AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ccc}5 & 5 x & x \\ 0 & x & 5 x \\ 0 & 0 & 5\end{array}\right] \) and \( \left|A^{2}\right|=25 \)
then \( |x| \) is equal to?
A \( \cdot \frac{1}{5} \)
B. 5
\( c \cdot 5^{2} \)
D.
Subject: Biology
Soham is 6 years old. He was playing in the garden. One of his teeth fell as he
dashed a pillar. He started crying because he was hurt. He also felt that
his teeth will never come back and he
will not be able to eat chocolates. How
will you console him?
A. By telling him that his tooth was milk tooth
B. By telling him that his tooth was permanent tooth
c. By telling him that his tooth will be replaced
D. Both A and C
Subject: Maths
Let \( f(x) \) be a continuous function
defined for \( 1 \leq x \leq 3 \). If \( f(x) \) takes
rational values for all \( x \) and \( f(2)=10 \)
then the value of \( \boldsymbol{f}(\mathbf{1} . \mathbf{5}) \) is
A . 7.5
B. 10
\( c .5 \)
D. none of these
Subject: Maths
If \( \boldsymbol{A}^{\prime}\left[\begin{array}{cc}-\mathbf{2} & \mathbf{3} \\ \mathbf{1} & \mathbf{2}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}-\mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{2}\end{array}\right] \) Find
\( [\boldsymbol{A}+\mathbf{2} \boldsymbol{B}] \)
Subject: Chemistry
\( A t 46^{\circ} C, K_{p} \) for the reaction
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \) is 0.667 atm.
Compute the percent dissociation of
\( N_{2} O_{4} \) at \( 46^{\circ} C \) at a total pressure fo 380
Torr.
A . 50\%
B. 70\%
c. \( 40 \% \)
D. 20\%
Subject: Physics
An electron gun with its collector at a
potential of \( 100 V \) fires out electrons in
a spherical bulb containing hydrogen gas at low pressure \( \left(\sim 10^{-2} m m \text { of } \mathrm{Hg}\right) \)
A magnetic field of \( 2.83 \times 10^{4} T \) curves
the path of the electrons in a circular
orbit of radius \( 12.0 \mathrm{cm} \). (The path can be viewed because the gas ions in the path
focus the beam by attracting electrons, and emitting light by electron capture, this method is known as the fine beam
tube method. Determine \( e / m \) from the
data.
Subject: Chemistry
The following equilibrium exists in aqueous solution:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{C H}_{3} \boldsymbol{C O O} \)
If dilute \( H C l \) is added:
A. The equilibrium constant will increase
B. The equilibrium constant will decrease
c. Acetate ion concentration will increase
D. Acetate ion concentration will decrease
Subject: Maths
Multiply the following and write your answer in lowest terms:
\( \frac{x^{2}-3 x-10}{x^{2}-x-20} \times \frac{x^{2}-2 x+4}{x^{3}+8} \)
A \( \cdot \frac{1}{x+4} \)
B. \( \frac{1}{x-4} \)
c. \( \frac{3}{x+4} \)
D. None of these
Subject: Physics
The magnitude of the force between a pair of conductors, each of length 110 \( \mathrm{cm}, \) carrying a current of \( 10 \mathrm{A} \) and separated by a distance of \( 10 \mathrm{cm} \) is
A \( \cdot 55 \times 10^{-5} N \)
B . \( 44 \times 10^{-5} N \)
c. \( 33 \times 10^{-5} N \)
D. \( 22 \times 10^{-5} N \)
Subject: Biology
If a non-degradable and fat soluble pollutant, such as DDT enters the food
chain, the pollutant
A. Magnifies in concentraition at each tropic level
B. Degrades at first trophic level
c. Accumulates in the body fat of organism at first trophic level and does not pass to second trophic level
D. Decreases inconcentration at each trophic level
Subject: Physics
The electric field at a point due to an electric dipole, or an axis inclined at an
angle \( \theta\left(<90^{\circ}\right) \) to the dipole axis, is perpendicular to the dipole axis, if the angle \( \boldsymbol{\theta} \) is
A \( \cdot \tan ^{-1} \)
B. \( \tan ^{-1}\left(\frac{1}{2}\right) \)
\( \mathbf{c} \cdot \tan ^{-1}(\sqrt{2}) \)
D \( \cdot \tan ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)
Subject: Chemistry
Identify the product \( A \) in the following
reaction.
