AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Given the reaction between 2 gases
represented by \( A_{2} \) and \( B_{2} \) to give the
compound \( \boldsymbol{A B}_{(\boldsymbol{g})} \)
\( \boldsymbol{A}_{2(g)}+\boldsymbol{B}_{2(g)} \rightleftharpoons \mathbf{2} \boldsymbol{A} \boldsymbol{B}_{(g)} \)
At equilibrium, the concentration
of \( \boldsymbol{A}_{2}=\mathbf{3} . \mathbf{0} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \)
of \( \boldsymbol{B}_{2}=\boldsymbol{4} . \boldsymbol{2} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \)
of \( \boldsymbol{A B}=\mathbf{2 . 8} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \)
If the reaction takes place in a sealed
vessel at \( 527^{\circ} C, \) then the value of \( K_{c} \)
will be:
A . 1.9
B. 0.62
c. 4.5
D. 2.0
Subject: Chemistry
In the solid state \( P C l_{5} \) exists as:
A \( \cdot\left[P C l_{4}\right]^{-} \) and \( \left[P C l_{6}\right]^{+} \) ions
B. covalent \( P C l_{5} \) molecules only
\( \mathbf{c} \cdot\left[P C l_{4}\right]^{+} \) and \( \left[P C l_{6}\right]^{-} \) ions
D. covalent \( P_{2} C l_{10} \) molecules only
Subject: Maths
Attempt the following:
The table gives the ages of husbands and wives:
Find:
a. The marginal frequency
distribution of the age of husbands.
b. The conditional frequency distribution of the age of husbands
when the age of wives lies between 25
35
\begin{tabular}{|c|c|c|c|c|}
\hline Age of wires (in years) & \multicolumn{3}{|c|} { Age of husbands (in years) } \\
\hline \( 15-25 \) & \( 20-30 \) & \( 30-40 \) & \( 40-50 \) & \( 50-60 \) \\
\hline \( 25-35 \) & \( - \) & 9 & 3 & \( - \) \\
\hline \( 35-45 \) & \( - \) & 10 & 25 & 2 \\
\hline \( 45-55 \) & \( - \) & \( - \) & 4 & 2 \\
\hline \( 55-65 \) & \( - \) & \( - \) & \( - \) & 16 \\
\hline
\end{tabular}
Subject: Physics
A person is walking along positive \( \boldsymbol{x} \)
axis for \( 10 m \) and then takes left turn by
angle \( 60^{\circ} \) and then moves for 8 m. The
direction of displacement of person with \( x- \) axis is:
\( ^{\mathrm{A}} \cdot_{\theta}=\tan ^{-1}\left(\frac{\sqrt{3}}{14}\right) \)
в. \( _{\theta}=\tan ^{-1}\left(\frac{\sqrt{3}}{7}\right) \)
c. \( _{\theta=\tan ^{-1}}\left(\frac{3 \sqrt{3}}{7}\right) \)
D. \( _{\theta=\tan ^{-1}}\left(\frac{2 \sqrt{3}}{7}\right) \)
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{2 1}\}, \boldsymbol{B}= \)
\( \{\mathbf{4}, \mathbf{8}, \mathbf{1 2}, \mathbf{1 6}, \mathbf{2 0}\}, \boldsymbol{C}= \)
\( \{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}, \mathbf{1 4}, \mathbf{1 6}\} \) and \( \boldsymbol{D}= \)
\( \{\mathbf{5}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{2 0}\} . \) Find \( \boldsymbol{A}-\boldsymbol{D} \)
Subject: Physics
The actual value of the acceleration of
gravity is \( 9.8 \mathrm{m} / \mathrm{s} \). Physics students in a laboratory experiment use a pendulum to determine the acceleration of gravity. Their experimental value is \( 9.2 m / s \)
What is their percent error?
