AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
For the reaction; \( N_{2} O_{5} \rightarrow 2 N O_{2}+\frac{1}{2} O_{2} \)
Given:
\( -\frac{\boldsymbol{d}\left[\boldsymbol{N}_{2} \boldsymbol{O}_{5}\right]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{K}_{1}\left[\boldsymbol{N}_{2} \boldsymbol{O}_{5}\right], \frac{\boldsymbol{d}\left[\boldsymbol{N} \boldsymbol{O}_{2}\right]}{\boldsymbol{d} \boldsymbol{t}}= \)
\( \boldsymbol{K}_{2}\left[\boldsymbol{N}_{2} \boldsymbol{O}_{5}\right], \frac{\boldsymbol{d}\left[\boldsymbol{O}_{2}\right]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{K}_{3}\left[\boldsymbol{N}_{2} \boldsymbol{O}_{5}\right] \)
The relation between \( \boldsymbol{K}_{1}, \boldsymbol{K}_{2} \) and \( \boldsymbol{K}_{3} \) is:
\( \mathbf{A} \cdot 2 K_{1}=K_{2}=4 K_{3} \)
в. \( K_{1}=K_{2}=K_{3} \)
\( \mathbf{c} \cdot 2 K_{1}=4 K_{2}=K_{3} \)
D. none of the above
Subject: Chemistry
In order to prepare a buffer of \( P^{H} 8.26 \)
the amount of \( \left(N H_{4}\right)_{2} S O_{4} \) required to
be mixed with 1L of 0.1 M \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}\left(\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}}=\right. \)
4.74) is:
A . 5 mol
B. 0.5 mol
c. 10 mol
D. 1 mol
Subject: Physics
Choose the wrong option regarding
miniature circuit breaker (MCB)?
A. MCB contains a metal which melts when the current passing through it exceeds a certain value and hence opens the circuit
B. Quick restoration of an MCB is possible just by switching on the operation when a breakdown occurs due to current overload
C. MCB switchess off the circuit automatically when the current passing through it exceeds a certain value
D. None of the above
Subject: Maths
Draw the histogram to represent the following data, hence find the mode.
Daily
\[
\begin{array}{llll}
\text { sales of } & 0- & 1000- & 2000- \\
\text { a store } & 1000 & 2000 & 3000 \\
\text { in (Rs.) } & & &
\end{array}
\]
Number
of days
12
in a month
\( \mathbf{A} \cdot \) Rs. 1500
B. Rs. 1600
c. Rs. 1700
D. Rs. 1800
Subject: Physics
An electric dipole coincides on the zaxis and its centre coincides with the
origin of the cartesian coordinate system. The electric field at an axial
point at a distance \( z \) from the origin is
\( E(z) \) and the electric field at an equatorial point at a distance \( y \) from
the origin is \( \boldsymbol{E}(\boldsymbol{y}) \)
Given that \( y=z>>a, \) which is true?
A. \( E(z) \) and \( E(y) \) are perpendicular
B. \( E(z) \) and \( E(y) \) are parallel
C. \( E(z) \) and \( E(y) \) are at \( 45^{\circ} \) to one another
D. None of these
Subject: Maths
If \( x \) and \( Y \) are the matrices of order \( 2 x \)
2 each and \( 2 X-3 Y=\left|\begin{array}{cc}-7 & 0 \\ 7 & -13\end{array}\right| \) and
\( \mathbf{3} \boldsymbol{X}+\mathbf{2} \boldsymbol{Y}=\left|\begin{array}{cc}\mathbf{9} & \mathbf{1 3} \\ \mathbf{4} & \mathbf{1 3}\end{array}\right|, \) then what is \( \boldsymbol{Y} \)
equal to?