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{A}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{F} \)
Subject: Physics
Consider a hemispherical surface of
radius \( r, \) a positive point charge \( q \) is kept at the centre of hemisphere. The electric flux through this hemisphere is
A . zero
в. \( \frac{q}{\varepsilon_{0}} \)
c. \( \frac{q}{2 \varepsilon_{0}} \)
D. \( \frac{2 q}{\varepsilon_{0}} \)
Subject: Maths
If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \) and
\( \boldsymbol{f}(\mathbf{2})=\mathbf{2}, \boldsymbol{f}(\boldsymbol{a}+\boldsymbol{b})= \)
\( \boldsymbol{f}(\boldsymbol{a}) \boldsymbol{f}(\boldsymbol{b}), \forall \boldsymbol{a}, \boldsymbol{b} \boldsymbol{\epsilon} \boldsymbol{R}, \) then
\( \boldsymbol{x}^{f(\mathbf{2})}, \boldsymbol{y}^{f(4)}, \boldsymbol{z}^{f(\boldsymbol{6})} \) are in
This question has multiple correct options
A. A.P
в. G.
c. н.
D. None
Subject: Biology
In order for the blood to flow from right ventricle to left ventricle in mammalian
heart, it must flow through
A. Right ventricle, pulmonary arteries, lungs, pulmonary veins and left atrium
B. Right ventricle, pulmonary arteries, lungs, pulmonary arteries and left atrium
c. Right ventricle, right atrium, , lungs, pulmonary veins and left atrium
D. Right ventricle, systemic aorta, Iungs, pulmonary veins and left atrium
Subject: Maths
Solve :
\( \int \frac{d x}{\sqrt{x-x^{2}}} \)
\( \mathbf{A} \cdot 2 \sin ^{-1} \sqrt{x}+c \)
B. \( 2 \sin ^{-1} x+c \)
\( \mathbf{c} \cdot 2 x \sin ^{-1} x+c \)
\( \mathbf{D} \cdot \sin ^{-1} \sqrt{x}+c \)
Subject: Maths
In a parallelogram \( A B C D, \) if \( A B=2 x+5 \) \( \mathrm{CD}=\mathrm{y}+1, \mathrm{AD}=\mathrm{y}+5 \) and \( \mathrm{BC}=3 \mathrm{x}-4 \) then the
ratio of AB:BC is
A . 71:21
B. 12:11
\( c \cdot 31: 35 \)
D. 4: 7
Subject: Physics
An electric dipole of moment P is placed along the lines of force of electric field \( E \)
and is in equilibrium. the work done in
deflecting it through an angle of \( 180^{0} \) is equal to-
\( \mathbf{A} \cdot P E \)
в. \( +2 P E \)
c \( .-2 P E \)
D. \( Z E R O \)
Subject: Physics
Magnesium fluoride \( \left(M g F_{2}\right) \) is generally used as anti-reflection coating.
If refractive index of \( M g F_{2} \) is 1.25 and
if the minimum thickness of film is not
technologically possible to manufacture, then next thickness of film required is (approximately) (Take \( \boldsymbol{\lambda}=\mathbf{5 0 0 n m}) \)
A. 300 nm
в. \( 12 n m \)
c. \( 750 n m \)
D. \( 550 n m \)
Subject: Chemistry
Statement 1: Transition metal
compounds are often colored.
Statement 2: They frequently possess partially filled d-orbitals.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement1
B. Both the Statement 1 and Statement 2 are correct, but Statement 2 is NOT the correct explanation of Statement 1.
c. Statement 1 is correct, but Statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct
Subject: Chemistry
In a reaction \( A+B \rightarrow \) products, the rate
of reaction is doubled when the
concentration of \( A \) is doubled and \( B \) is
kept constant and the rate of the
reaction is increased by 8 times when the concentrations of both \( A \) and \( B \) are
doubled, thus overall order of the
reaction is:
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)
Subject: Maths
\( \left|\begin{array}{ccc}\boldsymbol{a}^{2}+\mathbf{1} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{b} & \boldsymbol{b}^{2}+\mathbf{1} & \boldsymbol{b} \boldsymbol{c} \\ \boldsymbol{c} \boldsymbol{a} & \boldsymbol{c} \boldsymbol{b} & \boldsymbol{c}^{2}+\mathbf{1}\end{array}\right|=\mathbf{1}+\boldsymbol{a}^{2}+ \)
Subject: Maths
Represent the following data using suitable graphical representation.