A . \( 0.60 \% \)
B. \( 60 \% \)
\( c .6 .5 \% \)
D. \( 61 \% \)
E . \( 6.1 \% \)
Subject: Maths
The value of \( c \) in Lagrange mean
value theorem for \( f(x)=\log (\sin x) \) in \( \left[\frac{\pi}{6}, \frac{5 \pi}{6}\right] \) is
This question has multiple correct options
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{2} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{3 \pi}{4} \)
Subject: Physics
When the current changes from \( +2 A \) to
\( -2 A \) in 0.05 second, an e.m.f. of \( 8 V \) is
induced in a coil. The coefficient of self-
induction of the coil is
\( \mathbf{A} \cdot 0.2 H \)
в. \( 0.4 \mathrm{H} \)
c. \( 0.8 H \)
D. \( 0.1 H \)
Subject: Maths
Discuss the applicability of Rolle's theorem for the following function on the indicated interval:
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{3}[\boldsymbol{x}] \) for \( -\mathbf{1} \leq \boldsymbol{x} \leq \mathbf{1}, \) where \( [\boldsymbol{x}] \)
denotes the greatest integer not
exceeding \( \boldsymbol{x} \)
Subject: Maths
Let \( X \) denote the number of hours you
study during a randomly selected school day. The probability that \( X \) can
take the value 'x' has the following from, where 'k' is some unknown constant.
\( p=(X=X)= \)
\( \left\{\begin{array}{ll}\mathbf{0 . 1}, & \boldsymbol{i f} \boldsymbol{x}=\mathbf{0} \\ \boldsymbol{k} \boldsymbol{x}, & \boldsymbol{x}=\mathbf{1} \boldsymbol{o r} \mathbf{2} \\ \boldsymbol{k}(\mathbf{5}-\boldsymbol{x}), & \boldsymbol{i f} \boldsymbol{x}=\mathbf{3} \boldsymbol{o r} \mathbf{4} \\ \mathbf{0}, & \text { otherwise }\end{array}\right. \)
(a) find the value of 'k'
(b) what is the probability that you study :
(i) at least two hours?
(ii) exactly two hours??
(iii) at most 2 hours?
Subject: Chemistry
The table below shows recorded
concentration data for the following chemical reaction:
\[
\begin{array}{l}
\boldsymbol{C a C l}_{2}(\boldsymbol{a q})+\mathbf{2 A g} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{a q}) \rightarrow \\
\boldsymbol{C a}\left(\boldsymbol{N O}_{3}\right)_{2}(\boldsymbol{a q})+\boldsymbol{2 A g} \boldsymbol{C l}(\boldsymbol{s})
\end{array}
\]
Use the data to determine the
exponents \( x \) and \( y \) in the rate law:
\[
0.100
\]
\[
0.050
\]
\( 6.66 \times 10^{-} \)
100 100
\( 13.32 \times 10 \)
A \( . x=2, y=3 \)
B. \( x=1, y=2 \)
c. \( x=1, y=1 \)
D. \( x=2, y=2 \)
Subject: Chemistry
The reaction of zinc metal and \( H C l \)
produces which of the following?
¡. \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
¡¡¡. \( C l_{2}(g) \)
iii. \( Z n C l_{2}(a q) \)
A. ii only
B. iii only
c. i and ii only
D. i and iii only
E. i, ii and iii
Subject: Maths
Diagonals \( A C \) and \( B D \) of a trapezium
\( A B C D \) with \( A B \| D C \) intersect each
other at \( O . \) Prove that \( a r(A O D)= \)
\( \boldsymbol{a} \boldsymbol{r}(\boldsymbol{B O C}) \)
Subject: Physics
A plane electromagnetic wave travelling in a non magnetic medium is given by
\( \boldsymbol{E}=\left(\boldsymbol{9} \times \mathbf{1 0}^{8} \boldsymbol{N} \boldsymbol{C}^{-1}\right) \boldsymbol{s i n}[(\boldsymbol{9} \times \)
\( \left.10^{8} \text { rads}^{-1}\right) t-\left(6 m^{-1}\right) x \)
Where \( x \) is in metre and \( t \) is in second.
