AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If some coins each of diameter \( 1.5 \mathrm{cm} \)
and thickness \( 0.2 \mathrm{cm} \) are melted and a
right circular cylinder of height \( 10 \mathrm{cm} \)
and diameter \( 4.5 \mathrm{cm} \) is made, then find
the number of coins required to make the right circular cylinder
A . 336
в. 450
c. 512
D. 545
Subject: Maths
\( O \) is the centre of the circle with radius
\( 5 \mathrm{cm} . \) Chords \( A B \) and \( C D \) are parallel.
\( A B=6 \mathrm{cm} \) and \( C D=8 \mathrm{cm} . \) If \( P Q \) is
distance between \( A B \) and \( C D \), then the
length of \( \boldsymbol{P Q} \) is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c \cdot 7 \mathrm{cm} \)
D. \( 7 \sqrt{2} \mathrm{cm} \)
Subject: Chemistry
The rate constant is given by the equation \( \boldsymbol{K}=\boldsymbol{P} \boldsymbol{Z} \boldsymbol{e}^{-\boldsymbol{E} / \boldsymbol{R} \boldsymbol{T}} . \) Which factor
should register a decrease for the
reaction to proceed more rapidly?
A . T
B. z
\( c \cdot E \)
D.
Subject: Chemistry
Which of the following will produce only
one product on reduction with \( L i A l H_{4} ? \)
A \( \cdot C H_{3} O C O C H_{2} C H_{3} \)
в. \( C H_{3} C H_{2} \) ОСОСН\( _{2} \)СН\( _{3} \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{O} \mathrm{COCH}_{3} \)
D. \( C H_{3} C H_{2} O C O C H_{2} C H_{2} C H_{3} \)
Subject: Maths
\( \operatorname{Let} a_{1}, a_{2}, \dots \dots a_{50} \) are non constant
terms of an A.P. and sum of n terms is
given by \( \boldsymbol{S}_{\boldsymbol{n}}=\mathbf{5 0 n}+(\boldsymbol{n})(\boldsymbol{n}-\boldsymbol{7}) \frac{\boldsymbol{A}}{\mathbf{2}} \)
then ordered pair \( \left(d, a_{50}\right) \) is? (where dis the common difference
A. \( (A, 45 A) \)
B. \( (46 A+50) \)
c. \( (2 A, 46 A) \)
D. \( (2 A, 50+49 A) \)
Subject: Maths
The values of \( a \) for which \( f(x)= \) \( \frac{a^{2} x^{3}}{3}+\frac{3 a x^{2}}{2}+2 x+1 \) is strictly
decreasing at \( \boldsymbol{x}=\mathbf{1} \)
A. \( a \in(-2,-1) \)
в. \( a \in(-1,0) \)
c. \( a \in(1,2) \)
D. \( a \in(-2,1) \)
Subject: Physics
Assertion: Blue colour of sky appears
due to scattering of blue colour. Reason: Blue colour has shortest wave
length in visible spectrum.
A. both assertion and reason are true and reason is the correct explanation of assertion
B. both assertion and reason are true but the reason is not the correct explanation of assertion
c. assertion is true but reason is false
D. both the assertion and reason are false
E. reason is true but assertion is false
Subject: Maths
General value of \( \theta \) satisfying the
eqation \( \tan ^{2} \theta+\sec 2 \theta=1 \) is
\( \mathbf{A} \cdot m \pi, n \pi \pm \frac{\pi}{3}, m, n \in I \)
В \( \cdot m \pi, n \pi \pm \frac{\pi}{4}, m, n \in I \)
c. \( m \pi, n \pi \pm \frac{\pi}{6}, m, n \in I \)
D. \( m \pi, n \pi \pm \frac{\pi}{8}, m, n \in I \)
Subject: Maths
Divide the polynomial \( p(x) \) by the polynomial \( g(x) \) and find the quotient and remainder in each of the following. \( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}-\boldsymbol{3} \quad \boldsymbol{g}(\boldsymbol{x})= \)
\( x^{2}-2 \)
Subject: Maths
The function \( f(x)=x(x+3) e^{-(1 / 2) x} \)
satisfies the condition of Rolle's
theorem in \( [-3,0] . \) The value of \( c \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
c. -2
D. - 3
Subject: Chemistry
\( K_{a} \) for ascorbic acid, \( H A s c, \) is \( 5 \times \)
\( 10^{-5} . \) Calculate the hydrogen ion
concentration and percentage hydrolysis in an aqueous solution in
