AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A long spring is stretched by \( 2 \mathrm{cm} \) and
its potential energy is \( U . \) If the spring is stretched by \( 10 \mathrm{cm} ; \) its potential energy will be (in terms of \( U \) )
A. \( U / 5 \)
в. \( U / 25 \)
\( c .5 U \)
D. 25U
Subject: Maths
Decompose the vector \( \vec{b}=6 \hat{i}-3 \hat{j}-6 \hat{k} \) into two vectors, \( \vec{c} \) and \( \vec{d} \), one of which is parallel and the other perpendicular to the vector \( \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)
Subject: Maths
Evaluate in standard form: \( \frac{(2-3 i)}{(2-2 i)} \)
where \( i^{2}=-1 \)
A \( \cdot \frac{5}{4}-\frac{i}{4} \)
в. \( \frac{5}{4}+\frac{i}{4} \)
c. \( -\frac{5}{4}-\frac{i}{4} \)
D. \( -\frac{5}{4}+\frac{i}{4} \)
Subject: Chemistry
The correct order for decreasing atomic radius of the five atoms \( \boldsymbol{H}, \boldsymbol{B r}, \boldsymbol{I}, \boldsymbol{H} \boldsymbol{e} \)
and \( S \) is :
A \( . I>B r>S>H e>H \)
В. \( I>S>B r>H>H e \)
c. \( I>S>B r>H e>H \)
D. \( B r>I>S>H e>H \)
Subject: Physics
Assertion
If refractive index of one medium is
equal to refractive index of second
medium, then beam does not bend at
all.
Reason
The bending of light does not depend on refractive indices of media.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Chemistry
Heat of combustion of \( \boldsymbol{C H}_{4}, \boldsymbol{C}_{2} \boldsymbol{H}_{6} \) and
\( C_{3} H_{8} \) are respectively -210,-368.4 and
\( -526.8 \mathrm{Kcal} \) mol \( _{1} \) Hence, heat of
combustion of \( C_{8} H_{16} \) is approximately:
A. -1267.2 Kcal / mol
в. -684 Кса\( / \) (тод
c. \( -840 K c a l / m o l \)
D. \( -1000 K \) cal \( / \) mol
Subject: Physics
If in an unpolarised light \( \mathrm{E}=2 \vec{i}+3 \vec{j} \) and \( \vec{H}=3 \vec{i}-2 \vec{j}, \) then the direction of
propagation is given by
A \( -13 \vec{k} \)
the \( -13 \vec{k} \).
B . \( -13 \vec{j} \)
\( \mathbf{c} \cdot-6 \vec{i}+6 \vec{k} \)
D. \( 5 \vec{i}-4 \vec{k} \)
Subject: Physics
The velocity of a particle is \( \boldsymbol{v}=\boldsymbol{v}_{0}+ \)
\( g t+f t^{2} . \) If its position is \( x=0 \) at \( t=0 \)
then its displacement after unit time \( (\mathrm{t} \)
\( =1) \) is:
A \( \cdot v_{0}+2 g+3 f \)
В. \( v_{0}+\frac{g}{2}+\frac{f}{3} \)
\( \mathbf{c} \cdot v_{0}+g+f \)
D. \( v_{0}+\frac{g}{2}+f \)
Subject: Physics
Assertion
If we apply force to a lump of putty or mud, they have no gross tendency to regain their previous shape.
Reason
This type of substances are called
plastic substances.
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
Which of the following is the formula of prussian blue?
\( A \)
\( F e_{3}\left[F e(C N)_{6}\right]_{2} \)
в. \( F e_{2}\left[F e(C N)_{6}\right]_{3} \)
c. \( F e_{4}\left[F e(C N)_{6}\right]_{3} \)
D. \( F e_{3}\left[F e(C N)_{6}\right]_{4} \)
Subject: Physics
Find the typical de Broglie wavelength associated with a \( H e \) atom in helium
gas at room temperature \( \left(27^{\circ} C\right) \) and
1 atm pressure, and compare it with the mean separation between two atoms under these conditions.
