AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
When stationary waves are set up, pick
out the correct statement from the
following:
A. all the particles in the medium are in the same phase of vibration at all times and distances
B. the particles with an interval between two consecutive nodes are in phase, but the particles in two such consecutive intervals, are of opposite phase
C. the phase lag along the path of the wave increases as the distance from the source increases
D. only antinodes are in same phase
Subject: Physics
A circular track has a circumference of
\( 3140 \mathrm{m} \) with \( \mathrm{AB} \) as one of its diameter
shooter moves from A to B along the circular path with a uniform speed of 10
A. Distance covers by the scooter
B. Displacement of scooters
c. Time taken by the scooter in maching from A to B
D. None of these
Subject: Physics
In the diagram the area of cross section
of the pistons \( A \) and \( B \) are \( 8 c m^{2} \) and
\( 320 c m^{2} \) respectively then the thrust on
the piston at \( B \) is
A . \( 160 k g f \)
в. \( 320 k g f \)
c. \( 420 k g f \)
D. \( 80 k g f \)
Subject: Maths
\( \operatorname{Let} f(x)=\sin ^{2} \frac{x}{2}+\cos ^{2} \frac{x}{2} \) and \( g(x)= \)
\( \sec ^{2} x-\tan ^{2} x . \) The two functions are
equal over the set
A. \( \Phi \)
в. \( R \)
c. \( R-\left\{x \mid x=(2 n+1) \frac{\pi}{2}, n \in Z\right\} \)
D. None of these
Subject: Physics
Displacement \( (x) \) of a particle is related to time \( (t) \) as \( x=a t+b t^{2}+c t^{3} \) where
\( a, b \) and \( c \) are constants of motion. The velocity of the particle when its acceleration is zero, is given by:
A. \( _{a+\frac{b^{2}}{c}} \)
в. \( _{a-} \frac{b^{2}}{3 c} \)
c. \( _{a}+\frac{b^{2}}{3 c} \)
D. \( _{a-\frac{b^{2}}{4 c}} \)
Subject: Chemistry
The reaction that gives phenol as the
end product is/are:
This question has multiple correct options
\( \mathbf{A} \)
\( \sqrt{ }+\operatorname{conc.H}_{2} \operatorname{so}_{4} \frac{\text { Heat }}{\text { Fusion }}>\frac{\mathbf{H}^{+}}{\mathbf{H}_{2} \mathbf{O}} \)
B. \( \sqrt{\int}^{\mathrm{N} \mathrm{O}_{2}} \frac{\mathrm{NaNO}_{2}}{\mathrm{HCl}, 0^{\circ} \mathrm{C}} \)
\( c \)
\( y_{1}+\mathbf{k o H} \stackrel{300^{\circ} \mathbf{C}}{\longrightarrow} \stackrel{\mathbf{H C l}}{\longrightarrow} \)
\( \mathbb{P}+\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}_{2} \stackrel{\mathrm{H}^{+}}{\longrightarrow} \frac{\mathrm{O}_{2}}{\mathrm{KOH}}>\frac{\mathrm{H}^{+}}{ } \)
Subject: Chemistry
Write the structures of the following organic halogen compounds.
(i) 2-Chloro-3-methylpentane
(ii) p-Bromochlorobenzene
(iii) 1 -Chloro-4-ethylcyclohexane
(iv) 2 -(2-Chlorophenyl)-1-iodooctane
(v) 2 -Bromobutane
(vi) 4-tert-Butyl-3-iodoheptane
(vii) \( 1- \) Bromo- 4 -sec-butyl-2methylbenzene (viii) 1,4-Dibromobut2-ene
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{c}\mathbf{2} \\ -\mathbf{4} \\ \mathbf{1}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{5} & \mathbf{3} & -\mathbf{1}\end{array}\right] \) then
verify that \( (\boldsymbol{A} \boldsymbol{B})^{\prime}=\boldsymbol{B}^{\prime} \boldsymbol{A}^{\prime} \)
Subject: Physics
A ring and a disc are initially at rest, side by side, at the top of an inclined
plane which makes an angle \( 60^{\circ} \) with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is \( \frac{(2-\sqrt{3})}{\sqrt{10} s}, \) then the height of the top of the inclined plane, in meters.