The dielectric constant of the medium
is:
A. 5
B. 4
\( c \cdot 3 \)
D.
Subject: Physics
A beam of light of wavelength 600 nm from a distance source falls on a single
slit 1 mm wide and a resulting
diffraction pattern is observed on a
screen 2 m away. The distance between
the first dark fringes on either side of central bright fringe is
\( \mathbf{A} \cdot 1.2 \mathrm{cm} \)
B. \( 1.2 m m \)
c. \( 2.4 c m \)
D. \( 2.4 m m \)
Subject: Maths
Let tangents at \( A\left(z_{1}\right) \) and \( B\left(z_{1}\right) \) are drawn to the circle \( |z|=2 . \) Then which of the following is/are CORRECT ?
A \( \cdot \) The equation of tangent at \( A \) is given by \( \frac{z}{z_{1}}+\frac{\bar{z}}{\overline{z_{1}}}=2 \)
B. If tangents at \( A\left(z_{1}\right) \) and \( B\left(z_{2}\right) \) intersect at \( P\left(z_{p}\right) \), then \( z_{p}=\frac{2 z_{1} z_{2}}{z_{1}+z_{2}} \)
c. slope of tangent at \( A\left(z_{1}\right) \) is \( \frac{1}{i}\left(\frac{z_{1}+\bar{z}_{1}}{z_{1}-\bar{z}_{1}}\right) \)
D. If points \( A\left(z_{1}\right) \) and \( B\left(z_{2}\right) \) on the circle \( |z|=2 \) are such that \( z_{1}+z_{2}=0, \) then tangents intersect at \( \frac{\pi}{2} \)
Subject: Chemistry
In which of the following pair(s), is/are the stronger bond found in the first
species? This question has multiple correct options
A. \( O_{2}^{-}, O_{2} \)
в. \( N_{2}, O_{2}^{+} \)
c. \( N O^{+}, N O \)
D. \( O_{2}^{-}, O_{2}^{2+} \)
Subject: Physics
A bus travelling along a straight highway covers one-third of the total distance between two places with a velocity \( 20 k m h^{-1} . \) The remaining part
of the distance was covered with a
velocity of \( 30 k m h^{-1} \) for the first half of
the remaining time and with velocity
\( 50 k m h^{-1} \) for the next half of the time.
Find the average velocity of the bus for its whole journey.
Subject: Maths
\( \operatorname{Let} f(x)=\left(2-\frac{x}{a}\right)^{\tan \left(\frac{\pi x}{2 a}\right)}, x \neq a \)
The value which should be assigned to \( f \) at \( x=a \) so that it is continuous
everywhere is
A \( -\frac{2}{\pi} \)
B . \( e^{-2 / \pi} \)
\( c \cdot 2 \)
\( \mathbf{D} \cdot e^{2 / \pi} \)
Subject: Physics
A vessel of volume 4 litres contains a
mixture of \( 8 ~ g \) of \( 0_{2}, 14 \) g of \( \mathrm{N}_{2} \) and \( 22 \mathrm{g} \)
of \( \mathrm{CO}_{2} \) at \( 27^{\circ} \mathrm{C} \). The pressure exerted by the mixture is
A \( \cdot 5 \times 10^{6} N / m^{2} \)
B . \( 6 \times 10^{3} N / m^{2} \)
c. 10 atmosphere
D. \( 7.79 \times 10^{5} N / m^{2} \)
Subject: Maths
If \( \boldsymbol{x}, \mathbf{1}, \boldsymbol{z} \) are in \( \mathbf{A P} \) and \( \boldsymbol{x}, \boldsymbol{2}, \boldsymbol{z} \) are in \( \mathbf{G P} \)
then \( x, 4 ; z \) will be in
\( A \cdot A P \)
в. GP
c. нр
D. None of these
Subject: Chemistry
A. Carnallite
1. Zinc
B. Calamine
2. Titanium
C. Limonite
3. Magnesium
D. Chalcopyrite
4. Copper
Match List I with List II and select the
correct answer using the codes given below the lists.