A \( \cdot r_{0}=6.4 \times 10^{-9} \mathrm{m} \)
B . \( r_{0}=3.4 \times 10^{-9} \mathrm{m} \)
C \( \cdot r_{0}=4.4 \times 10^{-9} \mathrm{m} \)
D. \( r_{0}=5.4 \times 10^{-9} \mathrm{m} \)
Subject: Chemistry
The mole fraction of \( N_{2} O \) In a mixture of \( N_{2} O \) and \( N O \) is \( \frac{1}{3} . \) The mole fraction
of \( N O \) in a mixture of \( N O \) and \( N O_{2} \) is
3. The two mixtures are mixed in 3: 4
\( \overline{\mathbf{4}} \)
molar ratio. the mole fraction of \( N O_{2} \) in
the resulting mixture is:
Subject: Chemistry
Which of the following is least reactive in a nucleophilic subtitution reaction?
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} C-C l \)
в. \( C H_{2}=C H C l \)
c. \( C H_{3} C H_{2} C l \)
D. \( C H_{2}=C H C H_{2} C l \)
Subject: Maths
If \( \int f(x) d x=2\{f(x)\}^{3}+c, \) and
\( f(x) \neq 0 \) then \( f(x) \) is
A \( \cdot \frac{x}{2} \)
B . \( x^{3} \)
c. \( \frac{1}{\sqrt{x}} \)
D. \( \sqrt{\frac{x}{3}} \)
Subject: Physics
Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of \( 20 \mathrm{cm} \) are placed
with their convex surfaces in contact at
the centre. The intervening space is filled with oil of refractive index 1.7. The
focal length of the combination is
A. -50 cm
B. 50 \( \mathrm{cm} \)
\( c .-20 \mathrm{cm} \)
D. -25 cm
Subject: Physics
A spherical planet, far out in space, has
a mass \( M_{0} \) and diameter \( D_{0} . \) A particle of mass \( m \) falling freely near the surface of this planet will experience acceleration due to gravity which is
equal to:
A \( \cdot \frac{G M_{0}}{\left(D_{0}\right)^{2}} \)
в. \( \frac{4 m G M_{0}}{\left(D_{0}\right)^{2}} \)
c. \( \frac{4 G M_{0}}{\left(D_{0}\right)^{2}} \)
D. \( \frac{G m}{\left(D_{0}\right)^{2}} \)
Subject: Chemistry
A cell \( \boldsymbol{C u}\left|\boldsymbol{C u}^{2+} \| \boldsymbol{A} \boldsymbol{g}^{\oplus}\right| \boldsymbol{A} \boldsymbol{g} \) initially
contains \( 2 \mathrm{M} A g^{\oplus} \) and \( 2 \mathrm{M} C u^{2+} \) ions in
1 L solution each. The change in cell
potential after it has supplied 1 1 current for 96500 s is :
\( \mathbf{A} \cdot-0.003 V \)
в. \( -0.02 V \)
c. \( -0.04 V \)
D. None of these
Subject: Maths
The distance of the point \( \left(x_{1}, y_{1}\right) \) from
the origin
A \( \cdot x_{1}^{2}+y_{1}^{2} \)
B. \( \sqrt{x_{1}^{2}+y_{1}^{2}} \)
c. \( \frac{1}{\sqrt{x_{1}^{2}+y_{1}^{2}}} \)
D. \( \frac{1}{x_{1}^{2}+y_{2}^{2}} \)
Subject: Physics
A body of mass \( M_{1} \) collides elastically
with another body of mass \( M_{2} \) at rest. There is maximum transfer of energy
when
A. \( M_{1}>M_{2} \)
В. \( M_{1}<M_{2} \)
\( \mathbf{c} \cdot M_{1}=M_{2} \)
D. same for all values of \( M_{1} \) and \( M_{2} \)
Subject: Maths
n the given figure, it is given that
\( \boldsymbol{R T}=\boldsymbol{T} \boldsymbol{S}, \angle \mathbf{1}=\mathbf{2} \angle \mathbf{2} \) and \( \angle \mathbf{4}=\mathbf{2} \angle \mathbf{3} \)
Prove that \( \Delta R B T \cong \Delta S A T \)
Subject: Chemistry
Spin multiplicity is zero for:
\( A \)
\begin{tabular}{|l|l|l|}
\hline \( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\hline
\end{tabular}
в. \begin{tabular}{|l|l|l|}
\hline \( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{j} \) \\
\hline
\end{tabular}
\( c \)
\( \left|\begin{array}{ll}\hline \mid & \downarrow & \downarrow\end{array}\right| \)
D. \( \sqrt{ }|V| \)
Subject: Physics
An LC circuit has \( L=5 \mathrm{mH} \) and \( C=20 \mu \mathrm{F} \)
\( \boldsymbol{v}=\mathbf{5} \times \mathbf{1 0}^{-\mathbf{3}} \) coswt is supplied.
