AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
toppr
Q Type your question
shown in Fig. (a)
In figure (b) the second lens is an
equiconcave lens of focal length \( 10 \mathrm{cm} \)
and made of a material of refractive
index \( 1.5 . \) In both cases, the second lens
has an aperture equal to 1 cm.
Now, a liquid of refractive index \( \mu \) is
filled to the right of the second lens in
case \( B \) such that the area illuminated
in both the cases is the same.

Determine the refractive index of liquid.
\( \mathbf{a} \)
\( (\mathbf{b}) \)
A .
B . 2.5
\( c .3 \)
D. 1.5
Subject: Physics
If \( \hat{i}, \hat{j} \) and \( \hat{k} \) represent unit vectors along the \( x, y \) and \( z \) -axes respectively, then the angle \( \theta \) between the vectors \( (\hat{i}+\hat{j}+\hat{k}) \) and \( (\hat{\mathbf{i}}+\hat{\mathbf{j}}) \) is equal to:
A \( \cdot \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
B. \( \sin ^{-1}(\sqrt{\frac{2}{3}}) \)
c. \( \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
D. \( 90^{\circ} \)
Subject: Physics
Evaluate the magnitude and direction
of magnetic field at point \( \boldsymbol{O} \)
A \( \cdot \frac{3 \mu_{0} i}{8 a}, \) с
в. \( \frac{\mu_{0} i}{2 \sqrt{2} b}, \) с
с. \( \frac{3 \mu_{0} i}{8 a}+\frac{\mu_{0} i}{2 \sqrt{2} b}, \) с
D. \( \frac{3 \mu_{0} i}{8 a}+\frac{\mu_{0} i}{2 \sqrt{2} b}, \otimes \)
Subject: Physics
In the arrangement shown in fig. plate has a charge equal to \( 60 \mu C \) The ratio
\( d_{1} / d_{2} \) is \( 2 . \) Then
\( q_{1}=_{-} \)
\( q_{2}=_{-}-- \)
\( \mathbf{q}_{3}=_{-}- \)
\( \boldsymbol{q}_{4}=_{-}-- \)
\( \boldsymbol{q}_{5}=-- \)
\( \boldsymbol{q}_{6}=_{-}- \)
Subject: Maths
If \( \boldsymbol{A}=\left(\begin{array}{c}4-2 \\ 5-9\end{array}\right) \) and \( \boldsymbol{B}=\left(\begin{array}{cc}8 & 2 \\ -1 & -3\end{array}\right) \) find \( 6 A \)
3B.
Subject: Physics
A body is thrown vertically up to reach its maximum height in \( t \) seconds. The
total time from the time of projection to reach a point at half of its maximum height while returning ( in seconds) is
A \( \cdot \sqrt{2} t \)
B. \( \left[1+\frac{1}{\sqrt{2}}\right] t \)
c. \( \frac{3 t}{2} \)
D. \( \frac{t}{\sqrt{2}} \)
Subject: Chemistry
The acidic strength of two monobasic
acids may be compared by comparing the hydronium ion concentrations of
their aqueous solution of same molar concentration. The dissociation
constants of acids HA and HB are \( 4 \times \)
\( 10^{-6} \) and \( 2.5 \times 10^{9}, \) respectively. How
many times HA is stronger than HB? Assume that for both the acids, the degree of dissociation at the
concentration taken, is negligible.
Subject: Physics
A long elastic spring is stretched by \( 2 \mathrm{cm} \) and its potential energy is \( U \). If the
spring is stretched by \( 10 \mathrm{cm} \), the P.E., will be
A . \( 5 U \)
в. \( 25 U \)
c. \( U / 5 \)
D. \( U / 20 \)
Subject: Maths
Find \( n \) if the given value of \( x \) is the \( n^{t h} \) term of the \( A P: 5 \frac{1}{2}, 11,16 \frac{1}{2}, 22, \dots ; x= \)
\( \mathbf{5 5 0} \)
A . 100
в. 110
\( c \cdot 200 \)
D. 220
Subject: Maths
Prove that
\[
\left[\begin{array}{ccc}
\mathbf{1} & \mathbf{1} & \mathbf{1} \\
\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\
\boldsymbol{a}^{\mathbf{3}} & \boldsymbol{b}^{\mathbf{3}} & \boldsymbol{c}^{\mathbf{3}}
\end{array}\right] \mid=(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}-
\]
\( \boldsymbol{a})(\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}) \)
Subject: Maths
A straight line is drawn through the point \( p(2,3) \) and is inclined at an angle
of \( 30^{\circ} \) with the \( x- \) axis, the co-ordinates
of two points on it at a distance of 4 from \( p \) is/are
A \( \cdot(2+2 \sqrt{3}, 5),(2-2 \sqrt{3}, 1) \)
B . \( (2+2 \sqrt{3}, 5),(2+2 \sqrt{3}, 1) \)
c. \( (2-2 \sqrt{3}, 5),(2-2 \sqrt{3}, 1) \)
D. none of these
Subject: Chemistry
Assertion
Ferrous ion is a divalent ion.