A. A-1,B-3,C-2,D-4
B. A-1,B-3,C-4,D-2
C . A-3,B-1,C-4,D-2
D. A-3,B-1,C-2,D-4
Subject: Physics
The positive vector of a particle is
determined by the expression \( \vec{r}= \) \( 3 t^{2} \hat{i}+4 t^{2} \hat{j}+7 \hat{k} . \) The distance
traversed in first 10 sec is:
A. \( 500 \mathrm{m} \)
B. 300 \( m \)
c. \( 150 \mathrm{m} \)
D. \( 100 \mathrm{m} \)
Subject: Maths
If \( f(x)=\cos ^{-1}\left[\frac{1-(\log x)^{2}}{1+(\log x)^{2}}\right], \) then
\( \boldsymbol{f}^{\prime}(\boldsymbol{e})= \)
\( A \cdot \frac{1}{e} \)
B. \( \frac{2}{e^{2}} \)
\( c \cdot \frac{2}{e} \)
D. None of these
Subject: Physics
A force of magnitude 6 in the direction of the vector \( \vec{i}-2 \vec{j}+2 \vec{k} \) acts at the point whose position vector is \( \vec{i}-\vec{j} \). \( A \)
second force acting at the point with position vector \( \vec{j}-\vec{k} \) forms a couple
with the first force. Find the vector
moment of the couple.
\( \mathbf{A} \cdot-(2 \vec{i}+\vec{j}) \)
B . \( -2(2 \vec{i}+\vec{j}) \)
c. \( -4(2 \vec{i}+\vec{j}) \)
D. \( -8(2 \vec{i}+\vec{j}) \)
Subject: Chemistry
Balanced equation of the reaction of
formation of \( P b O_{2} \) at the anode is
\( P b^{2+}(a q)+x H_{2} O \rightleftharpoons P b O_{2} \downarrow \)
\( +\boldsymbol{y} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{z} \boldsymbol{e}^{-} \)
What will be value of y?
Subject: Maths
\( \mathrm{f}[\mathbf{2} \mathbf{1} \mathbf{3}]\left[\begin{array}{ccc}-\mathbf{1} & \mathbf{0} & \mathbf{1} \\ -\mathbf{1} & \mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1} & \mathbf{1}\end{array}\right]\left[\begin{array}{l}\mathbf{1} \\ \mathbf{0} \\ \mathbf{1}\end{array}\right]=\boldsymbol{A}, \) then
write the order of matrix \( \boldsymbol{A} \)
Subject: Maths
\( P \rightarrow(q \rightarrow r) \) is logically equivalent to
A \( \cdot(q \vee q) \rightarrow \sim r \)
в. \( (p \wedge q) \rightarrow \sim r \)
c. \( (p \vee q) \rightarrow r \)
D. \( (p \wedge q) \rightarrow r \)
Subject: Physics
A stone is thrown in vertically upward direction with a velocity of \( 5 m s^{-1} \). If the acceleration of the stone during its
motion is \( 10 \mathrm{ms}^{-2} \) in the downward direction, what will be the height
attained by the stone and how much time will it take to reach there?
A. Height=1.25 \( m \) and time \( =0.5 \) s
B. Height= 2.5 \( m \) and time \( =0.5 \) s
c. Height= \( 2.5 \mathrm{m} \) and time \( =0.05 \mathrm{s} \)
D. Height=1.25 \( m \) and time \( =0.05 \) s
Subject: Maths
\( \ln a \Delta A B C, D, E, F \) are respectively
the mid- points of \( B C, C A, \) and \( A B . \) If
the lengths of side \( A B, B C \) and \( C A \) are \( \mathbf{7} c \boldsymbol{m}, \mathbf{8} \boldsymbol{c m}, \mathbf{9} \boldsymbol{c m}, \) respectively, find the
perimeter of \( \Delta \) DEF.