is twice the resonant frequency. Find
the maximum charge stored in the
capacitor:
A. 66.6 nc
B. 11.3 nc
c. 23.2 nc
D. 33.3 nç
Subject: Maths
Find the median for the following data:
\( \begin{array}{ccccc}\mathbf{x} & \mathbf{6} & \mathbf{1 2} & \mathbf{1 8} & \mathbf{2 4} \\ \mathbf{F} & 2 & 4 & 6 & 8\end{array} \)
A . 17
B . 18
c. 19
D. 20
Subject: Physics
Centigrade (Celsius) scale can be
converted into Kelvin scale by formula
\( \mathbf{A} \cdot \Omega^{0} C= \) Temperature in \( \mathrm{Kelvin}+273.15 \)
B \( \cdot \Omega^{0} C= \) Temperature in Kelvin -273.15
\( \mathbf{C} \cdot \Omega^{0} C= \) Temperature in Fahrenheit +273.15
D. \( \Omega^{0} C= \) Temperature in Fahrenheit -273.15
Subject: Maths
A garden is 24 m long and 14 m wide.
There is a path \( 1 ~ m \) wide outside the
garden along its sides. If the path is to be constructed with square marble tiles \( 20 \mathrm{cm} \times 20 \mathrm{cm}, \) find the number of tiles
required to cover the path?
A. 1800
в. 200
c. 2000
D. 2150
Subject: Physics
Dimensional formula for electric field is
A \( \cdot\left[M L^{2} T^{-3} A^{-1}\right] \)
B \( \cdot\left[M L^{2} T^{-3} A^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L T^{-3} A^{-1}\right] \)
D \cdot \( \left[M^{0} L^{0} T^{0} A^{0}\right] \)
Subject: Physics
A Nall Ul mass U.c ng resus un diverica
post of height \( 5 \mathrm{m} \). A bullet of mass 0.01
kg, traveling with a velocity \( V m / s \) in a
horizontal direction, hits the centre of
the ball. After the collision, the ball and
bullet travel independently. The ball hits
the ground at a distance of \( 20 m \) and
the bullet at a distance of \( 100 \mathrm{m} \) from
the foot of the post. The initial velocity
\( V \) of the bullet is
\( A \cdot 250 m / s \)
B . \( 250 \sqrt{2} \mathrm{m} / \mathrm{s} \)
c. \( 400 \mathrm{m} / \mathrm{s} \)
D. \( 500 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Write the IUPAC name of the following
compound. \( C H \)
\( \mathbf{5} \)
\( \boldsymbol{C} \boldsymbol{H}_{3}-\underset{\boldsymbol{H}}{\boldsymbol{C}}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \equiv \boldsymbol{C} \boldsymbol{H} \)
\( \boldsymbol{C H}_{3} \)
Subject: Physics
In the following \( I \) refers to current and
other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity:
A \( \cdot M L^{-3} T^{-3} I^{2} \)
B. \( M^{-1} L^{-3} T^{3} I^{2} \)
c. \( M^{-1} L^{3} T^{3} I \)
D. \( M^{-1} L^{-3} T^{3} I \)
Subject: Physics
Three ions \( H^{+}, H e^{+} \) and \( O^{+2} \) having
same kinetic energy pass through a region in which there is a unit magnetic field perpendicular to their velocity,
then
A \( \cdot H^{+} \) will be least deflected
B. \( H e^{+} \) and \( O^{+2} \) will be deflected equally
c. \( O^{+2} \) will be deflected most
D. All will be deflected equally