Reason
Iron atom loses two electrons to carry
two positive charges.
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
Assertion
Both cis-1,3-dimethyl cyclobutane and trans-1,3-dimethyl cyclobutane are optically inactive.
Reason
cis-1,3-Dimethyl cyclobutane has the plane of symmetry, where as trans form has the centre of symmetry.
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
ff \( \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{3} & \mathbf{1} \\ -\mathbf{9} & -\mathbf{3}\end{array}\right) \) then
\( \left(1+2 A+3 A^{2}+\ldots . \infty\right)^{-1} \) equals
\( ^{A} \cdot\left(\begin{array}{cc}-5 & -2 \\ 18 & 7\end{array}\right) \)
B. \( \left(\begin{array}{rr}-5 & 18 \\ -2 & 7\end{array}\right) \)
c. \( \left(\begin{array}{cc}7 & -2 \\ 18 & -5\end{array}\right) \)
D. None of these
Subject: Maths
If \( \tan A, \tan B \) are the roots of \( x^{2}- \)
\( \mathbf{2} \boldsymbol{x}+\mathbf{2}=\mathbf{0} \) then \( \cot ^{2}(\boldsymbol{A}+\boldsymbol{B})= \)
A \( \cdot \frac{4}{5} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{3}{4} \)
D.
Subject: Physics
Find out the efficiency of the heat engine if it produces \( 100 J \) of heat, does
\( 30 J \) of work, and emits \( 70 J \) into a cold
reservoir.
\( \mathbf{A} \cdot 100 \% \)
B. \( 70 \% \)
c. \( 42 \% \)
D. 40\%
E . \( 30 \% \)
Subject: Maths
\( \left(\frac{1}{1-2 i}+\frac{3}{1+i}\right)\left(\frac{3+4 i}{2-4 i}\right)= \)
A. \( \frac{1}{2}+\frac{9}{2} i \)
B \( \cdot \frac{1}{2}-\frac{9}{2} i \)
c. \( \frac{1}{4}-\frac{9}{4} i \)
D. \( \frac{1}{4}+\frac{9}{4} i \)
Subject: Chemistry
Which of the following is correct IUPAC
name for \( \boldsymbol{K}_{\mathbf{2}}\left[\boldsymbol{C r}(\boldsymbol{C} \boldsymbol{N})_{2} \boldsymbol{O}_{2}(\boldsymbol{O})_{2} \boldsymbol{N} \boldsymbol{H}_{3}\right] ? \)
A. Potassium amminecyanoperoxodioxochromatic(IV)
B. Potassium amminecyanoperoxodioxochromium(V)
c. Potassium amminecyanoperoxodioxochromium(VI)
D. Potassium amminedicyanodioxoperoxochromate(VI)
Subject: Maths
A particle moving in straight line
diverse a distance \( x \) in that straight line
from a fixed point in time \( t . \) If \( \boldsymbol{x}= \) \( a \cos \sqrt{\mu} t\{\text { Where } \mu>0) . \) Find the
acceleration of the particle in time \( t \)
A. \( -\mu x \)
B. \( \mu x \)
c. \( -\sqrt{\mu} x \)
D. \( \sqrt{\mu} x \)
Subject: Physics
sides 2 a lies on a smooth horizontal
plane as shown in the figure. Three
point masses of mass m each strike the
block at \( A, B \) and \( C \) with speeds \( v \) as
shown. After the collision, the particles
come to rest. Then the angular velocity
acquired by the triangular block is (I is
the moment of inertia of the triangular
block about \( \mathrm{G} \), perpendicular to the
plane of the block)
\( A \)
clockwise
B. \( \frac{2 m v a}{l} \) clockwise
\( \frac{2 \sqrt{3} m v a}{l} \) clockwise
D. None of these
Subject: Physics
Calculate the amount of heat energy
required to raise the temperature of \( 2 g \) of mercury (Specific heat Capacity
\( \left.0.12 J g^{-1} o C^{-1}\right) \) from \( 10^{\circ} C \) to \( 30^{\circ} C \)