which the concentration of \( A s c^{-} \) ions is
\( \mathbf{0 . 0 2} \boldsymbol{M} \)
Subject: Maths
Write the order and degree of the differential equation \( \boldsymbol{y}=\boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+ \)
\( \boldsymbol{a} \sqrt{1+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\boldsymbol{a}|+|\boldsymbol{x}+\boldsymbol{b}|, \boldsymbol{x} \epsilon \boldsymbol{R}, \boldsymbol{b}> \)
\( \boldsymbol{a}>\mathbf{0} . \) Then
\( \mathbf{A} \cdot f^{\prime}\left(a^{+}\right)=1 \)
B . \( f^{\prime}\left(a^{+}\right)=0 \)
c. \( f^{\prime}\left(-b^{+}\right)=0 \)
D. \( f^{\prime}\left(-b^{+}\right)=1 \)
Subject: Maths
For construction of a \( \triangle P Q R, \) where
\( Q R=6 \mathrm{cm}, P R=10 \mathrm{cm} \) and \( \angle Q= \)
\( 90^{\circ}, \) its steps for construction is given
below in jumbled form. Identify the first step from the following.
1. At point \( Q \), draw an angle of \( 90^{\circ} \)
2. From \( R \) cut an arc of length \( P R= \)
\( 10.0 \mathrm{cm} \) using a compass.
3. Name the point of intersection of the
\( \operatorname{arm} \) of the angle \( 90^{\circ} \) and the arc drawn
in step \( 3, \) as \( P \)
4. Join \( P \) to \( Q . P Q R \) is the required
triangle.
5. Draw the base side \( Q R=6 \mathrm{cm} \)
\( A \cdot 2 \)
B. 1
\( c \cdot 3 \)
D. 5
E. 4
Subject: Chemistry
Polarisation of the electron cloud of
cation is less than anion because:
A. p/e ratio is more than one for anion
B. p/e ratio is less than one for cation
C. p/e ratio is more than one for cation by which electrons are relatively loosely held compared to anion
D. p/e ration is more than one for cation while less than one for anion by which electron cloud is relatively loosely held for anion
Subject: Maths
If \( \boldsymbol{M}=\int_{0}^{\pi / 2} \frac{\cos \boldsymbol{x}}{\boldsymbol{x}+\mathbf{2}} \boldsymbol{d} \boldsymbol{x}, \boldsymbol{N}= \)
\( \int_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x \quad, \) then the value of
\( M-N \) is \( ? \)
\( A \)
в.
c. \( \frac{2}{\pi-4} \)
D. \( \frac{2}{\pi+4} \)
Subject: Physics
There are four possible relative motions
between the source of a sound and the
listener
1) source moves towards stationary
listener
2) source moves away from stationary listener
3) listener moves towards stationary
source
4) listener moves away from stationary
source
In which of the cases, the change in frequency is the same. The magnitude of velocity of source or listener being
the same.
\( A \cdot 1 \) and 2
B. 2 and 3
\( c \cdot 3 \) and 4
D. 1 and 4
Subject: Maths
A line makes equal angles with the coordinate axis. The direction cosines of this line are
A \( \cdot\left(\frac{1}{3}, \frac{1}{3}, \frac{1}{3}\right) \)
B \( \cdot\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{1}{\sqrt{3}}, \frac{1}{3}, \frac{1}{3}\right) \)
D \( \cdot\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right) \)
Subject: Chemistry
\( A \) follows the first-order reaction.
\( (A) \longrightarrow \) product.
The concentration of \( A \) changes from \( 0 . \)
M to \( 0.025 \mathrm{M} \) in 40 minutes. Find the
rate of reaction of \( A \) when concentration
of \( A \) is \( 0.01 \mathrm{M} ? \)
A \( \cdot 3.47 \times 10^{-4} \mathrm{M} \min ^{-1} \)
В. \( 3.47 \times 10^{-5} \mathrm{M} \min ^{-1} \)
c. \( 1.73 \times 10^{-4} \mathrm{M} \min ^{-1} \)
D. \( 1.73 \times 10^{-3} \mathrm{M} \min ^{-1} \)
Subject: Maths
A medicine is known to be \( 75 \% \) effective
to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is curved by this medicine?