Subject: Physics
A wire of length L and 3 identical cells of negligible internal resistances are
connected in series. Due to the current,
the temperature of the wire is raised by
\( \Delta T \) in a time t. A number \( N \) of similar
cells is now connected in series with a
wire of the same material and cross-
section but the length 2 L. The temperature of the wire is raised by
the same amount \( \Delta T \) in the same t. The
value of \( \mathrm{N} \) is
\( A \cdot 3 \)
B. 2
\( c \cdot 6 \)
D. 4
Subject: Physics
A ray of light passing through an equilateral triangular prism gets
deviated at least by \( 30^{\circ} . \) Then, the
refractive index of the material of the
prism must be
\( A \cdot \leq \sqrt{2} \)
B. \( \geq \sqrt{2} \)
\( c \cdot \leq \sqrt{3} \)
\( D \cdot \geq \sqrt{3} \)
Subject: Physics
A block of mass \( m \) has initial velocity \( u \) having direction \( +x \) axis. The block stops after covering distance \( S \) causing
an extension in the spring of spring
constant \( K \) holding it. If \( \mu \) is the kinetic
friction between the block and the
surface on which it was moving, the distances \( \boldsymbol{S} \) is :
A \( \cdot \frac{1}{K} \mu^{2} m^{2} g^{2} \)
B. \( \frac{1}{K}\left(m K u^{2}-\mu^{2} m^{2} g^{2}\right)^{\frac{1}{2}} \)
c. \( \frac{1}{K}(\sqrt{\mu^{2} m^{2} g^{2}+m K u^{2}}-\mu m g) \)
D \( \cdot \frac{1}{K}\left(\mu^{2} m^{2} g^{2}-m K u^{2}+\mu m g\right)^{\frac{1}{2}} \)
Subject: Maths
Find \( k, \) so that \( (k-12) x^{2}+2(k- \)
12) \( x+2=0 \) has equal roots, where
\( k \neq 12 \)
\( \mathbf{A} \cdot k=4 \)
B. \( k=12 \)
c. \( k=14 \)
D. none of these
Subject: Physics
A street car moves rectilinearly from station \( \boldsymbol{A} \) (here car stops) to next
station \( B \) (here also car stops) with an acceleration varying according to the \( \operatorname{law} f=a-b x, \) where \( a \) and \( b \) are
positive constants and \( x \) is the distance
from station \( A \). If the maximum
distance between the two stations is \( \boldsymbol{x}=\frac{\boldsymbol{N} \boldsymbol{a}}{\boldsymbol{b}} \) then find \( \boldsymbol{N} \)
Subject: Biology
Mrs. Verma has an autosomal gene pair Bb' and she contain x-linked gene 'd'
What is the percentage of gamete, which contain 'bd' genes?
A. \( 1 / 2 \) or \( 50 \% \)
B. 1/4 or 25\%
c. 3/4 or 75\%
D. 1 or \( 100 \% \)
Subject: Physics
A ball falls from a height of \( 10 \mathrm{m} \) on to a horizontal plane. if the coefficient 0
restitution is 0.6. the height to which it
rebounds after 2 collision is
approximate.
\( \mathbf{A} \cdot 2.24 m \)
B. \( 0.47 m \)
\( \mathrm{c} .0 .3 \mathrm{m} \)
D. \( 1.296 \mathrm{m} \)
Subject: Chemistry
f the equilibrium constant for reaction
(i) is \( 2, \) what is the equilibrium constant for reaction (ii)?
