AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The initial rate of zero-order reaction of
the gaseous equation \( A(g) \rightarrow 2 B(g) \) is \( 10^{-2} \mathrm{M} \min ^{-1} \) if the initial
concentration of \( A \) is 0.1 M. What would
be a concentration of \( B \) after 60
seconds?
\( \mathbf{A} \cdot 0.09 M \)
в. \( 0.01 M \)
c. \( 0.02 M \)
D. \( 0.03 M \)
Subject: Physics
Two charged capacitors, have their outer plates fixed and inner plates connected by a spring of force constant
\( k^{\prime} . \) The charge on each capacitor is \( q \) Find the extension in the spring at equilibrium.
\( ^{A} \cdot \frac{q^{2}}{2 A \epsilon_{0} k} \)
в. \( \frac{q^{2}}{4 A \epsilon_{6} k} \)
c. \( \frac{q^{2}}{A \epsilon_{6} k} \)
D. Zero
Subject: Physics
In a given arrangement. Find out
velocity of water coming out of 'C'
\( \sqrt{\frac{2 g h_{3}}{1-\frac{a^{2}}{A^{2}}}} \)
\( \mathrm{B} \cdot \sqrt{\frac{3 g h_{3}}{1-\frac{a^{2}}{A^{2}}}} \)
\( \mathrm{c} \cdot \sqrt{\frac{2 g h_{3}}{1-\frac{a^{3}}{A^{2}}}} \)
\( D \)
Subject: Maths
If \( (1+a x)^{n}=1+8 x+24 x^{2}+\dots ; \) then
\( \frac{a-n}{a+n} \) is equal to
\( \mathbf{A} \cdot \mathbf{3} \)
B. \( \frac{-1}{3} \)
c. -3
D.
Subject: Physics
Assertion
Substances which at room temperature retain their ferromagnetic property for a long period of time are called
permanent magnets.
Reason
Permanent magnet can be made by placing a ferromagnetic rod in a solenoid and passing current through it.
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
If \( x y=\tan ^{-1}(x y)+\cot ^{-1}(x y), \) then \( \frac{d y}{d x} \)
is equal to
A \( \cdot \frac{y}{x} \)
B. \( -\frac{y}{x} \)
c. \( \frac{x}{y} \)
D. \( -\frac{x}{y} \)
Subject: Physics
Eight drops of water, each of radius 2 \( \mathrm{mm} \) are falling through air at a terminal
velocity of \( 8 c m s^{-1} . \) If they coalesce to form a single drop, then the terminal velocity of combined drop will be:
A \( .32 \mathrm{cms}^{-1} \)
B. \( 30 \mathrm{cms}^{-1} \)
c. \( 28 \mathrm{cms}^{-1} \)
D. \( 24 \mathrm{cms}^{-1} \)
Subject: Maths
The set of values of parameter \( a \) so that the equation \( \left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}= \)
\( a \pi^{3} \) has a solution.
\( \mathbf{A} \cdot\left[\frac{-1}{32}, \frac{7}{8}\right] \)
в. \( \left[\frac{1}{32},, \frac{9}{8}\right] \)
\( ^{\mathbf{c}} \cdot\left[0, \frac{7}{8}\right] \)
D. \( \left[\frac{1}{32}, \frac{7}{8}\right] \)
Subject: Maths
\( \sin \left[2 \cos ^{-1} \cot \left(2 \tan ^{-1} x\right)\right]=0 \) if
This question has multiple correct options
\( \mathbf{A} \cdot x=-1-\sqrt{2} \)
B. \( x=1+\sqrt{2} \)
\( \mathbf{c} \cdot x=1-\sqrt{2} \)
D. \( x=\sqrt{2}-1 \)
Subject: Physics
Six persons are situated at the corners
of a hexagon of side \( l \). They move at a
constant speed \( v . \) Each person
maintains a direction towards the
person at the next corner. When will the
persons meet?