A . \( 1.2 J \)
в. 2.4
c. \( 4.8 J \)
D. 9.6 .5
Subject: Chemistry
For the reaction, \( N_{2}+3 H_{2} \rightarrow 2 N H_{3} \)
The rate of change of concentration for
hydrogen is \( 0.3 \times 10^{-4} M s^{-1} . \) The rate
of change of concentration ammonia is:
A . \( -0.2 \times 10^{-4} \)
В. \( 0.2 \times 10^{-4} \)
c. \( 1 \times 10^{-4} \)
D. \( 0.3 \times 10^{-4} \)
Subject: Physics
A student performs an experiment for determination of \( \left(g=\frac{4 \pi^{2} l}{T^{2}}\right), \mid=1 \mathrm{m} \)
and he commits an error of \( \Delta l \) For T he
takes the time of \( n \) oscillations with the
stop watch of least count \( \Delta \boldsymbol{T} \) and he
commits a human error of 0.1 s. For
which of the following data, the
measurement of \( g \) will be most
accurate?
A. \( \Delta L=0.5, \Delta T=0.1, n=20 \)
B . \( \Delta L=0.5, \Delta T=0.1, n=50 \)
c. \( \Delta L=0.5, \Delta T=0.01, n=20 \)
D. \( \Delta L=0.5, \Delta T=0.05, n=50 \)
Subject: Chemistry
Which of the following species are hypervalent?
1. \( C l O_{4}^{-} \)
2. \( \boldsymbol{B F}_{\mathbf{3}} \)
\( \mathbf{3} . \boldsymbol{S} \boldsymbol{O}_{\boldsymbol{4}}^{2-} \)
4. \( \boldsymbol{C O}_{3}^{2-} \)
\( \mathbf{A} \cdot 1,2,3 \)
B. 1,3
\( c .3,4 \)
D. 1,2
Subject: Physics
The distance moved by a freely falling body (starting from rest) during the \( 1^{s t}, 2^{n d} \) and \( 3^{r d} \ldots n^{t h} \) second of its
motion, are proportional to
A \( \cdot(n-1) \)
в. \( (2 n-1) \)
c. \( \left(n^{2}-1\right) \)
D. \( (2 n-1) / n^{2} \)
Subject: Physics
A ball dropped freely takes \( 0.2 s \) to
travel the last 6 m distance before
hitting the ground. Total time of fall is \( \left(g=10 m s^{-2}\right) \)
A . \( 2.9 s \)
в. 3.1 s
\( c .2 .7 s \)
D. 0.2
Subject: Chemistry
Which of the following will not given butanoic acid as one of the product?
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} B r \frac{M g}{E t h e r} \quad \underbrace{(i) C O_{2}}_{(i i) H C l / H_{2}} \)
B \( \cdot C H_{3} C H_{2} C H_{2} B r \stackrel{N a C N(a q)}{\longrightarrow} \stackrel{H^{+} / H_{2} O}{\longrightarrow} \)
c. \( _{C H_{3} C H_{2} C H O+H C N} \stackrel{H^{+}+H_{2} \mathcal{O}}{\longrightarrow} \)
D. \( C H_{3} C H_{2} C H_{2} C H=C H_{2 H^{+} / H_{2} O}^{K M n O_{4}} \)
Subject: Maths
\( \int \frac{x^{3}-1}{x^{3}+x} d x \) equal to
\( \mathbf{A} \cdot x-\log x+\log \left(x^{2}+1\right)-\tan ^{-1} x+c \)
B. \( x-\log x+\frac{1}{2} \log \left(x^{2}+1\right)-\tan ^{-1} x+c \)
c. \( x+\log x+\frac{1}{2} \log \left(x^{2}+1\right)+\tan ^{-1} x+c \)
D. \( x+\log x-\frac{1}{2} \log \left(x^{2}+1\right)-\tan ^{-1} x+c \)
Subject: Maths
Solve \( : \boldsymbol{x}^{2} \boldsymbol{y} \boldsymbol{d} \boldsymbol{x}=\left(\boldsymbol{x}^{3}+\boldsymbol{y}^{3}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
Subject: Physics
Point charge \( +4 q,-q \) and \( +4 q \) are kept
on the \( x \) -axis at points \( x=0, x=a \) and
\( x=4 a \) respectively. Then:
A. Only-q is in stable equilibriummmmmm
B. None of the charges are in equilibrium.
c. All the charges are in unstable equilibrium.
