_{2} \) is decomposed and not \( K C l \)
This is because of :
A . lower decomposition voltage of \( M g C l_{2} \) than that of \( K C l \)
B. reverse reaction \( M g C l_{2}+2 K \rightarrow M g+2 K C l \), if \( K C l \) i decomposed under other experimental condition
c. both \( A \) and \( B \)
D. none of the above
Subject: Maths
Consider the following statements:
1. If 18 men can earn Rs. 1,440 in 5 days, then 10 men can earn Rs. 1,280 in 6 days.
2. If 16 men can earn Rs. 1,120 in 7
days, then 21 men can earn Rs. 800 in 4
days. Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Maths
Between the number 1 and \( 31, m \)
means are inserted so that the ratio of
\( 7^{t h} \) and \( (m-1)^{t h} \) means is \( 5: 9, \) then
the value of \( m \) is
A . 14
B. 10
\( c \cdot 7 \)
D. 3
Subject: Physics
Two conducting plates \( x \) and \( y \) each of area \( A \) are placed parallel to each other at a small separation \( \boldsymbol{d} . \boldsymbol{X} \) is given a charge \( 3 q \) and \( Y \) is given a charge \( q \) The potential difference between the plates is
A \( \cdot \frac{q d}{2 \varepsilon_{0} A} \)
в. \( \frac{q d}{\varepsilon_{0} A} \)
c. \( \frac{3 q d}{2 \varepsilon_{0} A} \)
D. \( \frac{2 q d}{\varepsilon_{0} A} \)
Subject: Physics
A galvanometer coil has a resistance of
\( 50 \Omega \) and the meter shows full scale
deflection for a current of \( 5 m A \). This
galvanometer is converted into
voltmeter of range \( 0-20 V \) by
connecting
A. \( 3950 \Omega \) in series with galvanometer
B. \( 4050 \Omega \) in series with galvanometer
c. \( 3950 \Omega \) in parallel with galvanometer
D. \( 4050 \Omega \) in parallel with galvanometer
Subject: Biology
When a cross is made between tall
plant with yellow seeds (TtYy) and tall plant with green seeds (Ttyy), what
proportions of phenotype in the offspring could be expected to be
(a) tall
and green (b) dwarf and green
Parents \( \begin{array}{ccc}\text { Tall Yellow } & \times & \text { Tall Green } \\ \pi \mathrm{T} & \mathrm{Ty} & \mathrm{Tt} \text { yy }\end{array} \) Gametes
Phenotypes Tall and Green \( =3 \) Dwarfand Gree war and Yellow
Total \( =8 \) Thus
a) Prooortion
(b) Proportion
Subject: Maths
If \( \alpha, \beta \) are the roots of the equation \( x^{2}- \)
\( 4 x+\lambda=0 \) and \( \gamma, \delta \) are the roots of the
equation \( \boldsymbol{x}^{2}-\mathbf{6 4} \boldsymbol{x}+\boldsymbol{\mu}=\mathbf{0} \) and \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}, \boldsymbol{\delta} \)
are given to be in increasing G.P. The value of \( \mu / \lambda \) be \( 2^{k} . \) Find \( k ? \)
Subject: Physics
A circular coil of 100 turns has an
effective radius of \( 0.05 m \) and carries a
current of \( 0.1 A \). How much work is
required to turn it in an external
magnetic field of \( 1.5 W b / m^{2} \) through
\( 180^{\circ} \) about its axis perpendicular to the magnetic field? The plane of the coil is initially perpendicular to the magnetic field :
A . 0.456 .5
в. \( 2.65 J \)
c. \( 0.2355 J \)
D. 3.95J
Subject: Physics
A body starts from rest and is uniformly
accelerated. for 30 s. The distance
travelled in the first 10 s is \( x_{1}, \) next 10 s
is \( x_{2} \) and the last 10 s is \( x_{3} . \) Then \( x_{1} \)
\( x_{2}: x_{3} \) is the same as
A .1: 2: 4
B. 1: 2: 5
\( c \cdot 1: 3: 5 \)
\( D \cdot 1: 3: 9 \)
Subject: Chemistry
Which of the above represents the formula for the most common
compound of \( A \) and \( B, \) where \( A \) and \( B \) represent given pairs of elements or polyatomic ions as indicated below?