A. \( \left|\begin{array}{cc}1 & 3 \\ -2 & 1\end{array}\right| \)
B. \( \left|\begin{array}{ll}1 & 3 \\ 2 & 1\end{array}\right| \)
\begin{tabular}{l|ll|l} 
& 3 & 2 \\
-1 & 5
\end{tabular}
D. \( \left|\begin{array}{cc}3 & 2 \\ 1 & -5\end{array}\right| \)
Subject: Chemistry
A monoprotic acid in a \( 0.1 \mathrm{M} \) solution ionises to \( 0.001 \% \). Its ionization
constant is:
\( \mathbf{A} \cdot 1 \times 10^{-11} \)
B. \( 1 \times 10^{-3} \)
C \( .1 \times 10^{-6} \)
D. \( 1 \times 10^{-8} \)
Subject: Biology
Assertion
In angiosperms, the ovule develops into
a seed after fertilization.
Reason
Fertilization is not essential for the
development of fruit.
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
Assertion
The laws of chemical combination
ultimately led to the idea of 'atoms' being the "smallest unit of" matter
Reason

The laws of chemical combination
played a significant role in the
development of Dalton's atomic theory
of matter
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
\( A B C D \) is a rectangle inscribed in a
quadrant of a circle having radius
10cm. If \( A D=2 \sqrt{5} c m \), find the area of
\( A B C D \)
\( A \cdot 30 c m^{2} \)
3. \( 50 \mathrm{cm}^{2} \)
\( c \cdot 40 c m^{2} \)
D. \( 35 c m^{2} \)
Subject: Maths
In the given figure, the straight line \( A B \)
and \( \mathrm{CD} \) are parallel to each other. If
angle \( \boldsymbol{p}=\mathbf{5 5}^{\circ}, \) and, \( \boldsymbol{q}=\mathbf{4 3}^{\boldsymbol{o}} \) then
answer the given questions. Find the
value \( x \)
\( \mathbf{A} \cdot 55^{\circ} \)
B. \( 82^{\circ} \)
\( \mathbf{c} \cdot 98^{\circ} \)
D. \( 108^{\circ} \)
Subject: Chemistry
Correct order of \( 1^{s t} \) IP among following elements Be, B, C, N, O is:
\( A \cdot B<B e<C<0<N \)
B. \( B<B e<C<N<0 \)
\( c \cdot B e<B<C<N<0 \)
\( D \cdot B e<B<C<0<N \)
Subject: Physics
\( \ln \) an \( A . C . \) circuit a capacitor of \( 1 \mu F \)
value is connected to a source of
frequency 1000 rad/sec. The value of capacitive reactance will be
A . \( 10 \Omega \)
в. 100\Omega
c. \( 1000 \Omega \)
D. \( 10,000 \Omega \)
Subject: Maths
The ratio in which the plane
\( r \cdot(\hat{i}-2 \hat{j}+2 \widehat{k})=17 \) divides the line
joining the points \( -2 \hat{i}+4 \widehat{j}+7 \widehat{k} \) and \( \mathbf{3} \hat{\mathbf{i}}-\mathbf{5} \hat{\mathbf{j}}+\mathbf{8} \widehat{\boldsymbol{k}} \) is
A .3: 7
B. 7: 10
c. 3: 10
D. 3: 5
Subject: Physics
In the electric field of charge \( Q \), another
charge is carried from \( \boldsymbol{A} \) to \( \boldsymbol{B} . \boldsymbol{A} \) to \( \boldsymbol{C}, \boldsymbol{A} \)
to \( D \) and \( A \) to \( E \), then work done will be
A. Minimum along path \( A B \).
B. Minimum along path \( A D \).
C. Minimum along path \( A E \).
D. zero along all the paths
Subject: Physics
If the terminal speed of a sphere of gold (density \( \left.=19.5 k g / m^{3}\right) \) is \( 0.2 m / s \) in a
viscous liquid (density \( \left.=1.5 k g / m^{3}\right) \)
find the terminal speed of a sphere of silver (density \( =10.5 k g / m^{3} \) ) of the
same size in the same liquid
A. \( 0.4 m / s \)
в. \( 0.133 \mathrm{m} / \mathrm{s} \)
c. \( 0.1 m / s \)
D. \( 0.2 m / s \)
Subject: Chemistry
In the reaction, \( \boldsymbol{P}+\boldsymbol{Q} \longrightarrow \boldsymbol{R}+\boldsymbol{S} \). The
time taken for \( 75 \% \) reaction of \( P \) is
twice the time taken for \( 50 \% \) reaction of
P. The concentration of \( Q \) varies with
reaction time as shown in the figure.