A . \( 12 \mathrm{cm} \)
B. \( 21 \mathrm{cm} \)
c. \( 24 \mathrm{cm} \)
D. \( 16 \mathrm{cm} \)
Subject: Physics
In a certain region of space, electric field is along the z-direction throughout The magnitude of electric field is, however, not constant but increases
uniformly along the positive z-direction, at the rate of \( 10^{5} N C^{-1} m^{-1} \) per metre. What are the force and torque
experienced by a system having a total
dipole moment equal to \( 10^{-7} \mathrm{Cm} \) in the negative z-direction?
Subject: Maths
Assertion
The largest term in the sequence \( a_{n}= \) \( \frac{n^{2}}{n^{3}+200}, n \in N \) is the \( 7^{t h} \) term
Reason
The function \( f(x)=\frac{x^{2}}{x^{3}+200} \) attains
local maxima at \( x=7 \)
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: Maths
Assume that water issuing from the end of a horizontal pipe, 7.5 m above the ground, describes a parabolic path. The vertex of the parabolic path is at the end of the pipe. At a position \( 2.5 \mathrm{m} \) below the line of the pipe, the flow of water has curved outward from \( 3 \mathrm{m} \), beyond the
vertical line through the end of the pipe. How far beyond this vertical line will the water strike the ground?
Subject: Chemistry
Oxidation number of iodine in
\( I O_{3}^{-}, I O_{4}^{-}, K I \) and \( I_{2} \) respectively
are
A. -1,-1,0,+1
B. +3,+5,+7,0
\( \mathbf{c} .+5,+7,-1,0 \)
D. -1,-5,-1,0
E. -2,-5,-1,0
Subject: Maths
ff \( f(x)=a x+b \) and \( g(x)=c x+d \)
\( \operatorname{then} f(g(x))=g(f(x)) \) implies
\( \mathbf{A} \cdot f(a)=g(c) \)
B. \( f(b)=g(b) \)
c. \( f(d)=g(b) \)
D. \( f(c)=g(a) \)
Subject: Maths
Assertion
\( \boldsymbol{P}(\boldsymbol{H} / \boldsymbol{E})>\boldsymbol{P}\left(\boldsymbol{E} / \boldsymbol{H}_{i}\right) \boldsymbol{P}\left(\boldsymbol{H}_{i}\right), \boldsymbol{i}= \)
\( \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots, \boldsymbol{n} . \operatorname{Let} \boldsymbol{H}_{1}, \boldsymbol{H}_{2}, \boldsymbol{H}_{3}, \dots . . \boldsymbol{H}_{n} \) be \( \mathbf{n} \)
mutually exclusive \& exhaustive
events with probability \( \boldsymbol{P}\left(\boldsymbol{H}_{\boldsymbol{i}}\right)>\mathbf{0}, \boldsymbol{i}= \)
\( 1,2,3, \dots n . \) Let \( E \) be any other event with
\( \mathbf{0}<\boldsymbol{P}(\boldsymbol{E})<\mathbf{1} \)
Reason
\( \sum_{i=1}^{n} \boldsymbol{P}\left(\boldsymbol{H}_{i}\right)=\mathbf{1} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Maths
Assertion
if \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{2}|+|\boldsymbol{x}-\mathbf{4}|+|\boldsymbol{x}-\mathbf{6}| \)
an identify function for \( 4<x<6 \)
Reason
\( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{A}, \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \) is an