No. of
\[
\begin{array}{llll}
\text { words } & \mathbf{3 0}- & \mathbf{4 0 -} & \mathbf{5 0 -} \\
\text { typed } & \mathbf{3 9} & \mathbf{4 9} & \mathbf{5 9} \\
\text { per } & &
\end{array}
\]
\( \operatorname{minute} \)
No. of typists
15
Subject: Maths
The dimensions of a rectangular box are in the ratio 1: 2: 4 and the difference
between the costs of covering it with the cloth and sheet at the rate of \( R s .20 \) and
Rs.20.50 per square metre, respectively
is \( R s .126 . \) Find the dimensions of the
box
A. \( 4 c m, 7 c m \) and \( 10 c m \)
B. \( 2 c m, 4 c m \) and \( 11 c m \)
c. \( 3 c m, 6 c m \) and \( 12 c m \)
D. \( 7 c m, 8 c m \) and \( 13 c m \)
Subject: Maths
If \( f(x)=\left(a x^{2}+b\right)^{3} \) then a function
\( g(x) \) such that \( f(g(x))=g(f(x)) \) is given by
A \( , \quad g(x)=\left(\frac{b-x^{1 / 3}}{a}\right)^{1 / 2} \)
B. \( g(x)=\frac{1}{\left(a x^{2}+b\right)^{3}} \)
c. \( g(x)=\left(a x^{2}+b\right)^{1 / 3} \)
\( g(x)=\left(\frac{x^{1 / 3}-b}{a}\right)^{1 / 2} \)
Subject: Chemistry
Some of the reactions taking place
during bessemerisation possibly are -
\( \boldsymbol{A}: \boldsymbol{F} \boldsymbol{e} \boldsymbol{O}+\boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{3} \)
\( B: 2 F e S+3 O_{2} \rightarrow 2 F e O+2 S O_{2} \)
\( \boldsymbol{C}: \mathbf{2} \boldsymbol{C u}_{2} \boldsymbol{S}+\mathbf{3} \boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{O}+ \)
\( 2 S O_{2} \)
\( \boldsymbol{D}: \boldsymbol{2} \boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{O}+\boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{S} \rightarrow \boldsymbol{6} \boldsymbol{C} \boldsymbol{u}+\boldsymbol{S} \boldsymbol{O}_{2} \)
Select reactions actually taking place :
\( A \cdot A, B \)
B. B,
\( c \cdot A, C \)
D. \( c, D \)
Subject: Maths
Let \( A \) be an invertible matrix then which
of the following is/are true
This question has multiple correct options
A \( \cdot\left|A^{-1}\right|=|A|^{-1} \)
- \( \left.^{-1}|A|^{-1}|=| A\right|^{-1} \)
B. \( \left(A^{2}\right)^{-1}=\left(A^{-1}\right)^{2} \)
C \( \cdot\left(A^{T}\right)^{-1}=\left(A^{-1}\right)^{T} \)
D. none of these
Subject: Physics
Consider two different metallic strips
and 2 ) of same dimensions (length \( l \)
width \( \boldsymbol{w} \) and thickness \( \boldsymbol{d} \) ) with carrier
densities \( n_{1} \) and \( n_{2} \) respectively. Strip 1
is placed in magnetic field \( B_{1} \) and strip
2 is placed in magnetic field \( B_{2}, \) both
along positive y-directions. Then \( V_{1} \) and
\( V_{2} \) are the potential differences
developed between K and M in strips
and \( 2, \) respectively.
This question has multiple correct options
A \( \cdot \) If \( B_{1}=B_{2} \) and \( n_{1}=2 n_{2} \), then \( V_{2}=2 V_{1} \)
B. If \( B_{1}=B_{2} \) and \( n_{1}=2 n_{2} \), then \( V_{2}=V_{1} \)
C. If \( B_{1}=2 B_{2} \) and \( n_{1}=n_{2}, \) then \( V_{2}=0.5 V_{1} \)
D. If \( B_{1}=2 B_{2} \) and \( n_{1}=n_{2} \), then \( V_{2}=V_{1} \)
Subject: Chemistry
Which one of the following has largest number of isomers?