A.
в. \( \frac{2 l}{3 v} \)
c. \( \frac{3 l}{2 v} \)
D. \( \frac{2 l}{v} \)
Subject: Physics
When two bodies approach each other
with different uniform speeds, the distance between them decreases by
\( 120 m \) per every 1 min. If they move in
the same direction, the distance between them increases by
\( 90 m \) per every 1 min. The speeds of the
bodies are respectively.
A \( .2 m / s, 0.5 m / s \)
B. \( 3 m / s, 2 m / s \)
c. \( 1.75 m / s, 0.25 m / s \)
D. \( 2.5 m / s, 0.5 m / s \)
Subject: Physics
Assertion
The number 1.202 has four significant
figures and the number 0.0024 has two significant figures.
Reason
All the non zero digits are significant.
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
If \( \frac{\sin x}{1+\sec x}+\frac{\sin x}{\sec x-1}=2 \) where
\( 0^{\circ}<x<90^{\circ} \) then cosec \( x \) has the value
equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
c. \( \sqrt{2} \)
D. \( \sqrt{3} \)
Subject: Physics
If \( A B C D \) is a parallelogram, \( A B= \) \( \mathbf{2} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}}-\mathbf{5} \hat{\boldsymbol{k}} \) and \( \boldsymbol{A} \boldsymbol{D}=\hat{\boldsymbol{i}}+\mathbf{2} \hat{\boldsymbol{j}}+\mathbf{3} \hat{\boldsymbol{k}} \)
then the unit vectors in the direction of
\( B D \) is
A \( \cdot \frac{1}{\sqrt{69}}(\hat{i}+2 \hat{j}-8 \hat{k}) \)
B \( \cdot \frac{1}{69}(\hat{i}+2 \hat{j}-8 \hat{k}) \)
c. \( \frac{1}{\sqrt{69}}(-\hat{i}-2 \hat{j}+8 \hat{k}) \)
D \( \cdot \frac{1}{69}(-\hat{i}-2 \hat{j}+8 \hat{k}) \)
Subject: Physics
A bullet travelling at \( 100 \mathrm{ms}^{-1} \) suddenly hits a concrete wall. If its K.E. is
converted completely into heat, the
raise in temperature is
\( \left(s=100 J k g^{-1} K^{-1}\right) \)
A. 20k
в. 40k
\( c . \) 50k
D. 60k
Subject: Physics
Outside a house, \( 1 k m \) from ground zero of a 100 kiloton nuclear bomb explosion, the pressure will rapidly rise to as high as 2.8 atm while the pressure inside the house is 1 atm. If the area
outside the house is \( 50 m^{2} \). The
resulting net force exerted by the air in front of the house is :
A \( \cdot 9.1 \times 10^{6} N \)
B . \( 2.1 \times 10^{7} N \)
c. \( 1.41 \times 10^{7} N \)
D. \( 1.63 \times 10^{7} N \)
Subject: Chemistry
\( (A) \) and \( (B) \) are:
\( A \)
\[
\mathbf{A} \text { and } \mathbf{B} \Rightarrow \mathbf{N} \equiv \mathbf{C} \ \prod_{\mathbf{O}}
\]
в.
\[
\mathbf{A} \text { and } \mathrm{B} \Rightarrow \mathbf{N} \equiv \mathrm{C} \overbrace{\mathrm{M}_{\mathrm{e}}}^{\mathrm{OH}} \mathbf{M}_{\mathrm{e}}
\]
\( c \)
\[
\begin{array}{c}
\mathbf{A} \Rightarrow \mathbf{N} \equiv \mathbf{C} \widehat{\|} \mathbf{N} \\
\mathbf{O} \\
\mathbf{B} \Rightarrow \mathbf{M} \mathbf{e}
\end{array}
\]
D.