The overall order of the reaction is:
A . 2
B. 3
c. 0
\( D \)
Subject: Maths
Let \( \boldsymbol{A}=\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x} \leq \mathbf{1} \) and \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{A} \)
be defined as \( f(x)=x(2-x), \) then
\( f^{-1}(x) \) is
A. \( 1+\sqrt{1-x} \)
B. \( 1-\sqrt{1-x} \)
c. \( \sqrt{1-x} \)
D. \( 1 \pm \sqrt{1-x} \)
Subject: Physics
In an experiment of verification of Ohm's law, following observations are obtained:
Potential difference \( 0.5 \quad 1.0 \quad 1.5 \) \( v \) (in volt')
Current in 0.2
\( 0.4 \quad 0.6 \)
ampere
What will be the current I when the
potential difference V is 0.75 V ?
A . \( 0.5 A \)
в. \( 0.3 A \)
c. \( 0.75 A \)
D. \( 0.6 A \)
Subject: Chemistry
The following reaction is balanced if \( \boldsymbol{X}+\boldsymbol{Y} \) is
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{X} \boldsymbol{C l} \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \)
\( \boldsymbol{X} \boldsymbol{C l}^{-}+\boldsymbol{Y} \boldsymbol{O}_{2}+\boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Physics
It experiences an increase in energy through a mechanical influence \( A \) 50 \( g \)
bullet moving with a velocity of \( 10 \mathrm{ms}^{-1} \)
strikes a block of mass 950 g at rest and gets embedded in it. The percentage loss in kinetic energy is
A . \( 100 \% \)
B. 95\%
c. 5\%
D. 50\%
Subject: Maths
If \( \int \frac{1}{1+\cot x} d x=A \log \mid \sin x+\cos \)
\( \boldsymbol{x} \mid+\mathrm{Bx}+c, \) then \( \boldsymbol{A}=\ldots \ldots . ., \boldsymbol{B}= \)
A \( \cdot-\frac{1}{2}, \frac{1}{2} \)
в. -1,1
\( c \cdot \frac{1}{3}, \frac{1}{2} \)
D. \( \frac{-1}{3}, \frac{1}{2} \)
Subject: Chemistry
The heat of formation of ethane is
\( -19.46 K c a l . \) Bond energies of \( H- \) \( -H, C--H, \) and \( C--C \) bonds are
104.18,99.0 and \( 80.0 K c a l \)
respectively. If the heat of atomisation of graphite is \( x \) then find out the value
of \( x \)
A . \( x=171 \) K cal \( l \)
В. \( x=-171 \) К cal
c. \( x=0 \) Kcal
D. None of these
Subject: Maths
The value of \( \frac{1}{x-y}\left|\begin{array}{ccc}1 & 0 & 0 \\ 3 & x^{3} & 1 \\ 5 & y^{3} & 1\end{array}\right| \) is
\( \mathbf{A} \cdot x+y \)
B . \( x^{2}-x y+y^{2} \)
c. \( x^{2}+x y+y^{2} \)
D. \( x^{3}-y^{3} \)
Subject: Chemistry
pH of some solution is given by \( \boldsymbol{p} \boldsymbol{H}= \) \( \frac{\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{1}}+\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{2}}}{\mathbf{2}} . \) This formula is valid for
the compound \( N a H_{2} B O_{3} \)
A . True
B. False
Subject: Maths