A \( \cdot \frac{1}{1024} \)
в. \( \frac{243}{1024} \)
c. \( \frac{1023}{1024} \)
D. \( \frac{781}{1024} \)
Subject: Chemistry
The oxidation number of phosphorus in \( \boldsymbol{B} \boldsymbol{a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{2}\right)_{2} \) is:
\( A \cdot+3 \)
B. +2
\( c \cdot+1 \)
D. -
Subject: Physics
A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral
A. A potential difference appears between the two cylinders when a charge density is given to the inner cylinder
B. A potential difference appears between the two cylinders when a charge density is given to the outer cylinder
c. No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.
D. No potential difference appears between the two cylinders when same charge density is given to both the cylinders.
Subject: Maths
Given that \( i-j, i+2 j \) are two vectors. Find a unit vector coplanar with these vectors and perpendicular to the first vector i - j. Find also the unit vector which is perpendicular to the plane of the two given vectors. Do you thus obtain an orthonormal triad?
This question has multiple correct options
A. \( k \)
B. \( \frac{1}{\sqrt{2}}(i+j) \)
\( c \cdot-k \)
D. \( \frac{1}{\sqrt{2}}(i-j) \)
Subject: Chemistry
Among the following species, identify the isostructural pairs.
\( N F_{3}, N O_{3}^{-}, B F_{3}, H_{3}^{+} O, H N_{3} \)
\( \mathbf{A} \cdot\left[N F_{3}, N O_{3}^{-}\right] \) and \( \left[B F_{3}, H_{3}^{+} O\right] \)
B . \( \left[N F_{3}, H N_{3}\right] \) and \( \left[N O_{3}^{-}, B F_{3}\right] \)
C \( \cdot\left[N F_{3}, H_{3}^{+} O\right] \) and \( \left[N O_{3}^{-}, B F_{3}\right] \)
D. \( \left[N F_{3}, H_{3}^{+} O\right] \) and \( \left[H N_{3}, B F_{3}\right] \)
Subject: Chemistry
\( \boldsymbol{C}_{2} \boldsymbol{H}_{6} \stackrel{\mathbf{9 0 0}^{\circ} \boldsymbol{C}}{\longrightarrow} \boldsymbol{C}_{2} \boldsymbol{H}_{4}+\boldsymbol{H}_{2} \)
Above reaction is called as
A. combustion
B. rearrangement
c. pyrolysis
D. cleavage
Subject: Chemistry
Resonance is possible in?
A. \( C H_{3}-C O-C H_{3} \)
В. \( C H_{3}=C H-C H O \)
\( \mathbf{c} \cdot C H_{2}=C H-C H_{2}-C H O \)
D. \( C H_{2}=C H-C H_{2}-C H=C H_{2} \)
Subject: Chemistry
\( 40 \% \) of \( P C l_{s} \) is not dissociated at
\( 300^{0} C . \) The reaction is carried out in a
flask of 1 litre capacity. The value of \( \boldsymbol{K}_{\boldsymbol{c}} \)
would be:
A. 3.2
B. 1.6
\( c .2 .8 \)
D. 0.9
Subject: Physics
A particle undergoing simple harmonic motion has time dependent displacement given by \( \boldsymbol{x}(\boldsymbol{t})=\boldsymbol{A} \sin \frac{\boldsymbol{\pi} \boldsymbol{t}}{\mathbf{9 0}} \)
The ratio of kinetic to potential energy of this particle at \( t=210 \) s will be :
\( \mathbf{A} \cdot \mathbf{3} \)
B. \( \frac{1}{9} \)
\( c \cdot \frac{1}{3} \)
D.