D. All the charges are in stable equilibrium.
Subject: Physics
A current of \( 0.2 A \) flows through a wire whose ends are at a potential difference
of \( 15 V . \) The heat energy produced in 1
minute will be
\( \mathbf{A} \cdot 60 J \)
в. \( 120 J \)
\( c .180 J \)
D. \( 90 J \)
Subject: Physics
The diode used in the circuit shown
below has a constant voltage drop of
\( 0.6 V \) at all currents and a maximum
power rating of 300 milli watt. What
should be the value of the resistance \( \boldsymbol{R} \)
if maximum current passes through the diode?
A . \( 4 \Omega \)
B . \( 2 \Omega \)
\( c .1 \Omega \)
D. \( 32 \Omega \)
Subject: Biology
What is the correct sequence from least
complex to most complex in terms of the amount of information they carry?
. Chromosomes
II. Base pair
III. Codon
IV. Gene
\( \mathbf{A} \cdot \mid \rightarrow\|\rightarrow\| \rightarrow \rightarrow \) ।
B. \( \|\rightarrow\| \dashv \rightarrow \perp \rightarrow \) ।
c. \( \|! \rightarrow\| \rightarrow 1 \rightarrow \) ।V
D. II \( \rightarrow \| \perp \rightarrow I V \rightarrow 1 \)
E . \( \|\rightarrow \mid V \rightarrow\| \rightarrow \) ।
Subject: Maths
fi \( a, b \& c \) are non-zero real numbers \( \operatorname{then} D=\left|\begin{array}{lll}b^{2} c^{2} & b c & b+c \\ c^{2} a^{2} & c a & c+a \\ a^{2} b^{2} & a b & a+b\end{array}\right|= \)
A \( \cdot a b c \)
B \( \cdot a^{2} b^{2} c^{2} \)
c. \( b c+c a+a b \)
D. zero
Subject: Maths
A solid metal sphere of surface area \( \boldsymbol{S}_{1} \)
is melted and recast into a number of
smaller spheres. \( S_{2} \) is the sum of the surface areas of all the smaller spheres.
Then
A. \( S_{1}>S_{2} \)
в. \( S_{2}>S_{1} \)
c. \( S_{1}=S_{2} \)
D. \( S_{1}>S_{2} \) only if all the smaller spheres of equal radii
Subject: Physics
An electron is accelerated through a
potential difference of \( 200 V . \) If e / m for the electron be \( 1.6 \times 10^{11} \) coulomb \( k g^{-1} \)
then the velocity acquired by the electron will be
\( \mathbf{A} \cdot 8 \times 10^{6} m s^{-1} \)
В. \( 8 \times 10^{5} \mathrm{ms}^{-1} \)
C . \( 5.9 \times 10^{6} \mathrm{ms}^{-1} \)
D. \( 5.9 \times 10^{5} \mathrm{ms}^{-1} \)
Subject: Physics
A conducting wire of length \( \ell \) and mass
\( m \) can slide without friction on two
parallel rails and is connected to
capacitance \( C . \) Whole system lies in a
magnetic field \( B \) and a constant force
\( F \) is applied to the rod. Then
This question has multiple correct options
A. the rod moves with constant velocity
B. the rod moves with an acceleration of \( \frac{F}{m+B^{2} \ell^{2} c} \)
c. there is constant charge on the capacitor
D. charge on the capacitor increases with time
E. answer required
Subject: Maths
If \( \boldsymbol{y}=\cot ^{-1}\left[\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right] \)
where \( 0<x<\frac{\pi}{2}, \) then \( \frac{d y}{d x} \) is equal to
A. \( -\frac{1}{2} \)
B. 2
\( c \cdot \sin x+\cos x \)
\( \mathbf{D} \cdot \sin x-\cos x \)
Subject: Maths
A dietician wishes to mix two types of
foods in such away that the vitamin contents of the mixture contains at
least 8 units of vitamin \( A \) and 10 units
of vitamin C. Food I contains 2 units/kg of vitamin \( A \) and 1 unit/kg of vitamin \( C \) while Food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamin 1 unit/kg of vitamin C. It costs \( R s .5 \) per
kg to purchase food I and \( R s .7 \) per kg to purchase Food II. Determine the maximum cost of such a mixture.