\( C O_{2} \rightleftharpoons C O+\frac{1}{2} O_{2 \cdots \cdots}(i) \)
\( 2 C O+O_{2} \rightleftharpoons 2 C O_{2} \dots( \) ii)
A.
в.
c. 1
D.
Subject: Chemistry
Q Type your question.
mechanics. However, it turns out that
the treatment of spin angular momentum is closely analogous to the treatment of orbital
angular momentum.
Spin angular momentum \( = \) \( \sqrt{s(s+1)} h \)
Orbital angular momentum \( = \) \( \sqrt{l(l+1)} h \)
Total spin of an atom or ion is a multiple of \( \frac{1}{2} . \) Spin multiplicity isa factor to confirm the electronic configuration of
an atom or ion.Spin multiplicity \( = \)
\( \left(2 \sum s+1\right) \)
The orbital angular momentum for a \( 2 p \)
electron is:
A \( \cdot \sqrt{3} h \)
в. \( \sqrt{6} h \)
c. zero
D. \( \sqrt{2} \frac{h}{2 \pi} \)
Subject: Maths
Assertion \( (A) \) If \( 0<x<\frac{\pi}{2} \) then
\( \sin ^{-1}(\cos x)+\cos ^{-1}(\sin x)=\pi-2 x \)
Reason
\( (\mathrm{R}) \cos ^{-1} x=\frac{\pi}{2}-\sin ^{-1} x \forall x \in \)
\( [\mathbf{0}, \mathbf{1}] \)
A. Both \( A \) and \( R \) are true and \( R \) is the correct explanation of \( A \)
B. Both A and R are true but R is not correct explanation of \( A \)
C. \( A \) is true but Ris false
D. A is false but \( R \) is true
Subject: Maths
The value of the determinant \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \mathbf{0} \\ \boldsymbol{0} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{0} & \boldsymbol{a}\end{array}\right| \)
is equal to
A \( \cdot a^{3}-b^{3} \)
В . \( a^{3}+b^{3} \)
\( c \cdot 0 \)
D. none of these
Subject: Chemistry
A few drops of concentrated ammonia
solution added to a calcium
bicarbonate solution causes a white
precipitate. The precipitate formed is:
A \( \cdot C a C O_{3} \)
в. \( M g C O_{3} \)
\( \mathrm{c} \cdot K_{2} \mathrm{CO}_{3} \)
D. \( M g S O_{4} \)
Subject: Physics
Light of wave length \( \lambda \) air enters into
two medium of refractive indices \( \mu \) and
\( \mu / 2 . \) Two points \( P_{1} \) and \( P_{2} \) lying along the path of this light as shown in the figure. The phase difference between these two point is \( k \frac{\left(\pi \mu X_{0}\right)}{\lambda} . \) Then find
the value of \( \mathrm{k} \)
\( A \)
B.
\( c .5 \)
D.
E. None of thes
Subject: Maths
The arithmetic mean of \( 1,8,27,64, \dots \) up to n terms is given by
A \( \cdot \frac{n(n+1)}{2} \)
B. \( \frac{n(n+1)^{2}}{2} \)
c. \( \frac{n(n+1)^{2}}{4} \)
D. \( \frac{n^{2}(n+1)^{2}}{4} \)
Subject: Maths
\( f(x)=\left\{\begin{array}{cl}\frac{\left(1-\sin ^{3} x\right)}{3 \cos ^{2} x}, & x<\frac{\pi}{2} \\ a, & x=\frac{\pi}{2} \\ \frac{b(1-\sin x)}{(\pi-2 x)^{2}}, & x>\frac{\pi}{2}\end{array}\right. \)
continuous at \( x=\frac{\pi}{2}, \) then the value of
\( \left(\frac{b}{a}\right)^{5 / 3} \) is
\( \mathbf{A} \)
B.