is \( _{-1} \). Take \( g=10 m s^{-2} \)
Subject: Maths
Mark the incorrect statement by the
graph of the function \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \)
A. \( f(0)=0 \)
B. \( f(-4)=4 \)
c. \( f(4)=-4 \)
D. The domain of \( f(x) \) is all real numbers
Subject: Physics
A wire is stretched by a force \( F . \) If \( s \) is the strain developed and \( Y \) is Young's modulus of material of wire, then work
done per unit volume is
A \( \cdot \frac{Y s^{2}}{2} \)
B. \( \frac{s^{2}}{2 Y} \)
c. \( \frac{1}{2} F s \)
D. \( \frac{Y}{2 s^{2}} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & -\mathbf{2} & \mathbf{3}\end{array}\right] \quad \boldsymbol{B}=\left[\begin{array}{c}-\mathbf{1} \\ \mathbf{2} \\ -\mathbf{3}\end{array}\right], \) then
\( \boldsymbol{A}+\boldsymbol{B} \)
\( \mathbf{A} \cdot\left[\begin{array}{lll}0 & 0 & 0\end{array}\right] \)
B. 0
0
\( \mathbf{c} \cdot\left[\begin{array}{ll}-1 & 4\end{array}\right] \)
D. not defined
Subject: Maths
Sum of the series \( 1+(1+2)+ \)
\( (1+2+3)+(1+2+3+4)+\ldots \) to \( n \)
terms be \( \frac{1}{m} n(n+1)\left[\frac{2 n+1}{k}+1\right] \)
Find the value of \( \mathrm{k}+\mathrm{m} \)
Subject: Maths
\( \boldsymbol{F}=\frac{9}{5} \boldsymbol{C}+\mathbf{3 2} ; \) make 'C' the subject of
formula.
A \( \cdot C=\frac{5}{9}(F-32) \)
B. \( C=\frac{9}{5}(F-32) \)
c. \( c=\frac{5}{9}(F+32) \)
D. none of the above
Subject: Chemistry
For the following reaction, \( \triangle G^{\circ}= \)
\( -163 k J m o l^{-1} \)
\( \mathbf{2} \boldsymbol{O}_{\boldsymbol{3}} \rightarrow \mathbf{3} \boldsymbol{O}_{\mathbf{2}} \)
If this reaction is spontaneous enter 1
else enter 0
Subject: Chemistry
Assign structures to \( A, B, C \) and \( D \) in
the following:
\( \mathbf{A} \cdot C H_{2} C H_{2} C H_{2} C H_{2}+a l c \cdot K O H \rightarrow A \)
\( B r \)
B \cdot \( \left(C H_{3}\right)_{3} C B r+C H_{3} C O O^{-} \rightarrow B \)
c. \( \left(C H_{3}\right)_{2} C H \underset{O_{H}}{C H} C H_{3}+H_{2} S O_{4} \triangleq C \)
\( D \)
Subject: Maths
The Venn diagram shows sets \( P, Q \) and \( R \) with regions labelled, I, II, III and IV.
State the region which represents set
\( \left[\boldsymbol{P} \cap(\boldsymbol{Q} \cup \boldsymbol{R})^{\prime}\right] \)
4
B.