\[
\mathbf{A} \Rightarrow \mathbf{N} \equiv \mathbf{C} \widehat{\mathbf{O}}
\]
\[
\mathrm{B} \Rightarrow \mathrm{Me} \overbrace{\mathrm{o}}^{\mathrm{OH}} \overbrace{\mathrm{Me}}^{\mathrm{M}}
\]
Subject: Physics
A lens is made of flint glass (refractive index \( =1.5 \) ). When the lens is immersed
in a liquid of refractive index \( 1.25, \) the
focal length:
A. Increases by a factor of 1.25
B. Increases by a factor of 2.5
c. Increases by a factor of 1.2
D. Remains same
Subject: Maths
If \( y=\tan ^{-1}\left(\frac{a \cos x-b \sin x}{b \cos x+a \sin x}\right), \) then
\( \frac{d y}{\operatorname{isequal}} \) to
\( d x \)
\( A \cdot 2 \)
B. -
\( c \cdot a \)
\( D \)
Subject: Chemistry
When \( 12.044 \times 10^{23} \) molecule of
\( H_{2} S O_{4} \) is dissolve in \( 195 \mathrm{cm}^{3} \) solution.
What is mass percent \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) in the solution. If the density of the solution is \( 1.25 g c m^{-3} \)
Subject: Chemistry
A sample of \( C a C O_{3} \) has \( C a=40 \% \)
\( C=12 \% \) and \( O=48 \% \). If the law of
constant proportion is true then the weight of calcium in \( 5 g \) of a sample of
\( \mathrm{CaCO}_{3} \) from another source will be:
A. \( 0.20 g \)
в. \( 2.0 g \)
c. \( 2.5 g \)
D. \( 4.0 g \)
Subject: Physics
Find \( \frac{\boldsymbol{r}_{\mathbf{1}}}{\boldsymbol{r}_{2}} \)
\( \mathbf{A} \cdot 2^{1 / 6} \)
B. \( \frac{1}{2^{1 / 6}} \)
\( \mathbf{C} \cdot 2^{1 / 12} \)
D. \( 2^{-1 / 12} \)
Subject: Chemistry
Write the equation for the formation of ammonia by the action of water on magnesium nitride.
A \( \cdot 2 M g_{3} N_{2}+6 H_{2} O \rightarrow 2 N H_{3}+6 M g(O H)_{2} \)
В \( \cdot M g_{3} N_{2}+3 H_{2} O \rightarrow N H_{3}+3 M g(O H)_{2} \)
\( \mathrm{c} \cdot_{3 M g_{3} N_{2}+6 H_{2}} O \rightarrow 6 N H_{3}+3 M g(O H)_{2} \)
D. \( M g_{3} N_{2}+6 H_{2} O \rightarrow 2 N H_{3}+3 M g(O H)_{2} \)
Subject: Physics
When temperature of a gas is \( 20^{\circ} \mathrm{C} \) and
pressure is changed from \( \boldsymbol{P}_{1}=\mathbf{1} . \mathbf{0} \times \)
\( 10^{5} P a \) to \( P_{2}=1.65 \times 10^{5} P a \) and the
volume is changed by \( 10 \% \). The bulk modulus is:
A \( .1 .55 \times 10^{5} P a \)
В. \( 1.15 \times 10^{5} P a \)
c. \( 1.4 \times 10^{5} P a \)
D. \( 1.01 \times 10^{5} \mathrm{Pa} \)
Subject: Physics
The width of a slit is \( 0.012 \mathrm{mm} \)
Monochromatic light is incident on it. The angular position of first bright line
is \( 5.2^{\circ} . \) The wavelength of incident light is : \( \left(\operatorname{given} \sin 5.2^{0}=0.0906\right) \)
A \( \cdot 6040 \),
в. 4026 \( ^{\circ} \)
\( c \cdot 5890 \stackrel{\circ}{A} \)
D. 7248 , \( ^{\circ} \)
Subject: Maths
If the point \( P(2,1) \) lies on the segment joining Points \( A(4,2) \) and \( B(8,4) \) then