Subject: Chemistry
Hydrolysis constant \( \left(K_{h}\right) \) of ammonium acetate is :
(Given that \( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}}, \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{2} \times \)
\( \mathbf{1 0}^{-\mathbf{5}}, \boldsymbol{K}_{\boldsymbol{w}}=\mathbf{1 0}^{-\mathbf{1 4}} \mathbf{)} \)
A \( \cdot 28 \times 10^{-5} \)
В. \( 2.8 \times 10^{-5} \)
c. \( 0.28 \times 10^{-10} \)
Subject: Chemistry
E.A.N. of \( \left[\boldsymbol{F e}\left(\boldsymbol{\eta}^{\boldsymbol{5}}-\boldsymbol{C}_{\boldsymbol{5}} \boldsymbol{H}_{\boldsymbol{5}}\right)(\boldsymbol{C O})_{2} \boldsymbol{C l}\right] \)
A . 36
B. 35
c. 37
D. 34
Subject: Chemistry
When an electron transitions from \( n= \)
2 to \( n=5, \) will it be visible to the naked
eye?
A. Yes, the emission occurs at 434 nm which is the blue range of light
B. Yes, the emission occurs at 434 nm which is the red range of light
c. No, the absorption occurs at the infrared red region of the electromagnetic spectrum
D. No, the absorption occurs in the blue range of light but our eyes are unable to detect absorption
Subject: Physics
A body of mass \( 0.1 k g \) is executing simple harmonic motion according to the equation \( \boldsymbol{x}=\mathbf{0 . 5} \cos \left(\mathbf{1 0 0} \boldsymbol{t}+\frac{\mathbf{3} \boldsymbol{\pi}}{\mathbf{4}}\right) \) metre. Find:
(i) the frequency of oscillation, (ii)
initial phase, (iii) maximum velocity,
(iv) maximum acceleration,
(v) total
energy.
Subject: Physics
The work done by a force \( \overline{\boldsymbol{F}}= \)
\( \left(-6 x^{3} i\right) N \) in displacing particle from
\( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{m} \boldsymbol{t} \boldsymbol{o} \boldsymbol{x}=-\boldsymbol{2} \boldsymbol{m} \) is
Subject: Chemistry
Arrange oxides \( \left(M_{2} O_{3}\right) \) of nitrogen family in increasing acidic nature:
A \( \cdot S b_{2} O_{3}<A s_{2} O_{3}<B i_{2} S_{3}<P_{2} O_{3}<N_{2} O_{3} \)
B. \( S b_{2} O_{3}>B i_{2} S_{3}>A s_{2} O_{3}>P_{2} O_{3}>N_{2} O_{3} \)
c. \( B i_{2} S_{3}<S b_{2} O_{3}<A s_{2} O_{3}<P_{2} O_{3}<N_{2} O_{3} \)
D. \( B i_{2} S_{3}>S b_{2} O_{3}>A s_{2} O_{3}>P_{2} O_{3}>N_{2} O_{3} \)
Subject: Physics
A body takes time \( t \) to reach the bottom
of an inclined plane of angle \( \theta \) will the horizontal. if the plane made rough, time takes now is \( 2 t . \) The coefficient of
frcition of the rough surface is
A \( \cdot \frac{3}{4} \tan \theta \)
B. \( \frac{1}{2} \tan \theta \)
c. \( \frac{2}{5} \tan \theta \)
D. \( \frac{1}{4} \tan \theta \)
Subject: Maths
Construct \( \square \) DEFG such that \( l(\mathrm{DE})=4.5 \)
\( \mathrm{cm}, l(\mathrm{EF})=6.5 \mathrm{cm}, l(\mathrm{DG})=5.5 \mathrm{cm}, l(\mathrm{DF}) \)
\( =\mathbf{7} . \mathbf{2} \mathrm{cm}, l(\mathrm{EG})=\mathbf{7 . 8} \mathrm{cm} \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function defined by
\( f(x)=\frac{e^{|x|}-e^{-x}}{e^{x}+e^{-x}}, \) then
A. \( f \) is a bijection
B. \( f \) is an injection only
c. \( f \) is surjection on only
D. \( f \) is neither injection nor a surjection
Subject: Physics
An inductor of \( 30 \mathrm{mH} \) is connected to a
\( 220 \mathrm{V}, 100 \mathrm{Hz} \) ac source. The inductive
reactance is then
A . \( 10.58 \Omega \)
в. \( 12.64 \Omega \)
c. \( 18.85 \Omega \)
D. 22.67\Omega
Subject: Chemistry
The resistance of \( 0.5 \mathrm{M} \) solution of an
electrolyte in a cell was found to be 50
\Omega. If the electrodes in the cell are \( 2.2 \mathrm{cm} \)
a part and have an area of \( 4.4 \mathrm{cm}^{2} \) than
the molar conductivity \( \left(\operatorname{in} S m^{2} m o l^{-1}\right) \)
of the solution is:
A . 0.2
B. 0.02
c. 0.002
D. None of these
Subject: Maths
Measure the length of \( A B \) with a ruler.