\( c \)
\( D \cdot|v| \)
Subject: Chemistry
Look at the following reactions carried
out in closed vessels:
(i) \( \boldsymbol{P C I}_{5} \rightarrow \boldsymbol{P C I}_{3}+\boldsymbol{C I}_{2} \)
\( (\text { ii }) N_{2}+O_{2} \rightarrow 2 N O \)
(iii) \( 2 K C I O_{3} \rightarrow 2 K C I+3 O_{2} \)
\( (\text { iv }) \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{S} \boldsymbol{C} \boldsymbol{N}_{-} \rightarrow \boldsymbol{F} \boldsymbol{e}(\boldsymbol{S} \boldsymbol{C} \boldsymbol{N})^{2+} \)
Which one of them is irreversible?
sc
A . \( (i) \)
B. (ii)
c. \( (i i i) \)
D. (iv)
Subject: Maths
The value of median of
\( \begin{array}{llll}\text { Income } & & & & \\ & 1000 & 1100 & 1200 & 1300\end{array} \) No. of
persons \( \quad 14 \quad 26 \quad 21 \)
\( A \cdot 1300 \)
B. 1200
c. 1250
D. 1150
Subject: Chemistry
Choose incorrect stability order:
\( \left.\mathbf{A} \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+}<C u(e n)_{2}\right]^{2+}<[C u(\text {trien})]^{2+} \)
B. \( \left[F e\left(H_{2} O\right)_{6}\right]^{3+}<\left[F e\left(N O_{2}\right)_{6}\right]^{3+}<\left[F e\left(N H_{3}\right)_{6}\right]^{3+} \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(H_{2} O\right)_{6}\right]^{3+}<\left[\operatorname{Rh}\left(H_{2} O\right)_{6}\right]^{3+}<\left[\operatorname{Ir}\left(H_{2} O\right)_{6}\right]^{3+} \)
\( \mathbf{D} \cdot\left[C r\left(N H_{3}\right)_{6}\right]^{1+}<\left[C r\left(N H_{3}\right)_{6}\right]^{2+}<\left[C r\left(N H_{3}\right)_{6}\right]^{3+} \)
Subject: Maths
A gas cylinder has a diameter of \( 14 \mathrm{m} \)
and height is \( 0.2 \mathrm{m} \). Find its surface area. \( (\pi=22 / 7) \)
A. \( 316.512 m m^{2} \)
B. \( 316.512 m \)
\( \mathbf{c} \cdot 316.512 m^{3} \)
D. \( 316.512 m^{2} \)
Subject: Physics
A small sphere of mass \( m \) and electric
charge \( \boldsymbol{q}, \) is suspended by a light thread. A second sphere carrying a
charge \( q_{2} \) is placed directly below the
first sphere at a distance \( ^{\prime} d^{\prime} \) away. Then
A. tension in thread may reduce to zero if the spheres are positively charged
B. tension in thread may reduce to zero if the spheres are oppositely charged
c. tension in thread can never be zero
D. tension in thread is independent of the nature of the charges
Subject: Chemistry
Bond dissociation enthalphies of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
and \( N_{2}(g) \) are \( 436.0 \mathrm{kJ} \) mol \( ^{-1} \) and 941.8
kJ mol \( ^{-1} \) respectively and enthalpy of
formation of \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \) is \( -46 \mathrm{kJ} \boldsymbol{m o l}^{-1} \)
What is enthalpy of atomization of
\( N H_{3}(g) ? \)
A. 390.3 kJ \( m o l^{-1} \)
B . 1170.9 kJ \( m o l^{-1} \)
c. 590 k \( \operatorname{mol}^{-1} \)
D. 720 kJ \( m o l^{-1} \)
Subject: Physics
A current of i ampere is flowing through each ofthe bent wires as shown the
magnitude and direction of magnetic field at 0 is
A \( \cdot \frac{\mu_{0} \mathrm{i}}{4}\left(\frac{1}{\mathrm{R}}+\frac{2}{\mathrm{R}^{\prime}}\right) \)
В. \( \frac{\mu_{0} \mathrm{i}}{4}\left(\frac{1}{\mathrm{R}}+\frac{3}{\mathrm{R}^{\prime}}\right) \)
c. \( \frac{\mu_{0} \text { i }}{8}\left(\frac{1}{R}+\frac{3}{2 R} \prime\right) \)
D. \( \frac{\mu_{0} \mathrm{i}}{8}\left(\frac{1}{\mathrm{R}}+\frac{3}{\mathrm{R}^{\prime}}\right) \)
Subject: Maths
Solution of the equation \( \frac{d y}{d x}=1+ \)
\( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{x}+\boldsymbol{y} \) is
\( \mathbf{A} \cdot(1+y)(1+x)=c \)
B \( \cdot \log (1+y)=1+x+c \)
\( ^{\mathbf{C}} \cdot \ln |1+y|=x+\frac{x^{2}}{2}+c \)
D \( \ln |1+y|+x+\frac{x^{2}}{2}+c=0 \)
Subject: Maths
A circle is inscribed in a square. If the
area of the square is 36 sq. units, what is the area of the circle?