The equation of the plane passing through a point with position vector \( \hat{\mathbf{i}}+ \) \( 2 \hat{j}+3 \hat{j} \) and parallel to the plane \( \vec{r} \cdot(3 \hat{i}+4 \hat{j}+5 \hat{j}) \)
A \( \cdot 3 x+4 y-5 z+26=0 \)
B. \( 3 x+4 y+5 z-26=0 \)
c. \( 3 x-4 y+5 z-26=0 \)
D. \( 3 x+4 y-5 z-26=0 \)
Subject: Chemistry
In which of the following species the angle around the central atom is
exactly equal to \( 109^{\circ} 28^{\prime} ? \)

This question has multiple correct options
\( \mathbf{A} \cdot S F_{4} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot 1 \mathrm{NH}_{4}^{+} \)
D. None of the above
Subject: Maths
In the given figure, \( P A \) and \( P B \) are
tangents from an external point \( \boldsymbol{P} \) to a
circle with center \( O . L N \) touches the
circle at \( M . \) Prove that \( \boldsymbol{P} \boldsymbol{L}+\boldsymbol{L} \boldsymbol{M}= \)
\( \boldsymbol{P} \boldsymbol{N}+\boldsymbol{M} \boldsymbol{N} \)
Subject: Physics
Two blocks of masses \( M_{1} \) and \( M_{2} \) are
connected by spring of constant \( \boldsymbol{K} \). The spring is initially compressed and the system is released from rest at \( t=0 \)
second. The work done by spring on the blocks \( M_{1} \) and \( M_{2} \) be \( W_{1} \) and \( W_{2} \) respectively by time t. The speeds of both the blocks at time t are non zero.
Then the value of \( \frac{W_{1}}{W_{2}} \) equals to
A \( \cdot \frac{M_{1}}{M_{2}} \)
в. \( \frac{M_{2}}{M_{1}} \)
\( ^{\mathrm{c}}\left(\frac{M_{1}}{M_{2}}\right)^{2} \)
\( ^{\mathrm{D}}\left(\frac{M_{2}}{M_{1}}\right)^{2} \)
Subject: Physics
At the instant when the current in an
inductor is increasing at a rate of \( \mathbf{0 . 0 6 4 0} \boldsymbol{A} / \boldsymbol{s}, \) the magnitude of the self-
induced emf is \( 0.0160 V . \) If the inductor
is a solenoid with 400 turns, what is the
average magnetic flux through each turn when the current is \( 0.720 A ? \)
Subject: Maths
If \( \boldsymbol{f}\left(\frac{\boldsymbol{x}-\boldsymbol{4}}{\boldsymbol{x}+\mathbf{2}}\right)=\mathbf{2} \boldsymbol{x}+\mathbf{1},(\boldsymbol{x} \in \boldsymbol{R}-\mathbf{1},-\mathbf{2}) \)
then \( \int f(x) d x \) is equal to:
(where \( C \) is constant of integration)
A \( \cdot 12 \log _{e}|1-x|+3 x+C \)
B. \( -12 \log _{e}|1-x|-3 x+C \)
C. \( 12 \log _{e}|1-x|-3 x+C \)
D. \( -12 \log _{e}|1-x|+3 x+C \)
Subject: Physics
A small ball is projected along the surface of a smooth inclined plane with
speed \( 10 m s^{-1} \) along the direction
shown at \( t=0 . \) The point of projection
is origin, \( z- \) axis is along vertical. The
acceleration due to gravity is \( 10 m s^{-2} \)
Column I lists the values of certain
parameters related to motion of ball
and Column II lists different time
instants Match appropriately.