Then \( A B=? \)
A \( .7 .5 \mathrm{cm} \)
B. \( 9.6 \mathrm{cm} \)
\( c .10 \mathrm{cm} \)
D. \( 8.4 \mathrm{cm} \)
Subject: Maths
Let \( F_{1} \) be the set all of parallelograms, \( F_{2} \)
be the set of the rectangles, \( F_{3} \) be the
set of rhombuses, \( F_{4} \) be the set of
squares \( F_{5} \) be the set of trapezium in a
plane then \( F_{1}= \)
A. \( F_{2} \cap F_{3} \)
B. \( F_{2} \cup F_{3} \cup F_{4} \)
c. \( F_{3} \cup F_{4} \cup F_{5} \)
D. \( F_{3} \cap F_{1} \)
Subject: Physics
A man stands on a rotating platform, with his arms stretched horizontally holding a \( 5 \mathrm{kg} \) weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then
brings his arms close to his body with the distance of each weight from the axis changing from \( 90 \mathrm{cm} \) to \( 20 \mathrm{cm} . \) The moment of inertia of the man together
with the platform may be taken to be
constant and equal to \( 7.6 \mathrm{kg} \mathrm{m}^{2} \).
(a) What is his new angular speed? (Neglect friction.)
(b) Is kinetic energy conserved in the process? If not, from where does the change come about?
Subject: Biology
Match the plants with their respective
rate of growth. Choose the answer which gives the correct combination of
alphabets of two columns.
Plants \( \quad \) Rate of growth plants
\( A \) cycas 40 centimeters
\( p \quad \) per day
в Gaint
bamboo 10 feet in
q \( \quad \) hundred years
Cucumber
tendril 6 centimeters per hour
A \( \cdot A-r, B-p, C-q \)
B. A-p, B-r, C-q
c. A-q, B-p, C-r
D. A-p, B-q, C- -
Subject: Chemistry
Which of the following complex can not exhibit geometrical isomerism:
\( \mathbf{A} \cdot\left[P t\left(N H_{3}\right)_{2} C l N O_{2}\right] \)
B・ \( \quad\left[P t(g l y)_{2}\right] \)
\( \mathbf{c} \cdot\left[C u(e n)_{2}\right]^{+} \)
D. \( \left[P t\left(H_{2} O\right)\left(N H_{3}\right) B r C l\right. \)
Subject: Chemistry
Identify the error(s) in the orbital notation diagram for oxygen in the in
the image \( a \)
a. \( \prod_{1 \mathrm{s}} \frac{|\uparrow \downarrow|}{2 \mathrm{s}} \frac{|\uparrow| \downarrow|\uparrow|}{2 \mathrm{p}} \)
\( \frac{\sqrt{11}}{1 \mathrm{s}} \frac{\sqrt{11}}{2 \mathrm{s}} \frac{\sqrt{\mathrm{t}} \uparrow 1}{2 \mathrm{p}} \)
e. \( \frac{\sqrt{\uparrow} \mid}{1 s} \)
\[
\frac{|\uparrow| \uparrow|\uparrow|}{2 p}
\]
This question has multiple correct options
A. The electrons are not drawn with the appropriate spins
B. This is not a picture of oxygen. It is nitrogen
c. The electrons are not filled out according to Aufbau's's Principle
D. The electrons are not filled out according to Hund's Rule
Subject: Physics
The density of the atmosphere at sea
level is \( 1.29 \mathrm{kg} / \mathrm{m}^{2} \). assume that it does not change with altitude. then how high would the atmosphere extend?
\( A \cdot 3 \mathrm{km} \)
в. 7 кт
\( c \cdot 8 k m \)
\( D \cdot 9 \mathrm{km} \)
Subject: Chemistry
For the hydrolysis of methyl acetate in aqueous solution, the above tabulated results were obtained:
(i) Show that it follow pseudo first order
reaction as the concentration of water
remains constant.