\( \mathbf{A} \cdot 6 \pi \)
в. \( 9 \pi \)
c. \( 12 \pi \)
D. \( 18 \pi \)
\( E .36 \pi \)
Subject: Maths
The sum and sum of squares
corresponding to length \( X \) (in \( \mathrm{cm} \) ) and
weight \( \boldsymbol{y} \)
(in \( g m) \) of 50 plant products are given below:
\[
\begin{array}{l}
\sum_{i=l}^{50} \boldsymbol{X}_{i}=\mathbf{2 1 2}, \sum_{i=l}^{50} \boldsymbol{X}_{i}^{2}= \\
\mathbf{9 0 2 . 8}, \sum_{i=l}^{50} \boldsymbol{y}_{i}=\mathbf{2 6 1}, \sum_{i=l}^{50} \boldsymbol{y}_{i}^{2}=\mathbf{1 4 5 7 . 6}
\end{array}
\]
Which is more varying the length or weight?
Subject: Chemistry
Iron can liberate \( \boldsymbol{H}_{2} \) from dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
but copper cannot liberate \( \boldsymbol{H}_{2} \) from dil.
\( H_{2} S O_{4} \) because :
A. iron is above than hydrogen in the activity series.
B. copper is below in activity series than hydrogen
c. both A and B
D. none of these
Subject: Maths
Kruti took a loan at simple interest at \( 6 \% \) in the first year with an increase of \( 0.5 \% \) in each subsequent year. She paid Rs. 3375 as interest after 4 year. How much loan did she take?
A. Rs. 12500
B. Rs. 15800
c. Rs. 33250
D. Rs. 30, 000
Subject: Chemistry
Identify the oxidation states of titanium \( (Z=22) \) and copper \( (Z=29) \) in their colourless compounds:
A \( \cdot T i^{3+}, C u^{2+} \)
B. \( T i^{2+}, C u^{2+} \)
c. \( T i^{4+}, C u^{+} \)
D. \( T i^{4+}, C u^{2+} \)
Subject: Physics
A small conducting sphere of radius \( r \) is Iying concentrically with a bigger
hollow conducting sphere of radius \( \boldsymbol{R} \)
The bigger and smaller spheres are
charged with \( Q \) and \( q \) respectively
\( (Q>q) . \) The two spheres are insulated
from one another. The potential difference between the spheres will be :
A \( \cdot \frac{1}{4 \pi \epsilon_{0}}\left(\frac{q}{r}-\frac{Q}{R}\right) \)
В. \( \frac{1}{4 \pi \epsilon_{0}}\left(\frac{q}{r}-\frac{q}{R}\right) \)
\( ^{\mathbf{C}} \cdot \frac{1}{4 \pi \epsilon_{0}}\left(\frac{q}{r}+\frac{Q}{R}\right) \)
D. \( \frac{1}{4 \pi \epsilon_{0}}\left(\frac{q}{R}-\frac{Q}{r}\right) \)
Subject: Maths
The perimeter of a rhombus is \( 100 \mathrm{cm} \) and one of the diagonals is \( 40 \mathrm{cm} \) Then the area of the rhombus is
A. \( 1000 \mathrm{cm}^{2} \)
В. \( 500 \mathrm{cm}^{2} \)
c. \( 1200 \mathrm{cm}^{2} \)
D. \( 600 \mathrm{cm}^{2} \)
Subject: Maths
The distance of the point (1,2) from the line \( x+y+5=0 \) measured along the
line parallel to \( 3 x-y=7 \) is equal to
A \( \cdot \frac{4}{\sqrt{10}} \)
B. 40
c. \( \sqrt{40} \)
D. \( 10 \sqrt{2} \)
Subject: Chemistry
How does ozone react with the
following?