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|} { Column I } & \multicolumn{2}{|c|} { Column II } \\
\hline i. & Distance from \( x \) -axis is \( 2.25 \mathrm{m} \) & a. & \( 0.5 \mathrm{s} \) \\
\hline ii. & Speed is minimum & b. & \( 1.0 \mathrm{s} \) \\
\hline iii. & Velocity makes angle \( 37^{\circ} \) with \( x \) -axis & c. & \( 1.5 \mathrm{s} \) \\
\hline & & d. & \( 2.0 \mathrm{s} \) \\
\hline
\end{tabular}
Subject: Chemistry
During the formation of \( N a C l \), transfer
of electron is from \( X \) orbital of \( N a \) to
the \( Y \) orbital of \( C l . \) Then \( X \) and \( Y \) are
respectively:
A. \( 3 s \) and \( 3 s \)
B. \( 3 s \) and \( 3 p \)
c. \( 3 p \) and \( 3 s \)
D. \( 3 p \) and \( 3 p \)
Subject: Maths
Obtain the differential equation by
eliminating the arbitrary constants from the following equation:
\( \boldsymbol{y}=\boldsymbol{c}_{1} \boldsymbol{e}^{2 \boldsymbol{x}}+\boldsymbol{c}_{2} \boldsymbol{e}^{-\boldsymbol{2} \boldsymbol{x}} \)
Subject: Biology
toppr \( x \)
Q Type your question
question.
The auxin was dissolved in a gelatin
block; gelatin does not affect the
biological activity of the auxin. Several
plant seedlings were prepared in a
gelatin block; gelatin does not affect the biological, activity of the auxin. Several
plant seedlings were prepared as described above and growth was
measured every 5 days.
Based on the results of the experiment,
one can conclude that the tip of the plant contains
What proves that auxin is necessary for
plant growth?
rem applied
A. Plant 1 grew faster than plants 2 or 3
B. Plant 4 grew faster than plants 2 or 3
C. Plant 5 grew faster than plant 1
D. Plant 3 grew faster than plant 2
E. Plant 4 grew faster than plant 5
Subject: Maths
Find the distance between parallel lines
\( (i) 15 x+8 y-34=0 \) and \( 15 x+8 y+ \)
\( \mathbf{3 1}=\mathbf{0} \)
\( (\text { ii })(x+y)+p=0 \) and \( (x+y)-r=0 \)
Subject: Physics
What is the range between \( f_{1} \) and \( f_{2} \) of
an RLC circuit that resonates at
\( 150 k H z \) and has a \( Q \) of \( 30 ? \)
A . \( 100.0 k H z \) to \( 155.0 k H z \)
B. \( 147.5 k H z \) to \( 152.5 k H z \)
c. \( 4500 k H z \) to \( 295.5 k H z \)
D. \( 149970 H z \) to \( 150030 H z \)
Subject: Chemistry
In the reaction sequence.
\( A, B \) and \( C \) are given by the set are:
\( \mathbf{A} \cdot C H_{3} C H_{2} C H O, C H_{3} C H_{2} C H_{2} C l, C H I_{3} \)
B. \( C H_{3} C O C H_{3}, C C l_{3}-C_{V}-C H_{3}, C H I_{3} \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{COCH}_{3}, \mathrm{CCl}_{3}-\underset{\mathrm{OH}}{C}\left(\mathrm{CH}_{3}\right)_{2}, \mathrm{CHI}_{3} \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}, \mathrm{CCl}_{3}-\underset{\mathrm{OH}}{\mathrm{CH}}-\mathrm{CH}_{2}-\mathrm{CH}_{3}, \mathrm{CHI}_{3} \)
Subject: Chemistry
Of the following statements:
\( (\boldsymbol{P}) \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N}=\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C}_{6} \boldsymbol{H}_{5} \) is a
Schiff's base.