\( ^{\mathbf{A}} \cdot A P=\frac{1}{3} A B \)
B. AB = PB
\( c \cdot p B=\frac{1}{3} A B \)
D. \( A P=\frac{1}{2} A B \)
Subject: Physics
The cube as shown in Fig. has sides of length \( L=10.0 \mathrm{cm} . \) The electric field is
uniform, has a magnitude \( \boldsymbol{E}=\mathbf{4 . 0 0} \times \)
\( 10^{3} N C^{-1}, \) and is parallel to the \( x y- \)
plane at an angle of \( 37^{\circ} \) measured from
the \( +x-a x i s \) towards the \( +y-a x i s \)
Electric flux passing through surface \( \boldsymbol{S}_{6} \)
is
A \( \cdot 24 N m^{2} C^{-1} \)
B. \( -24 N m^{2} C^{-1} \)
\( \mathbf{c} \cdot 32 N m^{2} C^{-1} \)
D. \( -32 N m^{2} C^{-1} \)
Subject: Physics
A galvanometer of resistance \( 50 \Omega \) is
connected to a battery of \( 8 V \) along with a resistance of \( 3950 \Omega \) in series. A full
scale deflection of 30 div is obtained in
the galvanometer. In division, the resistance in series should be
A. 1950
в. 7900
c. 2000
D. 7950
Subject: Physics
If kinetic energy' \( K \), velocity' \( v \) ' and
time 'T' are chosen as the fundamental
units, the formula for surface tension \( S \)
\( = \)
\( (A \text { is a constant }) \)
\( ^{\mathbf{A}} \cdot \frac{v^{2} K^{2}}{A K} \)
в. \( \frac{v^{2}}{A K T} \)
c. \( \frac{A K T^{2}}{v^{2}} \)
D. \( \frac{A K}{v^{2} T^{2}} \)
Subject: Physics
Which of the following statement is not correct regarding the motion of a particle in a straight line?
A. x-tgraph is a parabola, if motion is uniformly accelerated.
B. v-tus a straight line inclined to the time axis, if motion is uniformly accelerated.
c. x-tus a straight line inclined to the time axis, if motion is uniform and acceleratioin is zero
D. v-tgraph is a parabola, if motion is uniform and acceleratioin is zero
Subject: Maths
Find the value of \( \boldsymbol{x}: \) \( \boldsymbol{x}-\left[\mathbf{2} \boldsymbol{x}-\frac{\mathbf{3} \boldsymbol{x}-\mathbf{4}}{\mathbf{7}}\right]=\frac{\mathbf{4} \boldsymbol{x}-\mathbf{2 7}}{\mathbf{3}}-\mathbf{3} \)
Subject: Chemistry
If the concentration of \( O H^{-} \) ions in the
reaction \( \boldsymbol{F e}(\boldsymbol{O H})_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{F} \boldsymbol{e}^{+3}(\boldsymbol{a q} \cdot)+ \)
\( 3 O H^{-}(a q .) \) is decreased upto \( \frac{1}{4} \) times
then equilibrium concentration of \( \boldsymbol{F} \boldsymbol{e}^{+} \) will increase upto:
A. 16 times
B. 64 times
c. 4 times
D. 8 times
Subject: Chemistry
\( p K_{a} \) of weak acid is \( 3.0 . \) Effective range
of a buffer of \( \boldsymbol{H} \boldsymbol{A} \) and \( \boldsymbol{A}^{-} \) is about \( \boldsymbol{p} \boldsymbol{H}: \)
\( A \cdot 3 \) to 4
B. 3 to 6
c. 2 to 3
D. 2 to 4
Subject: Maths
If the sum of first \( n \) terms of an A.P is
\( \frac{1}{2}\left(3 n^{2}+7 n\right), \) then find its \( n \) th term Hence write its 20 th term.