Formulate the above as a LPP and solve
t graphically.
Subject: Chemistry
Hybridization and magnetic behaviour of complex \( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{M} \boldsymbol{n}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \) is:
A \( \cdot d^{2} s p^{3}, \) diamagnetic
B . \( d^{2} s p^{3} \), paramagnetic
\( \mathrm{c} \cdot s p^{3} d^{2}, \) diamagnetic
D. \( s p^{3} d^{2} \), paramagnetic
Subject: Physics
An alternating e.m.f. of \( 200 \mathrm{V} \) and 50 cycles is connected to a circuit of
resistance \( 3.142 \Omega \) and inductance
0.01H. The lag in time between the e.m.f. and the current is :
A . \( 1.5 \mathrm{ms} \)
B. 2.5 ms
c. 3.5ms
D. 0.5 ms
Subject: Physics
The potential barrier of a silicon junction diode is \( 0.7 V . \) If the thickness
of the depletion layer in it is \( 10^{-4} \mathrm{cm} \) Then the intensity of electric field across the junction is
A \( \cdot 7 \times 10^{3} V / m \)
в. \( 7 \times 10^{5} V / m \)
C \( .7 \times 10^{-5} V / m \)
D. \( 7 \times 10^{-4} V / m \)
Subject: Maths
If \( \boldsymbol{A}=\left(\left[\begin{array}{llll}1 & 2 & 3 & 4\end{array}\right] \text { and } A B=\left[\begin{array}{lll}3 & 4 & -1\end{array}\right]\right. \)
then the order of
matrix B is
\( A \cdot 2 \times 3 \)
B. 3x3
\( c \cdot 4 \times 3 \)
D. \( 1 \times 3 \)
Subject: Maths
For any two events \( A \) and \( B \) in a sample
space:
This question has multiple correct options
\( ^{\mathbf{A}} \cdot p(A / B) \geq \frac{P(A) P(B)-1}{P(B)} P(B) \neq 0 \) is always true
B \( \cdot P(A \cap \bar{B})=P(A)-P(A \cap B) \), does not hold
\( \mathbf{c} \cdot P(A \cup B)=1-P(\bar{A}) P(\bar{B}), \) if \( A \) and \( B \) are independent
D \( \cdot P(A \cup B)=1=P(\bar{A}) P(\bar{B}) \), if \( A \) and \( B \) are disjoint.
Subject: Physics
Two smooth cylindrical bars weighing Weach lie next to each other in contact.
A similar third bar is over the two bars
as shown in figure. Neglecting friction, the minimum horizontal force on each
lower bar necessary to keep them together is
A \( \cdot \frac{W}{2} \)
в.
c. \( \frac{W}{\sqrt{3}} \)
D. \( \frac{W}{2 \sqrt{3}} \)
Subject: Maths
In the figure at right, \( A B \) and \( C D \) are
straight lines through the centre 0 of a
circle. If \( \angle A O C=98^{\circ} \) and \( \angle C D E= \)
\( \mathbf{3 5}^{\circ} \)
Find (i) \( \angle D C E \)
(ii) \( \angle A B C \)
Subject: Chemistry
When \( K C l O_{3} \) is heated, it decomposes
into \( K C l \) and \( O_{2} . \) If some \( M n O_{2} \) is
added, the reaction goes much faster
because :
A. \( M n O_{2} \) decomposes to give \( O_{2} \)
B. \( M n O_{2} \) provides heat by reacting
C. Better contact is provided by \( M n O_{2} \)
D. \( M n O_{2} \) acts as a catalyst
Subject: Maths
State true or false.
In the figure, \( l \| \boldsymbol{m} \) and \( \mathrm{M} \) is the midpoint
of line segment \( A B . \) Then \( M \) is also the
midpoint of any line segment having its
endpoints \( C \) and \( D \) on \( l \) and \( m \)
respectively.