(ii) Calculate the average rate of reaction between the time interval 30 to
60 seconds.
(Given log \( 2=0.3010, \) log \( 4=0.6021 \) )
\begin{tabular}{|c|c|c|c|}
\hline \( \mathrm{t} / \mathrm{s} \) & 0 & 30 & 60 \\
\hline \( \mathrm{c} \mathrm{CH}_{3} \mathrm{COOH}_{3} \) & \( / \mathrm{moll}^{-1} \) & 0.60 & 0.30 & 0.15 \\
\hline
\end{tabular}
Subject: Physics
Assertion
From the relation \( C=\frac{q}{V} . \) We can say
that, if more charge q is given q is given to a conductor, its capacity should
increase.
Reason
Ratio \( \frac{q}{V} \) will remain constant for a given
conductor.
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: Physics
A resistance of \( 20 \Omega \) is connected to a
source of an alternating potential \( \boldsymbol{V}= \) \( 220 \sin (100 \pi t) . \) The time taken by the
current to change from the peak value
to rms value, is
A . \( 0.2 s \)
B. \( 0.25 s \)
c. \( 2.5 \times 10^{-2} s \)
D. \( 2.5 \times 10^{-3} s \)
Subject: Maths
ff \( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{l} \boldsymbol{n}|\boldsymbol{x}|+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{x} \) has its
extremum values at \( x=-1 \) and \( x=2 \)
then
A \( . a=2, b=-1 \)
в. \( a=2, b=-\frac{1}{2} \)
c. \( a=-2, b=\frac{1}{2} \)
D. none of these
Subject: Maths
Only tenth-, eleventh-, and twelfth-
grade students attend Washington High School. The ratio of tenth graders to the
school's total student population is 86:
\( 255, \) and the ratio of eleventh graders to
the school's total student population is
\( 18: 51 . \) If a student is selected at
random from the entire school, the
grade in which the student is most likely to be is:
A. Tenth
B. Eleventh
c. Twelfth
D. All grades are equally likely
E. Cannot be determined from the given information
Subject: Maths
If for a matrix \( \boldsymbol{A}, \boldsymbol{A}^{2}+\boldsymbol{I}=\boldsymbol{O} \) where \( \boldsymbol{I} \) is
the identity matrix, then \( A \) equals
\( \mathbf{A} \cdot\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
В. \( \left[\begin{array}{cc}i & 0 \\ i & -i\end{array}\right] \)
c. \( \left[\begin{array}{cc}1 & 2 \\ -1 & 1\end{array}\right] \)
D. \( \left[\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right] \)
Subject: Physics
The thigh bones(femurs),each of cross-
sectional area \( 10 \mathrm{cm}^{2} \) support the
upper part of the human body of mass 40 kg.Average pressure sustained by the femurs is:
\( \mathbf{A} \cdot 10^{3} N / m^{2} \)
B . \( 2 \times 10^{5} \mathrm{Nm}^{-2} \)
c. \( 6 \times 10^{-5} \mathrm{Nm}^{-2} \)
D. \( 10^{-3} \mathrm{Nm}^{-2} \)
Subject: Physics
The magnitude of the earth's magnetic
field at the north pole is \( B_{0} . \) A horizontal
conductor of length \( l \) moves with a
velocity \( v . \) The direction of \( v \) is
perpendicular to the conductor. The induced emf is
This question has multiple correct options
A. zero, if \( v \) is vertical
B. \( B_{0} l v, \) if \( v \) is vertical
c. zero, if \( v \) f is horizontal
D. \( B_{0} l v, \) if \( v \) is horizontal
E. answer required
Subject: Physics
A rock is \( 12.5 \times 10^{9} \) years old. The rock
contains \( ^{238} U \) which disintegrates to
form \( ^{206} U . \) Assume that there was no
\( ^{206} P b \) in the rock initially and it is the only stable product formed by the decay
The ratio of number of nuclei of \( ^{238} U \) to that of \( ^{206} P b \) in the rock is \( \frac{1}{2^{1 / x}-1} \)
Find \( x \) (Approximately). Half-life of \( ^{238} \boldsymbol{U} \) is \( 4.5 \times 10^{9} \) years.\( \left(2^{1 / 3}=1.259\right) \)
Subject: Maths
If the function \( f(x)=\frac{K \sin x+2 \cos x}{\sin x+\cos x} \)
is strictly increasing for all values of \( x \)
then
\( \mathbf{A} \cdot K<1 \)
в. \( K>1 \)
c. \( K<2 \)
D. \( K>2 \)
Subject: Physics
The International Space Station is
currently under construction. Eventually, simulated earth gravity may become a reality on the space station. What would the gravitational field through the central axis be like under
these conditions?