A \( \cdot a_{n}=5 n+2, a_{20}=12 \)
B \( \cdot a_{n}=7 n+2, a_{20}=62 \)
c \( \cdot a_{n}=3 n+2, a_{20}=62 \)
D. None of these
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined as \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}0, & x \text { is Irrational } \\ \sin |x|, & x \text { is Rational }\end{array} . \) Then, which of \right.
the following is true?
A. \( f \) is discontinuous for all \( x \)
B. \( f \) is continuous for all \( x \)
c. \( f \) is discontinuous at \( x=k \pi \), where \( k \) is an interger
D. \( f \) is continuous at \( x=k \pi, \) where \( k \) is an integer
Subject: Physics
If the charge \( +Q \) is now at the centre of
a cube of side \( 2 l \), what is the total flux
emerging from all the six faces of the
closed surface?
A \( \cdot \frac{Q}{\epsilon_{0}} \)
в. \( \frac{Q}{2 \epsilon_{0}} \)
c. \( \frac{Q}{4 \epsilon_{0}} \)
D. \( \frac{Q}{6 \epsilon_{0}} \)
Subject: Maths
The value of \( \int e^{x}\left[\frac{1+\sin x}{1+\cos x}\right] d x \) is
A \( \cdot \frac{1}{2} e^{x} \sec \frac{x}{2}+C \)
B \( \cdot e^{x} \sec \frac{x}{2}+C \)
c. \( \frac{1}{2} e^{x} \tan \frac{x}{2}+C \)
D. \( e^{x} \tan \frac{x}{2}+C \)
Subject: Physics
A bus accelerates uniformly from rest and acquires a speed of \( 75 k m / h r \) in \( 20 s . \) The acceleration of the bus
(rounded off to the nearest integer) is:
A \( \cdot 10 m / s^{2} \)
B . \( 5 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 2 m / s^{2} \)
D. \( 1 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Chemistry
Enthalpy of atomisation of a diamond is \( 600 k J / \) mol
\( \boldsymbol{C}(\text {diamond}) \rightarrow \boldsymbol{C}(\boldsymbol{g}) \)
Find the bond energy of the \( \boldsymbol{C}-\boldsymbol{C} \)
bond.
Give your answer in \( k J / \) mol.
Subject: Physics
Q Type your question
uniformly distributed over its circumference is hanging by an
insulated thread with the help of a
small smooth ring (not rigidly fixed with bigger ring). A time varying
magnetic field \( B=B_{0} \sin \omega t \) is
switched on at \( t=0 \) and the ring is
released at the same time. The induced
EMF in loop at time \( t=2 \pi / \omega \) is:
A . 0
в. \( \frac{B_{0} \pi \omega R^{2}}{2} \)
\( \mathbf{c} \cdot B_{0} \pi \omega R^{2} \)
D. \( -\frac{B_{0} \pi \omega R^{2}}{2} \)
Subject: Maths
Solve the given inequalities graphically:
\( \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \leq \mathbf{1 0}, \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{1}, \boldsymbol{x}-\boldsymbol{y} \leq \mathbf{0}, \boldsymbol{x} \geq \)
Subject: Physics
A string tied on a roof can bear a maximum tension of 50kgwt. The
minimum acceleration that can be
acquired by a man of \( 98 k g \) to descend
will be (Take \( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \) )
A \( \cdot 9.8 m / s^{2} \)
в. \( 4.9 m / s^{2} \)
c. \( 4.8 m / s^{2} \)
D. \( 5 m / s^{2} \)
Subject: Chemistry
Choose the correct answer among the alternatives given:
In the following reaction, product \( (P) \) is:
\( \boldsymbol{R}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C l} \frac{\boldsymbol{H}_{2}}{\boldsymbol{p} \boldsymbol{d} / \boldsymbol{B a S O}_{4}} \boldsymbol{P} \)
A. \( R C H O \)
в. \( R C H_{3} \)
c. \( R C O O H \)