identify function
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: Maths
Find the mean of the following
frequency distribution:
\( \begin{array}{lll}\text { Marks obtained } & \text { Number of students } \\ \text { 10-20 } & 6 \\ \text { 20-30 } & 8 \\ \text { 30-40 } & 13 \\ \text { 40-50 } & 7 \\ \text { 50-60 } & 3 \\ \text { 60-70 } & 2 \\ \text { 70-80 } & 1\end{array} \)
Subject: Physics
A radio isotope 'X' with a half life \( 1.4 \times \)
\( 10^{9} \) years decays to 'Y' which is stable. A
sample of the rock from a cave was found to contain ' \( X \) ' and ' \( Y \) ' in the ratio
1 : 7. The age of the rock is
A \( \cdot 1.96 \times 10^{9} \)years
В. \( 3.92 \times 10^{9} \) years
c. \( 4.20 \times 10^{9} \) years
D. \( 8.40 \times 10^{9} \) years
Subject: Maths
Let \( \boldsymbol{A}= \)
\( \{x \in W, \) the set of whole numb
\( \boldsymbol{B}= \)
\( \{\boldsymbol{x} \in \boldsymbol{N}, \) the set of natural num
and \( C=\{3,4\}, \) then how many
elements will \( (A \cup B) \times C \) conatin?
\( \mathbf{A} \cdot \mathbf{6} \)
B. 8
c. 10
D. 12
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\frac{\sin \boldsymbol{x}}{\boldsymbol{x}}\right) \)
A. \( \frac{x \cos x-\sin x}{x^{2}} \)
B. \( \frac{x \cos x+\sin x}{x^{2}} \)
c. \( \frac{x \cos x+\sin x}{x^{3}} \)
D. \( \frac{x \cos x-\sin x}{x^{3}} \)
Subject: Physics
A block of mass \( 100 g \) is moved with a speed of \( 5.0 m / s \) at the highest point in a closed circular tube of radius tube of
radius \( 10 \mathrm{cm} \) kept in a vertical plane. The cross-section of the tube is such
that the block just fits in it. The block makes several oscillations inside the
tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.
A. \( -1.45 \mathrm{J} \)
в. +1.45 J
c. \( -2.9 J \)
D. \( +2.9 J \)
Subject: Chemistry
\( Z n^{2+} \) salts appear acidic due to hydrolysis. Identify acid and base in the following:
\( \left[Z n\left(H_{2} O\right)_{4}\right]^{2+}+H_{2} O \rightleftharpoons \)
\( \left[Z n\left(H_{2} O\right)_{3} O H\right]^{+}+H_{3} O^{+} \)
\( \mathbf{A} \cdot\left[Z n\left(H_{2} O\right)_{4}\right]^{2+}(\text { base }),\left[Z n\left(H_{2} O\right)_{3} O H\right]^{+} \) (base)
B . \( \left[Z n\left(H_{2} O\right)_{4}\right]^{2+} \) (acid) \( ,\left[Z n\left(H_{2} O\right)_{3} O H\right]^{+} \) (base)
C \( \cdot\left[Z n\left(H_{2} O\right)_{4}\right]^{2+} \) (acid), \( H_{3} O^{+} \) (base)
D \( \cdot\left[\operatorname{Zn}\left(H_{2} O\right)_{3} O H\right]^{+} \) (acid), \( H_{3} O^{+} \) (base)
Subject: Biology
A woman has only daughters. Which of the following is the suitable explanation
for it?