A. True
B. False
Subject: Chemistry
The anodic half-cell of lead-acid battery
is recharged unsing electricity of 0.05
Faraday. The amount of \( P b S O_{4} \)
electrolyzed in g during the process is :
(Molar mass of \( \boldsymbol{P b S O}_{4}=\mathbf{3 0 3 g m o l}^{-1} \) )
A . 22.8
B. 15.2
\( c .7 .6 \)
D. 11.4
Subject: Physics
Threshold wavelength for a metal
having work function \( \omega_{0} \) is \( \lambda . \) Then the
threshold wavelength for the metal
having work function \( 2 \omega_{0} \) is
\( A \cdot 4 \lambda \)
B. 2\lambda
\( c \cdot \lambda / 2 \)
D. \( \lambda / 4 \)
Subject: Maths
The distance of the point (1,-2,3) from
the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) measured
parallel to the line \( \frac{x}{2}=\frac{y}{3}=\frac{z-1}{-6} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 4 \)
D. None of these
Subject: Maths
Find whether the following functions are
one-one, onto or not:
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{3} \) for
all \( \boldsymbol{x} \epsilon \boldsymbol{R} \)
Subject: Maths
Two \( n \times n \) square matrices \( A \) and \( B \) are
said to be similar if there exists a non-
singular matrix \( \boldsymbol{P} \) such that
\( \boldsymbol{P}^{-1} \boldsymbol{A} \boldsymbol{P}=\boldsymbol{B} \)
If \( A \) and \( B \) are similar and \( B \) and \( C \) are
similar, then
A. \( A B \) and \( B C \) are similar
B. \( A \) and \( C \) are similar
c. \( A+C \) and \( B \) are similar
D. none of these
Subject: Physics
Four identical pendulums are made by attaching a small ball of mass 100 g on a \( 20 \mathrm{cm} \) long thread and suspended from the same point. Now each ball is given charge \( Q \) so that balls move away from each other with each thread
making an angle of \( 45^{\circ} \) from the vertical. The value of \( Q \) is close to \( \left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \text { in Sl units }\right) \)
A . \( 1 \mu C \)
в. \( 1.5 \mu \) С
\( c \cdot 2 \mu c \)
D. 2.5 \( \mu \) C
Subject: Chemistry
Which of the following is the cell reaction that occurs when the following half-cells are combined?
\( \boldsymbol{I}_{2}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{I}^{-}(\boldsymbol{1} \boldsymbol{M}) ; \boldsymbol{E}^{o}=+\boldsymbol{0 . 5 4} \mathbf{V} \)
\( \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{B} \boldsymbol{r}^{-}(\boldsymbol{1} \boldsymbol{M}) ; \boldsymbol{E}^{o}=+\mathbf{1} . \boldsymbol{0} \boldsymbol{9} \)
\( \mathbf{V} \)
A \( \cdot 2 B r^{-}+I_{2} \rightarrow B r_{2}+2 I^{-} \)
В \( \cdot I_{2}+B r_{2} \rightarrow 2 I^{-}+2 B r^{-} \)
c. \( 2 I^{-}+B r_{2} \rightarrow I_{2}+2 B r \)
D. \( 2 I^{-}+2 B r^{-} \rightarrow I_{2} B r_{2} \)
Subject: Physics
Assertion
We can live very happily if the friction is
not present in nature
Reason
Aeroplane shape is stream lined to
reducec the effort of frictional force.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Chemistry
Assertion
Chemical bonds in organic compounds are covalent in nature.
Reason
Covalent bond is formed by the sharing of electrons in the bonding atoms.