D. \( R C H_{2} O H \)
Subject: Physics
A circular coil of 300 turns and
diameter \( 14 \mathrm{cm} \) carries a current of 15
A. The magnitude of magnetic moment associated with the loop is?
A . 51.7 J \( T^{-1} \)
B . 69.2 J \( T^{-1} \)
c. 38.6 J \( T^{-1} \)
D. 19.5 J \( T^{-1} \)
Subject: Physics
A projectile is given an initial velocity of \( \hat{\mathbf{i}}+2 \hat{j} . \) The cartesian equation of its
path is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A \( \cdot y=2 x-5 x^{2} \)
В . \( y=x-5 x^{2} \)
C \( .4 y=2 x-5 x^{2} \)
D. \( y=2 x-25 x^{2} \)
Subject: Chemistry
Assertion
Half-filled and fully-filled degenerate orbitals are more stable.
Reason
Extra stability is due to the symmetrical distribution of electrons
and exchange energy.
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
Light of wavelength 500 nm goes through a pinhole of \( 0.2 m m \) and falls on
a wall at a distance of \( 2 m \). What is the
radius of the central bright spot formed
on the wall?
A \( .2 .37 \mathrm{cm} \)
в. 1.37 ст
\( c .3 .37 \mathrm{cm} \)
D. \( 7.37 \mathrm{cm} \)
Subject: Maths
The measure of an angle in degrees,
grades and radians be \( \mathrm{D}, \mathrm{G} \) and \( \mathrm{C} \)
respectively, then relation between them \( \frac{\boldsymbol{D}}{\mathbf{9 0}}=\frac{\boldsymbol{G}}{\mathbf{1 0 0}}=\frac{\boldsymbol{2 C}}{\boldsymbol{\pi}} \) but \( \mathbf{1}^{\circ}= \)
\( \left(\frac{180}{\pi}\right)^{0} \simeq 57^{\circ}, 17^{\prime}, 44.8^{\prime \prime} \) and sum of
interior angles of a \( n \) -sided regular polygon is \( (2 n-4) \frac{\pi}{2} . \) On the basis of above information, answer the following
questions :The angles between the hour hand and minute hand of a clock at half
past three is -
\( A \cdot \frac{\pi}{3} \)
B. \( \frac{\pi}{4} \)
c. \( \frac{5 \pi}{12} \)
D. \( \frac{7 \pi}{12} \)
Subject: Physics
One end of a string of length \( L \) and cross-sectional area \( A \) is fixed to a
support and the other end is fixed to a bob of mass \( m \). The bob is revolved in a
horizontal circle of radius \( r \) with an
angular velocity \( \omega \) such that the string makes an angle \( \theta \) with the vertical. The stress in the string is :
A. \( \frac{m g}{A} \)
в. \( \frac{m g}{A}\left(1-\frac{r}{L}\right) \)
c. \( \frac{m g}{A}\left(1+\frac{r}{L}\right) \)
D. none of these
Subject: Chemistry
The hybrdisation of the complex \( \left[C u\left(N H_{3}\right)_{4}\right]^{+2} \) is :
\( A \cdot s p^{3} \)
B \( \cdot s p^{3} d \)
c. \( d s p^{2} \)
D. \( s p^{3} d^{2} \)
Subject: Maths
If vector \( \vec{a}=4 \hat{i}+5 \hat{j}-3 \hat{k} \) and \( \vec{b}=5 \hat{i}+ \)
\( 3 \hat{j}+8 \hat{k} \) then value of \( \frac{\text { projection of vector b on a }}{\text { projection of vector a on b }} \) is :
A \( \cdot \frac{7}{5} \)
B. \( \frac{2}{7} \)
\( c \cdot \frac{5}{8} \)