\( c \cdot 32 \)
D. 54
Subject: Chemistry
The correct decreasing order of following alkyl halides according to the rate of \( \beta \) - elimination reaction with
alcoholic KOH will be:
\( (\mathrm{i}) C H_{3}-\underset{C H_{3}}{C}^{H}-C H_{2} B r \)
(ii) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \)
(iii) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \)
\( A \cdot(\text { i) }>(\text { ii) }>(\text { iii }) \)
B. (iii) > (ii) > (i)
c. (ii)> (iii) > (i)
D. (i) > (iii) > (ii)
Subject: Maths
If the variance of a random variable \( X \) is
\( \sigma^{2}, \) then the variance of the random
variable X-5 is??
\( \mathbf{A} \cdot 5 \sigma^{2} \)
B . \( 25 \sigma^{2} \)
\( \mathbf{c} \cdot \sigma^{2} \)
D. \( 2 \sigma^{2} \)
Subject: Physics
What is E in the outer region of the first
plate?
A \( \cdot \frac{1}{2} \times 10^{-10} N / C \)
B . \( 2 \times 10^{-10} N / C \)
c. \( 0 N / C \)
D . \( 5 \times 10^{-10} \mathrm{N} / \mathrm{C} \)
Subject: Maths
The points \( P, Q, R, S, T, U, A \) and \( B \) on
the number line are such that, \( \boldsymbol{T} \boldsymbol{R}= \)
\( \boldsymbol{R S}=\boldsymbol{S U} \) and \( \boldsymbol{A P}=\boldsymbol{P Q}=\boldsymbol{Q B} . \) Name
the rational numbers represented by
\( P, Q, R \) and \( S \)
\( ^{\mathbf{A}} \cdot P=\frac{8}{3}, Q=\frac{7}{3}, R=\frac{-4}{3}, S=\frac{-5}{3} \)
B. \( P=\frac{7}{3}, Q=\frac{7}{3}, R=\frac{-5}{3}, S=\frac{-4}{3} \)
\( ^{\mathrm{C}} P=\frac{7}{3}, Q=\frac{8}{3}, R=\frac{-4}{3}, S=\frac{-5}{3} \)
D. \( \quad P=\frac{8}{3}, Q=\frac{7}{3}, R=\frac{-5}{3}, S=\frac{-4}{3} \)
Subject: Physics
Determine the loss in kinetic energy of the system as whole as a result of the
collision.
\( ^{\mathbf{A}} \cdot \frac{1}{6} m v^{2} \)
в. \( \frac{1}{7}^{m v^{2}} \)
\( \mathrm{c} \cdot m v^{2} \)
D. \( \frac{m v^{2}}{5} \)
Subject: Chemistry
What is the empirical formula for a compound containing \( 63.8 \% N \) and
\( 36.2 \% \) O?
A. \( N_{2} O_{5} \)
в. \( N_{2} O_{3} \)
c. \( N O_{2} \)
D. \( N O \)
E \( . N_{2} \)
Subject: Chemistry
\( \mathbf{n}\left[\boldsymbol{F} e\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right] \boldsymbol{C l}_{3}, \operatorname{six} \boldsymbol{H}_{2} \boldsymbol{O} \) are joined
by primary valency (PV) and three \( C l \) are joined by secondary valency (SV). If true enter 1 , else enter 0 .
Subject: Maths
The domain of \( \frac{1}{\log _{10}(1-x)}+ \)
\( \sqrt{(x+2)} \) is
A \( \cdot(-2 \leq x<-1) \cup(0<x<1) \)
B . \( (-2 \leq x<2) \)
c. \( (-2 \leq x<1) \)
D \cdot \( (-2 \leq x<0) \cup(0<x<1) \)
Subject: Chemistry
The equilibrium constant for the
reaction \( \boldsymbol{H}_{2}\left(\boldsymbol{g}()+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \) is \right.