( \( Q \) ) A dye is obtained by the reaction of
aniline and \( C_{6} H_{5} N^{+} \equiv N C l \)
\( (R) C_{6} H_{5} C H_{2} N H_{2} \) on treatment with \( \left[N a N O_{2}+H C l\right] \) gives diazonium salt
\( (S) p- \) Toluidine on treatment with
\( \left[H N O_{2}+H C l\right] \) gives diazonium salt
A . only \( (P) \) and \( (Q) \) are correct
B. only (P) and (R) are correct
c. only \( (R) \) and \( (S) \) are correct
D. \( (P),(Q) \) and \( (S) \) are correct
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors, then \( |\vec{a}-\vec{b}|^{2}+ \)
\( |\vec{b}-\vec{c}|^{2}+|\vec{c}-\vec{a}|^{2} \) does not exceed :
A . 4
B. 9
\( c \cdot 8 \)
D.
Subject: Physics
The ratio of the wavelengths of a photon and that of an electron of same energy \( \boldsymbol{E} \) will be \( [\boldsymbol{m} \text { is mass of electron }] \)
A \( \cdot \sqrt{\frac{2 m}{E}} \)
в. \( \sqrt{\frac{E}{2 m}} \)
\( c \cdot c \sqrt{\frac{2 m}{E}} \)
D. \( \sqrt{\frac{E c}{2 m}} \)
Subject: Chemistry
The decreasing order of priority for the
following functional groups is:
I. \( \boldsymbol{R}-\boldsymbol{O H} \)
II. \( \boldsymbol{R}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{R} \)
III. \( \boldsymbol{R}-\boldsymbol{O}-\boldsymbol{R} \quad \) IV. \( \boldsymbol{R}-\boldsymbol{N} \boldsymbol{H}_{2} \)
\( A \cdot(\mid V)>(\mid)>(||)>(\| \mid) \)
B. (IV) > (I) > (III) > (II)
\( c \cdot(1)>(\mid V)>(|| \mid)>(||) \)
D. (II) > (III) > (IV) > (I)
Subject: Chemistry
In a galvanic cell, the salt bridge
(i) does not participate chemically in the cell reaction
(ii) stops the diffusion of ions from one electrode to another
(iii) is necessary for the occurrence of the cell reaction
(iv) ensures mixing of the two electrolytic solutions.
A. (i) and (iii) only
B. (i) and (ii) only
c. (iii) and (iv) only
D. All of these
Subject: Chemistry
Among the halides, (i) \( -B C l_{3}, \) (ii)
\( -A l C l_{3}(\text { iii })-G a C l_{3}(\text { iv })-T l C l_{3} . \) The
order of lewis acidic nature is :
\( A \cdot(i)>(\text { ii })>(\text { iii })>(i v) \)
B. (ii) > (i) > (iii) > (iv)
c. (iv) \( > \) (iii) > (ii) > (i)
D. (iv) > (i) > (ii) > (iii
Subject: Biology
Assertion
Human regulated environment is also
called noosphere.
Reason
Man is the main cause for pollution in
our ecosystem due to exploitation of
natural resources.
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: Physics
A solid cylinder of mass \( M \) and radius
\( R \) rolls down an inclined plane without
slipping. The speed of its centre of mass when it reaches the bottom is
A \( \cdot \sqrt{(2 g h)} \)
в. \( \sqrt{\frac{4}{3} g h} \)
c. \( \sqrt{\frac{3}{4} g h} \)
D. \( \sqrt{(4 g / h)} \)
Subject: Physics
A heavy block of length \( b \) and height \( h \) is
placed at rest on a rough inclined plane of inclination \( \theta \) with the horizontal, as
shown in figure.
(a) The normal reaction from the
surface cannot pass through the centre
mass.Why?
(b) If \( \mu \) is the coefficient of friction
between the block and the inclined
plane, then discuss the conditions of
translational and rational equilibrium of the block.
A heavy block is placed at rest on a rough inclined plane.