A) \( B e \)
B) \( \boldsymbol{F} \)
\( \mathbf{A} \cdot A B \)
в. \( A B_{2} \)
c. \( A_{2} B \)
D. \( A B_{3} \)
E . \( A_{2} B_{3} \)
Subject: Maths
f \( P(x, y) \) is such that \( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{y} & \mathbf{1} \\ \boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \boldsymbol{1}\end{array}\right|+\left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{y} & \mathbf{1} \\ \boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \boldsymbol{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & 1\end{array}\right|=\mathbf{0} \) then the
line through \( A \) and \( P \) is
A. median of \( \Delta A B C \)
B. bisector of \( \angle A \)
c. altitude through vertex \( A \)
D. perpendicular bisector of the side \( B C \)
Subject: Maths
Evaluate \( \left(\frac{2 x}{7}-\frac{7 y}{4}\right)^{2} \)
A \( \cdot \frac{x^{2}}{49}+\frac{17 y^{2}}{16}-x y \)
B. \( \frac{4 x^{2}}{49}+\frac{49 y^{2}}{16}-x y \)
C \( \cdot \frac{4 x^{2}}{9}+\frac{49 y^{2}}{4}-x y \)
D. \( \frac{x^{2}}{13}+\frac{49 y^{2}}{13}-x y \)
Subject: Physics
Assume that the nuclear binding energy per nucleon (B/A) versus mass number
(A) is as shown in the figure. Use
this plot to choose the correct choice(s)
given below.
This question has multiple correct options
A. Fusion of two nuclei with mass numbers lying in the range of \( 1<A<50 \) will release energy
B. Fusion of two nuclei with mass numbers lying in the range of \( 51<A<100 \) will release energy
c. Fission of a nucleus lying in the mass range of 100 < \( A<200 \) will release energy when broken into two equal fragments
D. Fission of a nucleus lying in the mass range of \( 200< \) \( A<260 \) will release energy when broken into two
equal fragments
Subject: Maths
Find the values of a and \( b, \) if \( A=B, \) where
\[
\begin{array}{c}
\boldsymbol{A}=\left[\begin{array}{cc}
\boldsymbol{a}+\boldsymbol{4} & \boldsymbol{3} \boldsymbol{b} \\
\boldsymbol{8} & -\boldsymbol{6}
\end{array}\right] \text { and } \boldsymbol{B}= \\
{\left[\begin{array}{cc}
\boldsymbol{2} \boldsymbol{a}+\boldsymbol{2} & \boldsymbol{b}^{2}+\boldsymbol{2} \\
\boldsymbol{8} & \boldsymbol{b}^{2}-\boldsymbol{5} \boldsymbol{b}
\end{array}\right]}
\end{array}
\]
Subject: Chemistry
1.00 g of a hydrated salt contains 0.2014 g of iron, 0.1153 g of sulphur \( 0.2301 \mathrm{g} \) of oxygen and \( 0.4532 \mathrm{g} \) of water of crystallisation. How much water molecules are present in its empirical formula? \( (\boldsymbol{F} \boldsymbol{e}=\mathbf{5} \mathbf{6} ; \boldsymbol{S}= \)
\( \mathbf{3 2} ; \boldsymbol{O}=\mathbf{1 6} \)
Subject: Chemistry
Which is more stable in the below
given pair?
\( V^{2+}-- \)
\( \boldsymbol{V} \boldsymbol{O}_{4}^{3-} \)
A \( \cdot V^{2+}=V O_{4}^{3-} \)
B . \( V^{2+}<V O_{4}^{3-} \)
c. \( V^{2+}>V O_{4}^{3-} \)
D. None of these
Subject: Physics
Two pieces of resistance wire, \( A \) and \( B \) are cut from the same coil. A is twice as
long as B. The difference between the total resistance of the combination of
wires \( A \) and \( B \), when connected in series
and in parallel is \( 21 \Omega \). The resistance of
A will be.
A . \( 18 \Omega \)
B . \( 16.5 \Omega \)
c. \( 14 \Omega \)
D. \( 18.6 \Omega \)
Subject: Chemistry
What type of isomers are the following?
\( \left[(\boldsymbol{C O})_{5} \boldsymbol{M} \boldsymbol{n} \boldsymbol{S} \boldsymbol{C} \boldsymbol{N}\right] \boldsymbol{a} \boldsymbol{n} \boldsymbol{d}\left[(\boldsymbol{C} \boldsymbol{O})_{5} \boldsymbol{M} \boldsymbol{n} \boldsymbol{N} \boldsymbol{C} \boldsymbol{S}\right] \)
A. coordination
B. Linkage
c. solvate
D. lonization
Subject: Chemistry
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O}(s) \rightleftharpoons \boldsymbol{C u S O}_{4} \cdot \boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \)
\( +2 H_{2} O(g) ; K_{p}=4 \times 10^{-4} a t m^{2} \) if the
vapour pressure of water is 38 torr then percentage of relative humidity is:
Assume all data at constant
temperature)
\( \mathbf{A} \cdot \mathbf{4} \)
B. 10
c. 40
D. none of these
Subject: Physics
Water is poured from a height of \( 10 \mathrm{m} \) into an empty barrel at the rate of 1 litre per second. If the weight of the barrel is
\( 10 \mathrm{kg}, \) the weight indicated at time \( t= \)
60 s will be
A . \( 71.4 \mathrm{kg} \)
в. \( 68.6 \mathrm{kg} \)
c. \( 70.0 \mathrm{kg} \)
D. \( 84.0 \mathrm{kg} \)
Subject: Biology
Human heart is myogenic and it is supplied with sympathetic and vagus nerve branches that are
acceleratory and inhibitory in nature respectively.Which one of the following statement is incorrect w.r.t the heart
beat?