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
Both the organic compounds A and B can release hydrogen with Na. Only compound A can form a salt with NaOH,
whereas B cannot.When A reacts with B
in the presence of conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) a pleasant smelling compound is formed. The pair of compounds \( A \) and \( B \) can be respectively:
A \( \cdot C_{2} H_{5} O H \) and \( C_{2} H_{2} \)
в. \( C H_{3} C O O H \) and \( C_{2} H_{2} \)
c. \( C H_{3} C O O H \) and \( C_{2} H_{5} O H \)
D. \( C_{2} H_{5} O H \) and \( C H_{3} C O O H \)
Subject: Physics
\( \ln \mu_{e} \) and \( \mu_{h} \) are electron and hole
mobility. E be the applied electric field, the current density \( J \) for intristic semiconductor is equal to
\( \mathbf{A} \cdot n_{i} e\left(\mu_{e}+\mu_{h}\right) E \)
B \( \cdot n_{i} e\left(\mu_{e}-\mu_{h}\right) E \)
c. \( \frac{n_{i} e\left(\mu_{e}+\mu_{h}\right)}{E} \)
D. \( \frac{E}{n_{i} e\left(\mu_{e}+\mu_{n}\right)} \)
Subject: Chemistry
On adding \( H_{2} O \) to \( B i C l_{3} \) solution in \( H C l \) the compound produced is:
\( \mathbf{A} \cdot B i_{2} O_{3} \)
B \( \cdot B i(O H)_{3} \)
c. В гОС
D. \( B i O C l \)
Subject: Maths
The sum of series \( \frac{1^{2}}{1}+\frac{1^{2}+2^{2}}{1+2}+ \)
\( \frac{1^{2}+2^{2}+3^{2}}{1+2+3}+\ldots . \) upto \( n \) terms is
A \( \cdot \frac{1}{3}(2 n+1) \)
B. \( \frac{1}{3} n^{2} \)
c. \( \frac{1}{3}(n+2) \)
D. \( \frac{1}{3} n(n+2) \)
Subject: Chemistry
Given,
\( N H_{3}(g)+3 C l_{2}(g) \rightleftharpoons N C l_{3}(g)+ \)
\( 3 H C l(g) ;-\Delta H_{1} \)
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) ;-\Delta H_{2} \)
\( H_{2}(g)+C l_{2}(g) \rightleftharpoons 2 H C l(g) ; \Delta H_{3} \)
The heat formation of \( N C l_{3}(g) \) in terms
of \( \Delta H_{1}, \Delta H_{2} \) and \( \Delta H_{3} \) is:
\( ^{\mathbf{A}} \cdot \Delta H_{f}=-\Delta H_{1}+\frac{1}{2} \Delta H_{2}+\frac{3}{2} \Delta H_{3} \)
B. \( \Delta H_{f}=-\Delta H_{1}+\frac{1}{2} \Delta H_{2}-\frac{3}{2} \Delta H_{3} \)
\( \mathrm{c} \cdot_{\Delta H_{f}=\Delta H_{1}-\frac{1}{2} \Delta H_{2}-\frac{3}{2} \Delta H_{3}} \)
D. none of these
Subject: Maths
The value of \( \int_{a}^{b} \frac{\log x}{x} d x \) is
\( \mathbf{A} \cdot \log (a b) \log \left(\frac{b}{a}\right) \)
B \( \cdot \frac{1}{2} \log (a b) \log \left(\frac{b}{a}\right) \)
\( \mathbf{C} \cdot \log \left(a^{2}-b^{2}\right) \)
D. \( (a+b) \log (a+b) \)
Subject: Maths
The chord of contact of tangents from a
point \( \boldsymbol{P} \) to a circle passes through \( \boldsymbol{q} \). If
\( l_{1} \) and \( l_{2} \) are the lengths of the tangents
from \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) to the circle, then \( \boldsymbol{P} \boldsymbol{Q} \) is
equal to
A. \( \frac{l_{1}+l_{2}}{2} \)
в. \( \frac{l_{1}-l_{2}}{2} \)
C \( . \sqrt{\left|l_{1}^{2}-l_{2}^{2}\right|} \)
D. \( \sqrt[2]{l_{1}^{2}+l_{2}^{2}} \)
Subject: Physics
The coefficient of cubical expansion of
copper is \( 5.1 \times 10^{-5} \) per \( C . \) Coefficient
of linear expansion is \( \boldsymbol{K} \times \mathbf{1 0}^{-\mathbf{5}} \) per \( \boldsymbol{C} \)
Find value of \( \mathrm{K} \)
Subject: Maths
In the above figure, \( D \) and \( E \) are the
mid-points of the sides \( A C \) and \( B C \)
respectively of \( \triangle A B C . \) If
\( \boldsymbol{a} \boldsymbol{r}(\triangle \boldsymbol{B} \boldsymbol{E} \boldsymbol{D})=12 \boldsymbol{c m}^{2}, \) then
\( \boldsymbol{a} \boldsymbol{r}(\boldsymbol{A} \boldsymbol{B} \boldsymbol{E} \boldsymbol{D})= \)
\( \mathbf{A} \cdot 36 \mathrm{cm}^{2} \)
B. \( 48 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 24 \mathrm{cm}^{2} \)
D. None of these