Subject: Maths
If \( f^{1}(x)=\sin (\log x) \) and \( y= \)
\( f\left(\frac{2 x+3}{3-2 x}\right), \) then \( \frac{d y}{d x} \) equals
A. \( \frac{12}{(3-2 x)^{2}} \)
B. \( \sin \left[\log \left(\frac{2 x+3}{3-2 x}\right)\right] \)
c. \( \frac{12}{(3-2 x)^{2}} \sin \left[\log \left(\frac{2 x+3}{3-2 x}\right)\right] \)
D. \( \frac{12}{(3-2 x)^{2}} \cos \left[\log \left(\frac{2 x+3}{3-2 x}\right)\right] \)
Subject: Maths
If \( y=\tan ^{-1}\left(\frac{2^{x}}{1+2^{2 x+1}}\right) \) then \( \frac{d y}{d x} \) at
\( \boldsymbol{x}=\mathbf{0} \) is
A \( \cdot \frac{1}{10} \log 2 \)
B. \( \frac{1}{5} \log 2 \)
c. \( -\frac{1}{10} \log 2 \)
D. \( \log 2 \)
Subject: Maths
if \( f^{\prime}(x)<0 \forall x \in R \) and \( g(x)=f\left(x^{2}-\right. \)
2) \( +\boldsymbol{f}\left(\boldsymbol{6}-\boldsymbol{x}^{2}\right) \) then
\( A \cdot g(x) \) is an increasing in \( [2, \infty) \)
B. \( g(x) \) is an increasing in [-2,0]
c. \( g(x) \) has a local minima \( a t x=-2 \)
D. \( g(x) \) has a local maxima at \( x=2 \)
Subject: Physics
In figure,the cube is \( 40.0 \mathrm{cm} \) on each
edge.Four straight segments of wire \( a b, b c, c d \) and \( d a \) form a closed loop that
carries a current \( \mathrm{I}=5.00 \mathrm{A}, \) in the
direction shown.A uniform magnetic
field of magnitude \( B=0.020 \mathrm{T} \) is in the
positive y-direction.Determine the magnitude and direction of the
magnetic force on each segment
Subject: Physics
A conducting rod \( P Q \) of length \( l=2 m \)
is moving at a speed of \( 2 m s^{-1} \) making
an angle of \( 30^{\circ} \) with its length.
uniform magnetic field \( B=2 T \) exists
in a direction perpendicular to the plane of motion. Then
\( \mathbf{A} \cdot V_{P}-V_{Q}=8 V \)
B. \( V_{P}-V_{Q}=4 V \)
C \( . V_{Q}-V_{P}=8 V \)
\( \mathbf{D} \cdot V_{Q}-V_{P}=4 V \)
Subject: Maths
Following table gives frequency distribution of amount of bonus paid to
the workers in a certain factory.
Bonus Below Below Below paid \( 500 \quad 600 \)
\[
700
\]
(in Rs.)
No. of 12
24
workers
Find median amount of bonus paid to
the workers.
A. 801.27 Rs.
B. 812.27 Rs.
c. 846.27 Rs.