\( (R= \) alkyl group,en = ethylenediamine)
\( \mathbf{A} \cdot\left[R u\left(N H_{3}\right)_{4} C l_{2}\right]^{+} \)
B . \( \left[\operatorname{Co}\left(N H_{3}\right)_{5} C l\right]^{2+} \)
c. \( \left[I r\left(P R_{3}\right)_{2} H(C O)\right]^{2} \)
D. \( \left[\operatorname{Co}(e n)_{2} C l_{2}\right] \)
Subject: Maths
Find the roots of the following equation \( 2 y^{2}+\frac{15}{y^{2}}=12, \) then
A \( \cdot \quad y=\pm \sqrt{\frac{6+\sqrt{6}}{4}}, y=\pm \sqrt{\frac{6-\sqrt{6}}{2}} \)
в. \( \quad y=\pm \sqrt{\frac{6+\sqrt{6}}{2}}, y=\pm \sqrt{\frac{6-\sqrt{5}}{2}} \)
c. \( y=\pm \sqrt{\frac{6+\sqrt{6}}{2}}, y=\pm \sqrt{\frac{6-\sqrt{6}}{2}} \)
D. \( y=\pm \sqrt{\frac{6+\sqrt{5}}{2}}, y=\pm \sqrt{\frac{6-\sqrt{6}}{2}} \)
Subject: Maths
Find the values of \( c \) that satisfy the MVT for integrals on \( \left[\frac{3 \pi}{4}, \pi\right] \) \( \boldsymbol{f}(\boldsymbol{x})=\cos (\boldsymbol{2} \boldsymbol{x}-\boldsymbol{\pi}) \)
A \( \cdot c=\frac{5 \pi}{2}-\frac{1}{2} \cos ^{-1}\left(-\frac{2}{\pi}\right) \)
в. \( c=\pi-\frac{1}{2} \cos ^{-1}\left(-\frac{2}{\pi}\right) \)
\( c \cdot c=\frac{\pi}{2}+\frac{1}{2} \sin ^{-1}\left(-\frac{2}{\pi}\right) \)
D \( c=\frac{\pi}{2}+\frac{1}{2} \sin ^{-1}\left(\frac{2}{\pi}\right) \)
Subject: Biology
Consider the following statements and state true(T) or false(F).
(A) In Phycomycetes members, coenocytic mycelium is found.
(B) The common asexual spores in Basidiomycetes are conidia and
zoospores.
(C) Mycelium of Ascomycetes is branched and septate.
A \( \cdot(A)-T,(B)-T,(C)-T \)
B. (A)-T, (B)-F, (C)-T
c. \( (A)-T,(B)-T,(C)-F \)
D. (A)-F, (B)-T, (C)-F
Subject: Maths
mrs Razdan wants to use tiles of length
\( 20 \mathrm{cm} \) and breadth \( 10 \mathrm{cm} \) to cover the
floor of hger balcony shown in the figure.What is the area of the balcony? How many tiles does she neeed to buy \( (1 s q m=10,000 s q c m) ? \)
Subject: Maths
\( \left|\begin{array}{cc}\mathbf{2} & -\mathbf{4} \\ \mathbf{9} & \boldsymbol{d}-\mathbf{3}\end{array}\right|=\mathbf{4} \) then \( \boldsymbol{d}= \)
A . 1
B. -11
c. 12
D. -13
Subject: Chemistry
The total vapour pressure, \( \mathbf{P}_{\text {total }} \) (in torr)
for a mixture of thwo volatile
components, \( A \) and \( B \) is given by \( P_{\text {total }} \)
\( =220-110 X_{B} \)
Where, \( \mathbf{X}_{\mathbf{B}} \) is mole fraction of
component, \( B \) is mixture. Hence,
pressure (in torr) of pure components,
\( A \) and \( B \) are respectively:
A \( \cdot 220,110 \)
В. 110,220
\( c \cdot 220,330 \)
D. 220,150
Subject: Maths
A relation \( \rho \) on the set of real number \( \boldsymbol{R} \)
is defined as follows:
\( x \rho y \) if any only if \( x y>0 . \) Then which of
the following is/are true? This question has multiple correct options
A \( . \rho \) is reflexive and symmetric
B. \( \rho \) is symmetric but not reflexive
c. \( \rho \) is symmetric and transitive
D. \( \rho \) is an equivalence relation
Subject: Chemistry
In a first order reaction the
concentration of reactant decreases
from \( 800 \mathrm{mol} / \mathrm{dm}^{3} \) to \( 50 \mathrm{mol} / \mathrm{dm}^{3} \) is
\( 2 \times 10^{4} \) sec. The rate constant of
reaction in \( \sec ^{-1} \) is:
A \( \cdot 2 \times 10^{4} \)
В. \( 3.45 \times 10^{-5} \)
\( \mathbf{c} \cdot 1.386 \times 10^{-4} \)
D. \( 2 \times 10^{-4} \)
Subject: Maths
f \( \alpha, \beta, \gamma \) are non-constant terms in G.P
and equations \( \alpha x^{2}+2 \beta x+\gamma=0 \)
and \( x^{2}+x-1=0 \) has a common root
then \( (\gamma-\alpha), \beta \) is
\( A \cdot \alpha \beta \)
в. \( \beta \gamma \)
c. \( \gamma \alpha \)
D.