(i) \( C_{2} H_{4} \)
(ii) Moist \( \boldsymbol{I}^{-} \)
(iii) \( \boldsymbol{H} \boldsymbol{g} \)
(iv) \( \boldsymbol{A} \boldsymbol{g} \)
Subject: Chemistry
In the following reaction \( 2 H_{2} O_{2}(a q) \rightarrow \)
\( 2 H_{2} O(l)+O_{2}(g) \) rate of formation of
\( O_{2} \) is \( 36 g . m i n^{-1} \)
(a) What is rate of formation of \( \boldsymbol{H}_{2} \boldsymbol{O} \) ?
(b) What is rate of disappearance of
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)
Subject: Physics
An electron with kinetic energy \( \boldsymbol{E} \boldsymbol{e} \boldsymbol{V} \)
collides with a hydrogen atom in the ground state. The collision will be elastic
A. for all values of \( E \)
B. for \( E<10.2 e V \)
c. for \( E<13.6 e V \)
D. only for \( E<3.4 e V \)
Subject: Physics
Assertion
Stirring the liquid in thermal contact with the reservoir will convert the work
done into heat, is an irreversible
process.
Reason
If it is the reversible process it will violate the second law of
thermodynamics.
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
\( K_{P} \) for the reaction \( N_{2}+2 H_{2} \rightleftharpoons \)
\( 2 N H_{3} \) is \( 1.6 \times 10^{-4} a t m^{-2} \) at \( 400^{0} C \)
What will be \( K_{P} \) at \( 500^{0} C ? \) The heat of
reaction at this temperature is -25.14 kcal?
A \( \cdot K_{P_{2}}=1.428 \times 10^{-5} a t m^{-2} \)
B . \( K_{P_{2}}=15.55 \times 10^{-5} a t m^{-2} \)
C \( \cdot K_{P_{2}}=12 \times 10^{-4} a t m^{-2} \)
D. \( K_{P_{2}}=7.88 \times 10^{-5} a t m^{-2} \)
Subject: Physics
Two infinite parallel metal planes, contain electric charges with charge densities \( +\sigma \) and \( -\sigma \) respectively and
they are separated by a small distance
in air. If the permittivity of air is \( \epsilon_{0}, \) then
the magnitude of the field between the two planes with its direction will be:
A \( \cdot \sigma / \epsilon_{0} \) towards the positively charge plane
B . \( \sigma / \epsilon_{0} \) towards the negatively charged plane
C \( \cdot \sigma /\left(2 \epsilon_{0}\right) \) towards the positively charged plane
D. 0 and towards any direction
Subject: Physics
A stationary body explodes into two
fragments of masses \( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2} . \) If
momentum of one fragment is \( p \), the minimum energy of explosion is
\( ^{\mathbf{A}} \cdot \frac{p^{2}}{2\left(m_{1}+m_{2}\right)} \)
в. \( \frac{p^{2}}{2(\sqrt{m_{1} m_{2}})} \)
c. \( \frac{p^{2}\left(m_{1}+m_{2}\right)}{2 m_{1} m_{2}} \)
D. \( \frac{p^{2}}{2\left(m_{1}-m_{2}\right)} \)
Subject: Chemistry
Among the following oxoacids, the correct decreasing order of acid
strength is:
A. \( H C l O_{4}>H C l O_{3}>H C l O_{2}>H O C l \)
в. \( H C l O_{2}>H C l O_{4}>H C l O_{3}>H O C l \)
D. \( H C l O_{4}>H O C l>H C l O_{2}>H C l O_{3} \)
Subject: Maths
The construction of \( \Delta L M N \) when