D. 735.29 Rs.
Subject: Chemistry
Lactose is a disaccharide of :
A. \( \alpha-D \) -Glucose and \( \alpha-D \) -Fructose
B . \( \beta-D \) -Glucose and \( \beta-D \) -Galactose
C \( . \alpha-D \) -Glucose and \( \beta-D \) -Ribose
D. \( \alpha-D \) -Glucose and \( \alpha-D \) -Galactose
Subject: Maths
Prove that: \( \sec ^{6} \boldsymbol{A}-\tan ^{6} \boldsymbol{A}=\mathbf{1}+ \)
\( \mathbf{3} \tan ^{2} \boldsymbol{A}+\mathbf{3} \tan ^{\mathbf{4}} \boldsymbol{A} \)
Subject: Chemistry
Calculate the wave number of the
highest energy transition in the Balmer series of the hydrogen atom:
\( \left[\boldsymbol{R}_{\boldsymbol{H}}=\mathbf{1 0 9 6 7 8 c m}^{-1}\right] \)
A \( .27419 .5 \mathrm{cm}^{-1} \)
В. 2741.95 \( c m^{-1} \)
c. \( 274.195 \mathrm{cm}^{-1} \)
D. 274195.1 \( c m^{-} \)
Subject: Maths
In an equilateral triangle \( \Delta A B C \) with
sides \( 5 \mathrm{cm} . \) Angle bisectors of \( \angle A, \angle B, \angle C \) meet at point \( 0 . \) Measures of OA approximately is
A . 2.5
B. 4
\( c .3 .2 \)
D. 2.8
Subject: Maths
Use differentials to a approximate the values of ; (i) \( \sqrt{\mathbf{3 6 . 6}} \) and (ii) \( \sqrt[3]{\mathbf{2 6}} \)
A . (i) 6.02
(ii) \( \frac{80}{9} \)
B. (i) 6.03
(ii) \( \frac{80}{18} \)
c. \( (\text { i) } 6.25 \)
(ii) \( \frac{80}{27} \)
D. (i) 6.05
(ii) \( \frac{80}{27} \)
Subject: Physics
A man of 50 kg mass is standing in a gravity free space at a height of \( 10 \mathrm{m} \) above the floor. He throws a stone of 0.5
kg mass downwards with a speed 2 \( \mathrm{m} / \mathrm{s} . \) When the stone reaches the
floor,the distance of the man above the floor will be
\( A \cdot 9.9 \mathrm{m} \)
B. \( 10.1 \mathrm{m} \)
\( c \cdot 10 m \)
D. 20 \( m \)
Subject: Maths
The value of \( \int_{1 / 2}^{1} \frac{d x}{x \sqrt{3 x^{2}+2 x-1}} \) is?
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 3 \)
c. \( \pi / 6 \)
D. \( \pi / \sqrt{2} \)
Subject: Chemistry
The normal boiling point of a liquid is that temperature at which vapour pressure of the liquid is equal to:
A. zero
B. 380 mm of Hg
c. \( 760 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 100 \mathrm{mm} \) of \( \mathrm{Hg} \)
Subject: Physics
A black body at \( 200 \mathrm{K} \) is found to emit
maximum energy at a wavelength of 14
\( \mu \mathrm{m} . \) When its temperature is raised to
1000 \( \mathrm{K}, \) the wavelength at which maximum energy is emitted is :
\( A \cdot 14 \mu m \)
B. 70 \( \mu \) m
c. \( 1.8 \mu \mathrm{m} \)
D. 2.8 \( \mu \) m
Subject: Chemistry
The \( \left[\boldsymbol{H}_{3} \boldsymbol{O}^{+}\right] \) in a solution having \( \left[\boldsymbol{O H}^{-}\right]=\mathbf{5} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \) is:
A \( \cdot 2 \times 10^{-3} \)
B. \( 2 \times 10^{-12} \)
c. \( 5 \times 10^{-3} \)
D. none of these
Subject: Biology
Match the columns
\( \begin{array}{llll} & \text { । } & \text { I } & \\ \text { a } & \text { Aerobic } & \text { I } & \text { Frankia } \\ \text { b } & \text { Cyanobacteria } & 2 . & \text { Azospirilum } \\ \text { c. } & \text { Casuarina } & 3 . & \text { Clostridum } \\ \text { d. } & \text { Tropical grasses } & 4 . & \text { Aulosira } \\ & & 5 . & \text { Azotobacter }\end{array} \)
\( \mathbf{A} \)
\( a-4, b-3, c-2, d-1 \)
B. \( a-5, b-3, c-4, d-1 \)
c. \( a-5, b-4, c-1, d-2 \)
D. \( a-3, b-5, c-4, d-2 \)
E \( . a-2, b-1, c-3, d-5 \)
Subject: Physics
The dimensions of torque are
\( \mathbf{A} \cdot\left[M L^{3} T^{-3}\right] \)
В \( \cdot\left[M L^{-1} T^{-1}\right] \)
c. \( \left[M L^{2} T^{-2}\right] \)
D \( \cdot\left[M T^{-2}\right] \)