Subject: Physics
An electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{4} \boldsymbol{x} \hat{\boldsymbol{i}}-\left(\boldsymbol{y}^{2}+\right. \)
1) \( \hat{j} N / C \) passes through the box shown
in figure. The flux of the electric field
through surfaces \( A B C D \) and \( B C G F \)
are marked as \( \phi_{I} \) and \( \phi_{I I} \) respectively.
The difference between \( \left(\phi_{I}-\phi_{I I}\right) \) is \( ( \) in
\( \left.N m^{2} / C\right) \)
Subject: Physics
An ideal spring with a pointer attached to its end, hangs next to a scale. With a \( 100 \mathrm{N} \) weight attaches and in
equilibrium, the pointer indicates '40 on the scale as shown. Using a \( 200 \mathrm{N} \) weight instead in'60' on the scale. Using
an unknown weight 'X' instead results in '30' on the scale. The value of X is
\( A \cdot 80 N \)
B. 60 N
\( c \cdot 50 N \)
D. \( 40 \mathrm{N} \)
Subject: Physics
A container is partially filled with hot water, sealed and left to cool. Which
statements are correct?
1. As the temperature decreases, water molecules lose kinetic energy.
2. As the temperature decreases, more water molecules move from vapour to
liquid.
3. As the temperature decreases, the
vapour pressure of the water decreases.
A. 1,2 and 3 are correct
B. 1 and 2 only are correct
C. 2 and 3 only are correct
D. 1 only is correct
Subject: Maths
In a town of 10,000 families it was found that \( 40 \% \) families buy newspaper A, \( 20 \% \) families buy newspaper \( B \) and 10
\( \% \) families buy newspaper \( C .5 \% \) families buy A and B, 3\% buy B and C
and \( 4 \% \) buy \( A \) and \( C . \) If \( 2 \% \) families buy
all the three newspaper, the member of families which buy A only is
Subject: Maths
Determine the differential equation of
parabolas with foci at origin and axes
along X-axis.
Hint: \( y^{2}=4 a(x-a) \)
\( \mathbf{A} \cdot y^{3}\left(\frac{d y}{d x}\right)^{2}=2 x y \frac{d y}{d x}-1 \)
B \( y^{4}\left(\frac{d y}{d x}\right)^{2}=2 x y \frac{d y}{d x}-1 \)
\( ^{\mathbf{C}} y^{3}\left(\frac{d y}{d x}\right)^{2}=2 x y \frac{d y}{d x}-2 \)
D \( y^{4}\left(\frac{d y}{d x}\right)^{3}=2 x y \frac{d y}{d x}-1 \)
Subject: Chemistry
Select the correct statements.