\( M N=7 \mathrm{cm} \) and \( m \angle M=45^{\circ} \) is not
possible when difference of \( L M \) and
\( \boldsymbol{L} \boldsymbol{N} \) is equal to:
A . 4.5
B. 5.5
\( c .6 .5 \)
D. 7.5
Subject: Maths
Assertion
The resultant of the three vector
\( \overrightarrow{O A}, \overrightarrow{O B} \) and \( \overrightarrow{O C} \) as shown in the figure is \( \boldsymbol{R}(1+\sqrt{2}) . \) Here \( \boldsymbol{R} \) is the radius of the
circle.(Here \( \left.\angle A O B=\angle B O C=45^{\circ}\right) \)
Reason
\( \overrightarrow{O A}+\overrightarrow{O C} \) is along \( \overrightarrow{O B} \) and \( (\overrightarrow{O A}+ \) \( \overrightarrow{O C})+\overrightarrow{O B} \) is along \( \overrightarrow{O B} \)
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
\( \int \frac{x}{\sqrt{\left(4-x^{4}\right)}} d x \)
A \( \cdot \sin ^{-1}\left(\frac{1}{2} x^{2}\right) \)
B \( \cdot \frac{1}{2} \sin ^{-1}\left(x^{2}\right) \)
C \( \cdot \frac{1}{2} \sin ^{-1}\left(\frac{1}{2} x^{2}\right) \)
D. \( \frac{1}{2} \cos ^{-1}\left(\frac{1}{2} x^{2}\right) \)
Subject: Maths
If for the complex numbers \( z_{1}, z_{2}, \dots ., z_{n} \)
\( \left|z_{1}\right|=\left|z_{2}\right|=\ldots . .=\left|z_{n}\right|=1 . \) Then prove
that \( |\overline{z_{1}+z_{2}+\ldots . .+z_{n}}|= \)
\( \left|\frac{\mathbf{1}}{z_{1}}+\frac{1}{z_{2}}+\ldots \ldots+\frac{1}{z_{n}}\right| \)
Subject: Chemistry
Which of the following is not formed in
the reaction of \( X e \) with \( F_{2} ? \)
A. \( \mathrm{xeOF}_{4} \)
в. \( \mathrm{XeF}_{2} \)
c. \( \mathrm{xeF}_{4} \)
D. XeF \( _{6} \)
Subject: Physics
24 cells, each having the same e.m.f. and 2 ohm internal resistance, are used to draw maximum current through an
external resistance of 3 ohm. The cells
should be connected:
\( \mathbf{A} \cdot \) In series
B. in parallel
c. \( \ln 4 \) rows, each row having 6 cells
D. In 6 rows, each row having 4 cells
Subject: Chemistry
The chemical composition of the slag formed during smelting process is :
A \( \cdot \) Cusio \( _{3} \)
в. Fesi Оз\( _{3} \)
\( \mathrm{c} \cdot \operatorname{casi} O_{3} \)
D. \( C u_{2} O . S i O_{2} \)
Subject: Chemistry
The enthalpy change of which reaction
corresponds to \( \Delta H_{f}^{o} \) for \( N a_{2} C O_{3} \) at \( 298 K ? \)
A \( \cdot \operatorname{Na(s)}+C(s)+\frac{3}{2} O_{2}(g) \rightarrow N a_{2} C O_{3}(s) \)
в. \( N a_{2} O(s)+C O_{2}(g) \rightarrow N a_{2} C O_{3}(s) \)
c. \( 2 N a^{+}(a q .)+C O_{3}^{2-}(a q .) \rightarrow N a_{2} C O_{3}(s) \)
D \( \cdot 2 N a^{+}(a q)+2 O H^{-}(a q .)+C O_{2}(a q .) \longrightarrow N a_{2} C O_{3}(s)+ \)
\( H_{2} O \)
Subject: Physics
In medium wave broadcast a radio can
be tuned in the frequency range 800 \( \mathrm{kHz} \) to \( 1200 \mathrm{kHz} \). In L-C circuit of this
radio effective inductance is \( 200 \mu H \)
what should be the range of the variable capacitor?