A. zero
B. \( 0.25 g \)
\( \mathrm{c} .0 .5 \mathrm{g} \)
D. \( 0.75 g \)
E . \( 1 g \)
Subject: Maths
In a triangle \( A B C, D \) and \( E \) are the
midpoints of \( A B \) and \( A C . \) If the area of
\( \triangle A B C=60 \mathrm{sq.cm}, \) then the area of the
\( \triangle A D E \) is equal to
A . 15 sq.m
в. 20 sq.m
\( c .25 \mathrm{sq.m} \)
D. 30 sq.m
Subject: Maths
If the roots of the equation \( \frac{1}{x+p}+ \) \( \frac{1}{x+q}=\frac{1}{r} \) are equal in magnitude and opposite in \( \operatorname{sign}, \) then This question has multiple correct options
A. \( p+q=r \)
в. \( p+q=2 r \)
c. product of roots \( =-\frac{1}{2}\left(p^{2}+q^{2}\right) \)
D. Sum of roots \( =1 \)
Subject: Chemistry
\( 18.72 \mathrm{g} \) of a substance 'X' occupies 1.81 \( c m^{3} . \) What will be its density measured in correct significant figures?
A \( \cdot 10.3 \mathrm{g} \mathrm{cm}^{-3} \)
В. \( 10.34 \mathrm{g} \mathrm{cm}^{-3} \)
C. \( 10.4 \mathrm{g} \mathrm{cm}^{-3} \)
D. \( 10.3425 \mathrm{g} \mathrm{cm}^{-3} \)
Subject: Chemistry
For a zero-order reaction \( \boldsymbol{A} \rightarrow \) product
the rate constant is \( 10^{-2} \) mol \( L^{-1} s^{-1} \)
Starting with 10 moles of \( A \) in a 1 L
vessel, how many moles of \( A \) would be left unreacted after 10 minutes?
A. 5 moles
B. 6 moles
c. 4 moles
D. 10 moles
Subject: Physics
A trian of length \( 200 m \), travelling at \( 30 m s^{-1} \) overtakes another train of
length \( 300 m \) travelling at \( 20 m s^{-1} . \) The time taken by the first train to pass the second train is
A .30 sec
B. 50 sec
c. 10 sec
D. 40 sec
Subject: Physics
If a dipole of dipole moment \( \vec{p} \) is placed in a uniform electric field \( \vec{E} \), then
torque acting on it is given by :
\( \mathbf{A} \cdot \vec{\tau}=\vec{p} \cdot \vec{E} \)
В . \( \vec{\tau}=\vec{p} \times \vec{E} \)
C \( \cdot \vec{\tau}=\vec{p}+\vec{E} \)
D . \( \vec{\tau}=\vec{p}-\vec{E} \)
Subject: Physics
The magnetic flux through a circular
carrying a current of \( 2.0 A \) is 0.8 weber.
If the current reduces to \( 1.5 A \) in \( 0.1 s \)
the induced emf be
A . \( 2.0 V \)
в. \( 4.0 V \)
\( c .8 .0 V \)
D. None of the above
Subject: Chemistry
Show that the Balmer series occurs between \( 3647 \dot{A} \) and \( 6563 \hat{A} \)
\( \left(\boldsymbol{R}=\mathbf{1} . \mathbf{0} \mathbf{9} \mathbf{6} \mathbf{8} \times \mathbf{1} \mathbf{0}^{\mathbf{7}} \boldsymbol{m}^{-\mathbf{1}}\right) \)
Subject: Maths
In the quadrilateral (3) given below,
\( A B|| D C, E \) and \( F \) are mid point of of
non-parallel sides \( A D \) and \( B C \) respectively. Calculate \( \boldsymbol{E F} \) if \( \boldsymbol{A B}=\boldsymbol{6 c m} \) and \( \boldsymbol{D C}=\boldsymbol{4 c m} \)