50 at \( 500 \mathrm{K} . \) In presence of suitable catalyst, equilibrium is attained four times faster. The equilibrium constant of the reaction at \( 500 \mathrm{K} \) in the presence
of catalyst should be-
A . 200
в. \( 4 \times 10^{4} \)
\( c \cdot 50 \)
D. 83.6
Subject: Chemistry
Assertion
Alcohols are dehydrated to hydrocarbons in the presence of acidic
zeolites
Reason
Zeolites are porous catalysts.
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 particle moves along the curve \( y= \)
\( a x^{2}, \) with constant speed \( v . \) The
acceleration at the origin of coordinates
being (where \( a \text { is a constant }) \)
A \( \cdot \frac{v^{2}}{2 a} \)
B. \( 2 a v^{2} \)
c. \( \frac{v^{2}}{a} \)
D. \( a v^{2} \)
Subject: Maths
In a square box, a glass is to be surrounded by a \( 2 \mathrm{cm} \) glass border. If
the total area of the square is \( 121 \mathrm{cm}^{2} \) Find the dimension of the glass box.
A. \( 5 \mathrm{cm} \)
в. \( 6 \mathrm{cm} \)
\( c \cdot 7 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)
Subject: Physics
Determine the electric dipole moment
of the system of three charges,placed on the vertices of an equilateral triangle as shown in the figure:
A \( \cdot(q l) \frac{\hat{i}+\hat{j}}{\sqrt{2}} \)
В \( \cdot \sqrt{3} q l \frac{\hat{j}-\hat{i}}{\sqrt{2}} \)
\( \mathbf{c} .-\sqrt{3} q l \hat{j} \)
D. \( 2 q l \hat{j} \)
Subject: Physics
\( A \) and \( B \) are two points on the axis and the perpendicular bisector respectively of an electric dipole. A and B are far away from the dipole and at equal distances from its centre. The fields at \( A \) and \( \mathrm{B} \) i.e. \( \overrightarrow{\boldsymbol{E}_{A}} \quad \) and \( \overrightarrow{\boldsymbol{E}_{B}} \) are respectively
such that
\( \mathbf{A} \cdot \overrightarrow{E_{A}}=\overrightarrow{E_{B}} \)
B . \( \overrightarrow{E_{A}}=2 \overrightarrow{E_{B}} \)
c. \( \overrightarrow{E_{A}}=-2 \overrightarrow{E_{B}} \)
D. \( \overrightarrow{E_{A}}=\frac{1}{2} \overrightarrow{E_{B}} \)
Subject: Maths
toppr
Q Type your questiò
(i) \( \frac{-}{2 x}+\frac{-}{3 y}=2 ; \frac{-}{3 x}+\frac{-}{2 y}=\frac{-}{6} \)
(ii) \( \frac{\mathbf{2}}{\sqrt{\boldsymbol{x}}}+\frac{\mathbf{3}}{\sqrt{\boldsymbol{y}}}=\mathbf{2} ; \frac{\mathbf{4}}{\sqrt{\boldsymbol{x}}}-\frac{\mathbf{9}}{\sqrt{\boldsymbol{y}}}=-\mathbf{1} \)
(iii) \( \frac{4}{x}+3 y=14 ; \frac{3}{x}-4 y=23 \)
(iv) \( \frac{\mathbf{5}}{\boldsymbol{x}-\mathbf{1}}+\frac{\mathbf{1}}{\boldsymbol{y}-\mathbf{2}}=\mathbf{2} ; \frac{\mathbf{6}}{\boldsymbol{x}-\mathbf{1}}- \)
\( \frac{3}{y-2}=1 \)
\( (v) \frac{7 x-2 y}{x y}=5 ; \frac{8 x+7 y}{x y}=15 \)
(vi) \( 6 x+3 y=6 x y ; 2 x+4 y=5 x y \)
(vii) \( \frac{\mathbf{1 0}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{2}}{\boldsymbol{x}-\boldsymbol{y}}=\mathbf{4} ; \frac{\mathbf{1 5}}{\boldsymbol{x}+\boldsymbol{y}}- \)