This question has multiple correct options
A. Contraction of bond angle in \( H_{2} O \) relative to methane
is \( 4^{\circ} \)
B. The molecules having cation with 18 electron valence shell are more covalent than those having 8 electron valence shell
C. \( C o^{3+} \) ion is less stable than \( F e^{3+} \) ion
D. \( S n^{4+} \) is less stable than \( S n^{2+} \)
Subject: Chemistry
Which of the following reactions will yield propan-2-ol? This question has multiple correct options
A \( \cdot C H_{2}=C H-C H_{3}+H O H \stackrel{H}{\rightarrow} \)
B. \( C H_{3}-C H O^{C H_{3} M g B r / H O H} \rightarrow^{C H} \)
\( \mathrm{c} \cdot \mathrm{CH}_{2} \mathrm{O}^{C_{2} \mathrm{H}_{5} \text { МуТ } / \text {НОН}} \)
D. None of the above
Subject: Maths
The function \( \boldsymbol{f}:[\mathbf{2}, \infty) \rightarrow \boldsymbol{Y} \) defined by
\( f(x)=x^{2}-4 x+5 \) is both one-one \( \& \)
onto if:
A \( . Y=R \)
В. \( Y=[1, \infty) \)
c. \( Y=[4, \infty) \)
D. \( Y=[5, \infty) \)
Subject: Maths
If \( \left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=\left|z_{4}\right|=1 \) and \( z_{1}+ \)
\( z_{2}+z_{3}+z_{4}=0, \) then least value of the
expression
\[
\begin{array}{c}
\boldsymbol{E}=\left|\boldsymbol{z}_{1}-\boldsymbol{z}_{2}\right|^{2}+\left|\boldsymbol{z}_{2}-\boldsymbol{z}_{3}\right|^{2}+\mid \boldsymbol{z}_{3}- \\
\left.\boldsymbol{z}_{4}\right|^{2}+\left|\boldsymbol{z}_{4}-\boldsymbol{z}_{1}\right|^{2} \text { is }
\end{array}
\]
\( A \cdot 6 \)
B. 8
c. 10
D. 12
Subject: Physics
The angular velocity of a wheel is 70 rad/s. If the radius of the wheel is
\( \mathbf{0 . 5} \boldsymbol{m}, \) then linear velocity of the whee
is
A. \( 70 \mathrm{m} / \mathrm{s} \)
B. \( 35 \mathrm{m} / \mathrm{s} \)
c. \( 30 m / s 30 m / s \)
D. 20m/s2om/s
Subject: Physics
For energy density, power and intensity of any wave choose the correct options.
A \( \cdot u= \) energy density \( =\frac{1}{2} \rho \omega^{2} A^{2} \)
B. \( P= \) power \( =\frac{1}{2} \rho \omega^{2} A^{2} v \)
c. \( _{I}= \) intensity \( =\frac{1}{2} \rho \omega^{2} A^{2} S v \)
D. \( _{I}=\frac{P}{S} \)
Subject: Maths
In a row of girls, Mridula is \( 18^{t h} \) from the
right and Sanjana is \( 18^{t h} \) from the left. If both of them interchange their position, Sanjana becomes \( 25^{t h} \) from the left,
how many girls are there in the row?
A . 40
B. 41
c. 42
D. 35 5
Subject: Maths
If one of the zeroes of the
quadratic polynomial \( (k-1) x^{2}+ \)
\( k x+1 \) is \( (-3), \) then \( k \) equals to
A \( \cdot \frac{4}{3} \)
в. \( -\frac{4}{3} \)
\( c \cdot \frac{2}{3} \)
D. \( -\frac{2}{3} \)
Subject: Maths
Compute \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}), \) if \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 2 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 1 8} \)
\( P(B)=0.25 \)
Subject: Maths
There are three copies each of four different books. The number of ways in
which they can be arranged in a shelf is
A \( \cdot \frac{12 !}{(3 !)^{4}} \)
в. \( \frac{12 !}{(4 !)^{3}} \)
c. \( \frac{12 !}{(3 !)^{4} 4 !} \)
D. \( \frac{12 !}{(4 !)^{3} 3 !} \)
Subject: Chemistry
Use the figure below to answer the question that follows. Which molecule or molecules has/have the same empirical formula as one of the others?