\( A \cdot 88 \) pF to 198 pF
B. 98 pF to 198 pF
C. 78 pF to 146 pF
D. 20 pF to 112 pF
Subject: Maths
\( \int \frac{1}{\left[\left(1-x^{2}\right)\left\{\left(2 \sin ^{-1} x\right)^{2}-9\right\}\right]^{1 / 2}} d x \)
A. \( \frac{1}{2} \log \left[2 \sin ^{-1} x+\sqrt{\left(2 \sin ^{-1} x\right)^{2}-9}\right] \)
B. \( \log \left[2 \sin ^{-1} x+\sqrt{\left(2 \sin ^{-1} x\right)^{2}-9}\right] \)
c. \( \frac{1}{2} \log \left[2 \sin ^{-1} x+\sqrt{\left(2 \sin ^{-1} x\right)^{2}+9}\right] \)
D. \( \frac{1}{2} \log \left[2 \sin ^{-1} x+\sqrt{\left(2 \cos ^{-1} x\right)^{2}-9}\right] \)
Subject: Physics
A frame \( C D E F \) is laced in a region
where a magnetic field \( \vec{B} \) is present. \( \mathbf{A} \)
rod of length one metre moves with
constant velocity \( 20 m / s \) and strength
of magnitude field is one tesia. The
power spent in the process is (take
\( R=0.2 \Omega \) and all other wires and rod
have zero resistance)
\( \mathbf{A} \cdot 1 k W \)
\( \mathbf{B} \cdot 2 k W \)
\( \mathbf{c} .3 k W \)
\( \mathbf{D} \cdot 4 k W \)
Subject: Chemistry
The ion which shows maximum
paramagnetic character among the bivalent ions of the first transition
metal series is :
\( A \cdot C_{0}^{2} \)
B. \( c u^{2} \)
\( c \cdot c r^{2} \)
D. \( \mathrm{Fe}^{2} \)
\( E \cdot M n^{2} \)
Subject: Chemistry
You may have noticed that chicken-egg is very strong along its long axis so much so that it does not break even
when pressed very hard. Which of the following is the main constituent of egg-shell?
A. \( \operatorname{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \)
B. \( C a S O_{4} \cdot \frac{1}{2} H_{2} O \)
\( \mathrm{c} \cdot \operatorname{casio}_{3} \)
\( \mathrm{D} \cdot \mathrm{CaCO}_{3} \)
Subject: Maths
\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{lll}\boldsymbol{a} & \mathbf{0} & \mathbf{0} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right| \) then \( \left|\begin{array}{lll}\boldsymbol{p}^{2} \boldsymbol{a} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{p} \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{p c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right| \) is
equal to
A \( . p \Delta \)
B . \( p^{2} \Delta \)
c. \( p^{3} \Delta \)
D. \( 2 p \Delta \)
Subject: Maths
Find the coordinate of the point \( \boldsymbol{P} \) where the line through \( A(3,-4,-5) \) and \( B(2,-3,1) \) crosses the plane passing through three points \( \boldsymbol{L}(\mathbf{2}, \mathbf{2}, \mathbf{1}), \boldsymbol{M}(\mathbf{3}, \mathbf{0}, \mathbf{1}) \) and \( \boldsymbol{N}(\mathbf{4},-\mathbf{1}, \mathbf{0}) \)
Also, find the ratio in which \( P \) divides
the line segment \( \boldsymbol{A B} \)
Subject: Physics
A long straight wire is carrying current
in \( +z \) direction. The \( x \) -y pkane contains a closed circular loop carrying current
\( I_{2} \) and not encircling the straight wire. The force on the loop will be.
B . \( \mu_{0} I_{1} I_{2} / 4 \pi \)
c. zero
D. Depends on the distance of the circle of the loop from the wire
Subject: Chemistry
Arrange the following in the increasing order of their basicities.