\( \frac{5}{x-y}=-2 \)
(viii) \( \frac{1}{3 x+y}+\frac{1}{3 x-y}= \)
\( \frac{3}{4} ; \frac{1}{2(3 x+y)}-\frac{1}{2(3 x-y)}=\frac{-1}{8} \)
Subject: Maths
Using the reals \( a_{n} ;(n=1,2, \dots, 5), \) if \( l, m, n \in\{1,2,3,4,5\} m<n \)
A \( \cdot\left(\sum a_{n}\right)^{2}=\sum\left(a_{l}^{2}\right)+2\left(\sum a_{m} a_{n}\right) \)
B . \( 0=\sum\left(a_{l}^{2}\right)-\sum\left(a_{m} a_{n}\right) \)
C \( \cdot\left(\sum a_{n}\right)^{2}=\sum\left(a_{l}^{2}\right)-2\left(\sum a_{m} a_{n}\right) \)
D. \( \left(\sum a_{n}\right)^{2}=\sum\left(a_{l}^{2}\right)+\sum\left(a_{m} a_{n}\right) \)
Subject: Maths
The value of \( \sin ^{-1}\left(\cos \frac{53 \pi}{5}\right) \) is
A \( \cdot \frac{3 \pi}{5} \)
в. \( \frac{-3 \pi}{5} \)
c. \( \frac{\pi}{10} \)
D. \( \frac{-\pi}{10} \)
Subject: Physics
Work done by air when it expands from
\( \mathbf{5 0} \) litres to 150 litres at a constant
pressure of 2 atmosphere is
A \( \cdot 2 \times 10^{4} \) joules
B. 2 \( \times 100 \) joules
C \( .2 \times 10^{5} \times 100 \) joules
D. \( 2 \times 10^{6} \times 100 \) joules
Subject: Physics
Assertion
\( V_{r m s} \) and \( V_{\text {mean }} \) of gaseous molecules is nearly of the order of velocity of sound.
Reason
The sound travels in air because of
vibrational molecular motion.
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
Two springs of force constants \( \mathbf{1 0 0 0} N / \boldsymbol{m} \) and \( \mathbf{2 0 0 0} \boldsymbol{N} / \boldsymbol{m} \) are
stretched by same force. The ratio of their respective potential energies is
A .2: 1
B. 1: 2
c. 4: 1
D. 1: 4
Subject: Maths
If \( a \neq b \neq c, \) the value of \( x \) which
satisfies the question \( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{x}-\boldsymbol{a} & \boldsymbol{x}-\boldsymbol{b} \\ \boldsymbol{x}+\boldsymbol{a} & \mathbf{0} & \boldsymbol{x}-\boldsymbol{c} \\ \boldsymbol{x}+\boldsymbol{b} & \boldsymbol{x}+\boldsymbol{c} & \mathbf{0}\end{array}\right|=\mathbf{0} \) is
\( \mathbf{A} \cdot x=0 \)
B. \( x=a \)
\( \mathbf{c} \cdot x=b \)
D. \( x=c \)
Subject: Maths
Theo bakery sells red velvet cakes and
cheese cakes in boxes of 12 at a cost of
\( \$ 15 \) per box of red velvet and \( \$ 9 \) per box
of cheese cakes. On Monday and Tuesday, the shop earned \( \$ 396 \) by selling a total of 46 boxes of these two
items. If \( r \) and \( l \) represent the number of
boxes of red velvet and cheese cakes
respectively, which of the following systems of equations could be used to
find the number of boxes of each type of item sold?
\( \mathbf{A} \cdot r+l=46 \)
\[
15 r+9 l=396
\]
B . \( r+l=12 \times 46 \)
\[
15 r+9 l=396
\]
\( \mathbf{c} \cdot r+l=46 \)
\[
15 r+9 l=\frac{396}{2}
\]
D. \( r+l=46 \times 12 \)
\( 15 r+9 l=\frac{396}{12} \)