A. In foetal heart the heart rate is \( 140-130 \) beats per minutes
B. Mental status such as depression and grief decrease heart rate
C. An excess of \( C a^{++} \) ion decreases heart beat rate
D. High levels of \( N a^{+} \) and \( K^{+} \) decreases the strength of contraction
Subject: Maths
The number of ways in which the letters
of the word \( A R R A N G E \) can be
permuted such that the \( R \) 's occur together is
A. \( \frac{7 !}{2 ! 2 ! ! !} \)
в. \( \frac{7 !}{2 !} \)
c. \( \frac{6 !}{2 !} \)
D. \( 5 ! \times 2 ! \)
Subject: Chemistry
Assertion \( (A): \ln B r F_{3} \) oxidation state
of \( \boldsymbol{F} \) is \( +\mathbf{3} \)
Reason (R): Electronegativity of \( \boldsymbol{F} \) is more than that of bromine.
A. A and R are true, R is correct explanation of A
B. A and R are true, R is not correct explanation of A
c. A is true, but R is false
D. A is false, but R is true
Subject: Chemistry
Elements of the group- 15 form
compounds in +5 oxidation state. However, bismuth forms only one wellcharacterized compound in +5 oxidation state. The compound is:
A. \( B i_{2} O_{5} \)
в. \( B i F_{5} \)
c. \( B i C l_{5} \)
D. \( B i_{2} S_{5} \)
Subject: Biology
Which of the following statements is/are true?
(a) One ATP molecule yields \( 30-32 \) kJ of
energy.
(b) Pentose phosphate pathway was discovered by Dickens.
(c) When tripalmitin is used as a substance, the R.Q is 0.9
(d) Energy released by one molecule of glucose on complete oxidation corresponds to about \( 1292 \mathrm{kJ} \)
\( A \). a and b only
B. c and donly
c. a and donly
D. a, c and donly
E. conly
Subject: Chemistry
From the given data of the following reactions;
\[
\begin{aligned}
\boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{H}_{2}(\boldsymbol{g}) & \rightleftharpoons \boldsymbol{C a}(\boldsymbol{s})+\\
\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) ; & \boldsymbol{K}=\mathbf{6 7 0} \\
\boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}(\boldsymbol{g}) & \rightleftharpoons \boldsymbol{C a}(\boldsymbol{s})+\\
\boldsymbol{C O}_{2}(\boldsymbol{g}) ; & \boldsymbol{K}=\mathbf{4 9 0}
\end{aligned}
\]
The value of \( K_{c} \) (nearest integer) for the given reaction is
\[
\begin{array}{c}
\boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+ \\
\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})
\end{array}
\]
Subject: Physics
A particle is travelling along a straight line \( O X . \) The distance \( x \) (in metre) of
the particle from \( \boldsymbol{O} \) at a time \( ^{\prime} \boldsymbol{t}^{\prime} \) is given
by \( \boldsymbol{x}=\mathbf{3 7}+\mathbf{2 7 t}-\boldsymbol{t}^{3}, \) where 't' is time in
second. The distance of the particle
from \( O \),when it comes to rest is:
A. \( 81 m \)
в. \( 91 m \)
c. \( 101 m \)
D. \( 111 m \)
Subject: Chemistry
(a) Define molar conductivity of a solution and explain how molar
conductivity changes which change in concentration of solution for a weak and
a strong electrolyte?
(b) The resistance of a conductivity cell
containing \( 0.001 M \) KCl solution at 298
Kis \( 1500 \Omega \). What is the cell constant if
the conductivity of \( 0.001 \mathrm{M} \) KCl solution
at \( 298 \mathrm{K} \) is \( 0.146 \times 10^{-3} \mathrm{S} \mathrm{cm}^{-1} \) ?