D. None of these.
Subject: Chemistry
The correct chemical formula for
ammonium phosphate is:
A. \( N_{2} H_{6} P O_{4} \)
в. \( \left(N H_{3}\right)_{3} P O_{4} \)
\( \mathrm{c} \cdot\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4} \)
D. \( \left(N H_{4}\right)_{2} P O_{4} \)
Subject: Maths
A point on the parabola \( y^{2}=18 x \) at
which the ordinate increases at twice
the rate of the abscissa is
в. (2,-4)
\( ^{\mathrm{c}} \cdot\left(-\frac{9}{8}, \frac{9}{2}\right) \)
D \( \cdot\left(\frac{9}{8}, \frac{9}{2}\right) \)
Subject: Physics
The velocity of a ball of mass m density
d1d1 becomes constant after some
time.The viscous force acting on the
ball will be:
A. non of these
в. \( _{m g}\left(1-\frac{d_{2}}{d_{1}}\right) \)
c. \( m g\left(\frac{d_{1}+d_{2}}{d_{1}}\right) \)
D. \( _{m g}\left(\frac{d_{1}+d_{2}}{d_{2}}\right) \)
Subject: Physics
The equation of an incident wave travelling along +X direction is given by \( y=A \sin (2 t-5 x) . \) This wave gets reflected at a rigid boundary. The change in phase of the wave is
A. \( \pi / 2 \) radians
B. \( \pi \) radians
c. \( \pi / 3 \) radians
D. 2\pi/3 radians
Subject: Physics
The voltage of clouds is \( 4 \times 10^{6} \) volt
with respect to round. In a lightening strike lasting 100 m sec , a charge of 4 coulombs is delivered to the ground. The power of lightening strike is:
A. \( 160 M W \)
в. 80 М \( W \)
\( \mathrm{c} .20 \mathrm{MW} \)
D. \( 500 K W \)
Subject: Physics
A small body of mass 10 gram is making harmonic oscillations along a straight line with a time period of \( \frac{\pi}{4} \) and the maximum displacement is 10 cm. The energy of oscillation is
в. \( 0.16 \times 10^{-2} \mathrm{J} \)
c. \( 0.6 \times 10^{-2} J \)
D. \( 0.56 \times 10^{-2} J \)
Subject: Maths
Special relativity is a branch of physics that deals with the relationship between space and time. The Lorentz
term, is the factor by which time, length and relativistic mass change for an object while that object is moving, is given by the following formula: \( \gamma= \)
\( \sqrt{1-\frac{v^{2}}{c^{2}}} \)
where, v is the relative velocity of the object \( c \) is the speed of light in a vacuum Which of the following equations
correctly represents the relative velocity
A \( \cdot v=c \sqrt{\frac{1}{\gamma^{2}}-1} \)
B . \( v=c \sqrt{1-\gamma^{2}} \)
c. \( v=c\left(1-\frac{1}{\gamma^{2}}\right) \)
D. \( v=c \sqrt{1-\frac{1}{\gamma^{2}}} \)
Subject: Chemistry
Assertion (A): Balloons made by nylon films are better for containing helium than the conventional rubber balloons. Reason (R): R.M.S. velocity of helium is very high. So helium atoms can effuse out through rubber balloons.