A. The man produces sperms with \( x \) and \( Y \) chromosome but only that with \( Y \) chromosomes are viable
B. The man produces sperms with \( x \) and \( Y \) chromosome but only that with \( x \) chromosomes are viable
c. The man produces sperms with \( x \) and \( Y \) chromosome and all are viable
D. None of the above
Subject: Physics
The induced EMF in loop at time \( t= \)
\( 2 \pi / \omega \) is :
\( A \cdot O \)
B. \( \frac{B_{0} \pi \omega R^{2}}{2} \)
\( \mathbf{c} \cdot B_{0} \pi \omega R^{2} \)
D. \( -\frac{B_{0} \pi \omega R^{2}}{2} \)
Subject: Maths
On a plane are two points \( A \) and \( B \) at a
distance of 5 units apart. The number of straight lines in this plane which are at distance of 2 units from \( A \) and 3 units
from \( \mathrm{B} \) are:
A . 1
B. 2
\( c .3 \)
D. 4
Subject: Physics
On interchanging the resistances, the balance point of a meter bridge shifts to
the left by \( 10 \mathrm{cm} . \) The resistance of their series combination is \( 1 k \Omega \). How much
was the resistance on the left slot
before interchanging the resistances?
A . \( 550 \Omega \)
в. \( 910 \Omega \)
\( \mathbf{c} .990 \Omega \)
D. \( 505 \Omega \)
Subject: Chemistry
Calculate the enthalpy change on freezing of 1.0 mol of water at \( 10.0^{\circ} \mathrm{C} \) to
ice at \( -10.0^{\circ} \mathrm{C} \)
\( \triangle_{f u s} H=6.03 K J m o l^{-1} \) at \( 0^{\circ} C \)
\( \boldsymbol{C}_{\boldsymbol{p}}\left[\boldsymbol{H}_{2} \boldsymbol{O}(1)\right]=\mathbf{7 5 . 3} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1} \)
\( \boldsymbol{C}_{\boldsymbol{p}}\left[\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s})\right]=\boldsymbol{3} \boldsymbol{6} \cdot \boldsymbol{8} \boldsymbol{J} \boldsymbol{m} \boldsymbol{o l}^{-1} \boldsymbol{K}^{-1} \)
Subject: Physics
An equiconvex lens is cut into two
halves a long (i) \( \mathrm{XOX} \) and (ii) YOY as
shown in the figure let \( f . f^{\prime}, f^{\prime \prime} \) be the
focal lengths of the complete lens of each half in case (i) and of each half in
case (ii) respectively Choose the correct statement from the
following:
\( \mathbf{A} \cdot f^{\prime}=f, f^{\prime \prime}=f \)
B. \( f^{\prime}=2 f, f^{\prime \prime}=2 f \)
C . \( f^{\prime}=f, f^{\prime \prime}=2 f \)
D. \( f^{\prime}=2 f, f^{\prime \prime}=f \)
Subject: Chemistry
Which of the following reaction(s) can be used for the preparation of alkyl halides?
(I) \( C H_{3} C H_{2} O H+H C l \quad \) anh. \( Z n C l_{2} \)
(II) \( C H_{3} C H_{2} O H+H C l \rightarrow \)
\( (\| I)\left(C H_{3}\right)_{3} C O H+H C l \rightarrow \)
\( (\mathrm{IV})\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H O H}+\boldsymbol{H C l} \stackrel{\boldsymbol{a n h . Z n C l}_{2}}{\longrightarrow} \)
\( \mathbf{A} \cdot(I V) \) only
B. (III) and (IV) onlyyy y
c. \( (I),(I I I) \) and \( (I V) \) only
D. \( (I) \) and \( (I I) \) only
Subject: Chemistry
The number of Glucose molecules
present in 10 ml of decimolar solution
is:
A \( .6 .0 \times 10^{20} \)
В . \( 6.0 \times 10^{19} \)
c. \( 6.0 \times 10^{21} \)
D. \( 6.0 \times 10^{22} \)
Subject: Chemistry
\( \Delta H>\Delta E \)
Which of the following reaction follows
the above relation?