Subject: Physics
The weight of a rider, driving scooter is assumed to be evenly distributed on both the tyres. The area of contact of
each tyre with the ground is \( 10 \mathrm{cm}^{2} \). If the pressure inside the tyres is 2 bar,
find the mass of the rider. \( (\boldsymbol{g}= \)
\( \left.10 m s^{-2}\right) \)
A. \( 40 \mathrm{kg} \)
B. 50 kg
\( c \cdot 60 \mathrm{kg} \)
D. 70 kg
Subject: Chemistry
If \( 33 \% \) HI decompose at a particular
temperature, \( K_{c} \) for the reaction is
equal to?
\( \mathbf{2} \boldsymbol{H} \boldsymbol{I} \rightleftharpoons \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \)
A . \( 1 / 6 \)
B . \( 1 / 4 \)
c. \( 1 / 16 \)
D. \( 1 / 8 \)
Subject: Maths
\( \int \sec ^{2} x \cdot \operatorname{cosec}^{2} x d x= \)
\( \mathbf{A} \cdot \tan x-\cot x+c \)
B. \( \tan x+\cot x+c \)
c. \( -\tan x+\cot x+c \)
\( D \cdot \sec x \tan x+c \)
Subject: Maths
Eccentricity of hyperbola \( \frac{\boldsymbol{x}^{2}}{\boldsymbol{k}}-\frac{\boldsymbol{y}^{2}}{\boldsymbol{k}}=\mathbf{1} \)
A \( \cdot \sqrt{1+k} \)
B. \( \sqrt{1-k} \)
\( c \cdot \sqrt{2} \)
\( D \cdot 2 \sqrt{2} \)
Subject: Chemistry
In the reaction \( 2 N O_{(g)}+2 H_{2_{(g)}} \rightarrow \)
\( N_{2_{(g)}}+2 H_{2} O, \) if initial concentration of
hydrogen is kept constant and the concentration of NO is doubled, the rate
of reaction increases by 4 times. This shows that rate is directly proportional
to
A. catalyst
B. concentration of nitric oxide
c. concentration of Hydrogen
D. concentration of water
Subject: Physics
In the figure given below, there are two
convex lens \( L_{1} \) and \( L_{2} \) having focal
length of \( f_{1} \) and \( f_{2} \) respectively. The
distance between \( L_{1} \) and \( L_{2} \) will be
\( A \cdot f_{1} \)
B \( \cdot f_{2} \)
\( c \cdot f_{1}+f_{2} \)
D. \( f_{1}-f_{2} \)
Subject: Maths
Events \( E_{1}, E_{2}, E_{3} \) are possible events of an experiment and their probabilities are recorded.Mark the possible correct
answers.
This question has multiple correct options
\( \begin{array}{ll}\text { A } \cdot P\left(E_{1}\right)=0.3, & P\left(E_{2}\right)=0.4, \quad P\left(E_{3}\right)=0.3\end{array} \)
B - \( P\left(E_{1}\right)=0.1, \quad P\left(E_{2}\right)=0.4, \quad P\left(E_{3}\right)=0.5 \)
C \( \cdot P\left(E_{1}\right)=0.6, \quad P\left(E_{2}\right)=-0.3, \quad P\left(E_{3}\right)=0.7 \)
D \( \cdot P\left(E_{1}\right)=0.4, \quad P\left(E_{2}\right)=0.2, \quad P\left(E_{3}\right)=0.3 \)
Subject: Physics
An electric heater consists of a
nichrome coil and runs under \( 220 V \)
consuming \( 1 k W \) power. Part of its coil
burned out and it was reconnected after
cutting off the burnt portion, The power
it will consume now is:
A. More than \( 1 k W \)
B. Less that \( 1 k W \), but not zero
\( \mathrm{c} .1 \mathrm{kW} \)
D. \( 0 k W \)
Subject: Chemistry
Pick out the correct statement.
A. Compared to a strong acid, a weak acid titration with base starts at a higher pH
B. Compared to a strong acid, a weak acid titration with base starts at a lower pH
\( \mathbf{C} \cdot H C N(a q)+N O_{2}^{-}(a q) \longrightarrow H N O_{2}(a q)+C N^{-}(a q) \)
D. None of these
Subject: Chemistry
Choose the correct answer among the alternatives given:
Study the following sequence of reaction and identify the compounds
\( (X) \) and \( (Y) \)
A. \( X= \) Benzaldehyde, \( Y= \) Benzoic acid
B. \( X=2 \) -Chlorotoluene, \( Y=2 \) -chlorobenzoic acid
c. \( X=2, \) 4 - Dichlorobenzene, \( Y= \) Benzoic acid
Subject: Maths
Prove that \( \left|\begin{array}{ccc}a^{2} & b c & a c+c^{2} \\ a^{2}+a b & b^{2} & a c \\ a b & b^{2}+b c & c^{2}\end{array}\right| \)
\( =4 a^{2} b^{2} c^{2} \)