A. Both \( A \) and \( R \) are correct and \( R \) is the correct explanation of \( A \)
B. Both \( A \) and \( R \) are correct and \( R \) is not the correct explanation of \( A \)
c. \( A \) is true but \( R \) is false
D. \( A \) is false but \( R \) is true.
Subject: Maths
n given figure \( D \) and \( E \) are respectively
the points on the sides \( A B \) and \( A C \) of a
\( \triangle A B C \) such that \( A B=5.6 \mathrm{cm}, A D= \)
1.4 \( c m, A C=7.2 \mathrm{cm} \) and \( A E=1.8 \mathrm{cm} \)
show that \( D E \| B C \)
Subject: Maths
If \( \angle B_{1} O A_{1}=60^{\circ} \& \) radius of biggest
circle is r. According to figure trapezium
\( \boldsymbol{A}_{1} \boldsymbol{B}_{1} \boldsymbol{D}_{1} \boldsymbol{C}_{1}, \boldsymbol{C}_{1} \boldsymbol{D}_{1} \boldsymbol{D}_{2} \boldsymbol{C}_{2}, \boldsymbol{C}_{2} \boldsymbol{D}_{2} \boldsymbol{D}_{3} \boldsymbol{C}_{3} \ldots \)
and so on are obtained. Sum of areas of
all the trapezium is -
A \( \cdot \frac{r^{2}}{2 \sqrt{3}} \)
B. \( \frac{9 r^{2}}{2 \sqrt{3}} \)
\( \mathrm{c} \cdot \frac{9 r^{2}}{\sqrt{3} r^{2}} \)
D. \( \frac{r^{2}}{9 \sqrt{3}} \)
Subject: Physics
There wires are situated at the same
distance. A current of \( 1 A, 2 A, 3 A \) flows
through these wires in the same
direction. What is ratio \( \boldsymbol{F}_{1} / \boldsymbol{F}_{2} \) where \( \boldsymbol{F}_{1} \)
is force on 1 and \( F_{2} \) on \( 2 ? \)
A . \( 7 / 8 \)
B.
c. \( 9 / 8 \)
D. none of the above
Subject: Chemistry
An open flask contains air at \( 27^{\circ} \mathrm{C} \). At
what temperature should it be heated so that \( 1 / 3 r d \) of air present in it goes
out?
A \( \cdot 177^{\circ} \mathrm{C} \)
B. \( 100^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 300^{\circ} \mathrm{C} \)
D. \( 150^{\circ} \mathrm{C} \)
Subject: Chemistry
For a reaction \( \boldsymbol{A}+\boldsymbol{B} \rightarrow \) Products, it is
observed that doubling the concentration of \( B \) caused the reaction
rate to increase four times, but
doubling the concentration of \( A \) has no effect on the rate of reaction. The rate
equation is therefore:
A \( \cdot \) rate \( =K[A]^{2} \)
B . rate = \( K[B]^{2} \)
c. rate \( =K[A][B] \)
D. rate = \( K[A] \)
Subject: Maths
If \( \boldsymbol{x}=\frac{1}{2}, \boldsymbol{y}=1, \boldsymbol{z}=2 \operatorname{then} \boldsymbol{x}^{100} \boldsymbol{y}^{99} \boldsymbol{z}^{99}+ \)
\( \boldsymbol{x}^{99} \boldsymbol{y}^{100} \boldsymbol{z}^{99}+\boldsymbol{x}^{99} \boldsymbol{y}^{99} \boldsymbol{z}^{100}= \)
\( A \cdot \frac{5}{2} \)
B. \( \frac{7}{2} \)
\( c \cdot \frac{3}{2} \)
D.
Subject: Maths
Let \( A \) be a square matrix all of whose
entries are integers. Then, which one of
the following is true?
\( \mathbf{A} \cdot \) If \( \operatorname{det} A=\pm 1, \) then \( A^{-1} \) exists and all its entries are
integers
B. If \( \operatorname{det} A=\pm 1, \) then \( A^{-1} \) need not exist
C. If \( \operatorname{det} A=\pm 1, \) then \( A^{-1} \) exists but all its entries are
not necessarily integers
D. If det \( A \neq\pm 1 \), then \( A^{-1} \) exists and all its entries are non-integers
Subject: Chemistry
Which of the following methods are used for the conversion of carboxylic acids into acid chlorides
\( (R C O O H \longrightarrow R C O C l) ? \)
This question has multiple correct options
A \( \cdot R C O O H+S O C l_{2} \longrightarrow \)
в. \( R C O O H+P C l_{5} \rightarrow \)
c. \( R C O O H+C l_{2} \rightarrow \)
D. \( R C O O H+P+C l_{2} \rightarrow \)