\( \mathbf{A} \cdot C H_{4}(g)+2 O_{2}(g) \rightarrow C O_{2}(g)+2 H_{2} O(g) \)
B \( . N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
\( \mathbf{c} \cdot C_{2} H_{4}(g)+3 O_{2}(g) \rightarrow 2 C O_{2}(g)+2 H_{2} O(g) \)
D. \( \operatorname{CaCO}_{3}(s) \rightarrow \operatorname{CaO}(s)+C O_{2}(g) \)
Subject: Maths
Simplify: \( (\boldsymbol{x}+\mathbf{5})(\boldsymbol{x}+\mathbf{4}) \)
A \( \cdot x^{2}+27 x+20 \)
B . \( x^{2}+9 x+20 \)
c. \( x^{2}+18 x+20 \)
D. \( x^{2}+x+20 \)
Subject: Physics
The resistance of a galvanometer is 50 ohm and the maximum current which
can be passed through it is \( 0.002 A \) What resistance must be connected to
it in order to convert it into an ammeter
of range \( 0-0.5 A ? \)
A. 0.2 onm
B. 0.002 ohm
c. 0.02 ohm
D. 0.5 ohm
Subject: Maths
If the surface area of a sphere is
\( 144 \pi \mathrm{cm}^{2}, \) then its radius is:
\( A \cdot 6 c m \)
B. \( 8 \mathrm{cm} \)
\( \mathrm{c} \cdot 12 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Maths
A line in the \( x y \) -plane passes through the origin and has a slope of \( \frac{1}{7} . \) Which of the following points lies on the line?
\( \mathbf{A} \cdot(0,7) \)
В \( \cdot(1,7) \)
c. (7,7)
D \cdot (14,2)
Subject: Physics
Four particles, each having charge \( \boldsymbol{q} \)
are placed at four verticals of a regular
pentagon. The distance of each corner
from the center is \( a \). The electric field at
the center \( O \) of the pentagon is:
A \( \cdot \frac{q}{4 \pi \epsilon_{0} a^{4}} \) along \( E O \)
B. \( \frac{q}{2 \pi \epsilon_{0} a^{2}} \) along \( E O \)
c. \( \frac{q}{\pi \epsilon_{0} a^{2}} \) along \( E O \)
D. \( \frac{q}{4 \pi \epsilon_{0} a^{2}} \) along \( E O \)
Subject: Physics
Choose the correct statement.
A. Polar molecules have permanent electric dipole moment
B. \( C O_{2} \) molecule is a polar molecule
\( \mathrm{C} \cdot \mathrm{H}_{2} \mathrm{O} \) is a non-polar molecule
" The dipole field at large distances falls of as \( \frac{1}{r^{2}} \)
E. The dipole moment is a scalar quantity
Subject: Physics
The length of the arm of a nutcracker is 15cm. A force of 22.5kgwt is required to cut a nut without cracker. Where should
the nut be placed on the cracker in order to cut it by a force of \( 2.25 k g / w t ? \)
A. \( 1 \mathrm{cm} \) from fulcrum
B. 1.5cm from fulcrum
\( \mathrm{c} .0 .5 \mathrm{cm} \) from fulcrum
D. \( 2.0 \mathrm{cm} \) from fulcrum
Subject: Maths
If \( A \) is \( 3 x 3 \) matrix and \( \operatorname{det} \operatorname{adj}(A)=k \)
then
\( \operatorname{det}(\operatorname{adj} 2 A)= \)
\( A \cdot 2 k \)
в. 8k
\( c \cdot 16 k \)
D. \( 64 k^{2} \)
Subject: Maths
An event \( X \) can take place in
conjunction with any one of the mutually exclusive and exhaustive events \( A, B \) and \( C . \) If \( A, B, C \) are equiprobable and the probability of \( X \) is \( 5 / 12 \) and the probability of \( X \) taking place when A has happened is 3/8 while it is \( 1 / 4 \) when \( \mathrm{B} \) has taken place, then
the probability of \( X \) taking place on conjunction with \( \mathrm{C} \) is
A . \( 5 / 8 \)
в. \( 3 / 8 \)
\( c \cdot 5 / 24 \)
D. none of these