I. \( p- \) Toluidine
II. \( N, N- \) Dimethyl - \( p \) - toluidine
III. \( p- \) Nitroaniline
IV. Aniline
A. \|\|\( <\|v<1<\| \)
B. II \( <\mid V<1<11 \)
c. \( \|<\|<1<1 V \)
Subject: Maths
The equation of the circle having centre (1,-2) and passing through the point of intersection of the lines \( 3 x+y=14 \)
and \( 2 x+5 y=18 \) is
A \( \cdot x^{2}+y^{2}-2 x+4 y-20=0 \)
B . \( x^{2}+y^{2}-2 x-4 y-20=0 \)
C. \( x^{2}+y^{2}+2 x-4 y-20=0 \)
D. \( x^{2}+y^{2}+2 x+4 y-20=0 \)
Subject: Physics
Two point charges \( +3 \mu C \) and \( +8 \mu C \) repel each other with a force of \( 40 N . \) If a
charge of \( -5 \mu C \) is added to each of them, the force between them will become:
A \( .-10 N \)
B. \( 10 N \)
\( c .20 N \)
D. \( -20 N \)
Subject: Physics
If Earth is supposed to be a sphere of
radius \( R, \) if \( g_{30^{\circ}} \) is value of acceleration
due to gravity at latitude of \( 30^{\circ} \) and \( g \) at
the equator, the value of \( g-g_{30^{\circ}} \) is
A \( \cdot \frac{1}{4} \omega^{2} R \)
в. \( \frac{3}{4} \omega^{2} R \)
c. \( \omega^{2} R \)
D. \( \frac{1}{2} \omega^{2} R \)
Subject: Physics
One way in which the operation of an \( n \) -
\( p-n \) transistor differ from that of a \( p-n-p \)
transistor is that
A. the emitter junction is reverse biased in \( n-p-n \)
B. the emitter junction injects minority carriers into the base region of the \( \mathrm{p}-\mathrm{n}-\mathrm{p} \)
C. the emitter injects holes into the base of the pnp and electrons into the base region of \( n-p-n \)
D. the emitter injects holes into the base of \( n-p-n \)
Subject: Maths
If \( \boldsymbol{P}=\left[\begin{array}{ccc}1 & 2 & -3 \\ 3 & -1 & 2 \\ -2 & 1 & 3\end{array}\right], Q= \)
\( \left[\begin{array}{lll}2 & 3 & 1 \\ 3 & 1 & 2 \\ 1 & 2 & 3\end{array}\right], \) then find matrix \( R \) such
that \( \boldsymbol{P}+\boldsymbol{Q}+\boldsymbol{R} \) is a zero matrix
Subject: Chemistry
In a set of the given reactions, acetic acid yields a product \( C . \) Product \( C \) would be:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{P C l}_{5} \rightarrow \)
\( \boldsymbol{A} \frac{C_{6} \boldsymbol{H}_{6}}{\text {Anhy.AlCl}_{3}} \boldsymbol{B} \frac{C_{2} \boldsymbol{H}_{5} M \boldsymbol{g} \boldsymbol{B r} / \text {ether}}{(i i) \boldsymbol{H}^{+}} \boldsymbol{C} \)
A \( \cdot C H_{3} C H(O H) C_{2} H_{5} \)
в. \( C H_{3} C O C_{6} H_{5} \)
c. \( C H_{3} C H(O H) C_{6} H_{5} \)
D. \( \quad c_{2} \), и\( _{5} \)
\[
C H_{3}-C-(O H) C_{6} H_{5}
\]
Subject: Maths
The value of
\( \left\{s i n^{-1}\left[x^{2}+\frac{1}{2}\right]+\cos ^{-1}\left[x^{2}-\frac{1}{2}\right]\right\} \)
where \{\} and \( [.] \) denote fractional part
function and greatest integer function respectively
\( \mathbf{A} \cdot \pi-3 \)
B. \( 4-\pi \)
\( c \cdot 2-\frac{\pi}{2} \)
D. o