\[
\begin{array}{ll}
O=\mathbf{O} & \quad 0=\text { lone pair } \\
D=\mathbf{N} & 0=\text { partially filled } \\
\text { orbital }
\end{array}
\]
\[
0=\mathbf{H}
\]
II
A. II only.
B. III and IV
c. IV only
D. I and III, and III and IV
Subject: Physics
In the figure shown, a block A moving with velocity \( 10 ~ m / s \) on a horizontal surface collides with another block B at
rest initially. The coefficient of restitution is \( \frac{1}{2} . \) Neglect friction everywhere. The distance between the blocks at \( 5 s \) after the collision takes
place is \( 5 x(\text { in } m) . \) Then \( x \) is
Subject: Maths
A trader purchases \( 70 \mathrm{kg} \) of tea at Rs 15 per kg and 30 kg of tea at Rs. 18.50 per kg. If the packing charges are 2 percent, then at what price he must sell the mixture of two to gain \( 15 \% ? \)
A. Rs. 18.80 per kg
B. Rs. 18 per kg
c. Rs. 18.50 per \( \mathrm{kg} \)
D. Rs. 17.80 per kg
Subject: Physics
The displacement of a particle in
S.H. \( M . \) is indicated by equation \( y= \)
\( \mathbf{1 0} \sin (\mathbf{2 0 t}+\boldsymbol{\pi} / \mathbf{3}) \) where \( \boldsymbol{y} \) is in
metres. The value of maximum velocity
of the particle will be :
A . \( 100 \mathrm{m} / \mathrm{sec} \)
B . 150 m/sec.
c. \( 200 \mathrm{m} / \mathrm{sec} \)
D. 400 \( \mathrm{m} / \mathrm{sec} \)
Subject: Maths
Which of the following is NOT a
quadratic polynomial?
\( \mathbf{A} \cdot p(x)=p x^{2}+q x+r \)
B \( \cdot p(x)=a x^{2}+b x+c \)
\( \mathbf{c} \cdot p(x)=x \cdot x^{2}+x \cdot x+x \)
D \( \cdot p(x)=m x^{2}+n x+l \)
Subject: Chemistry
Calculate the value of the following expression in celsius scale.
\( \frac{\left(298 K \times 50^{o} C\right)}{\left(275 K+3^{o} C\right)} \)
\( \mathbf{A} \cdot 300^{\circ} C \)
B . \( 250^{\circ} \mathrm{C} \)
c. \( 200^{\circ} \mathrm{C} \)
D. \( 350^{\circ} \mathrm{C} \)
Subject: Chemistry
An electron in ground state absorbs 1.5 times as much energy required to escape from H atom. The wavelength of
electron emitted in \( A^{\circ} \) is :
A \( .4 .21 A^{\circ} \)
B . \( 4.71 A^{\circ} \)
c. \( 3.52 A^{\circ} \)
D. \( 3.711 A^{\circ} \)
Subject: Maths
If \( \log _{10}\left(x^{3}+y^{3}\right) \)
\( \log _{10}\left(x^{2}+y^{2}-x y\right) \leq 2, \) then the
maximum value of \( x y, \) for all \( x \geq \)
\( \mathbf{0}, \boldsymbol{y} \geq \mathbf{0}, \) is
A . 2500
в. 3000
c. 1200
D. 3500
Subject: Chemistry
Given that the rate of disappearance of
bromine is \( -3.5 \times 10^{-4} M / s \) for the
following reaction:
\( \boldsymbol{H}_{2(g)}+\boldsymbol{B} \boldsymbol{r}_{2(g)} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}_{(a q)} \)
What is the rate of formation for \( \boldsymbol{H} \boldsymbol{B r} \) ?
A. \( -7.0 \times 10^{-4} \mathrm{M} / \mathrm{s} \)
В. \( -3.5 \times 10^{-4} \mathrm{M} / \mathrm{s} \)
c. \( 3.5 \times 10^{-4} M / s \)
D. \( 7.0 \times 10^{-4} \mathrm{M} / \mathrm{s} \)
Subject: Maths
If \( \bar{P} Q \) is a chord of a circle with centre \( O \)
and \( P R \) is a tangent to the circle at \( P \)
then \( \angle P O Q= \)
A. \( 4 \angle R P Q \)
B. \( 3 \angle R P Q \)
c. \( 2 \angle R P Q \)
D. \( \angle R P Q \)
Subject: Physics
Equal volume of two solution having pH \( =2 \) and \( p H=10 \) are mixed together at 90C. Then pH of resulting solution is :
(Take \( \left.K w \text { at } 90 C=10^{-12}\right) \)
A. \( 2+\log 2 \)
B. 10 \( \log 2 \)
c. 7
\( D \cdot 6 \)
Subject: Chemistry
The I.U.P.A.C name of the coordination
compound \( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is :
A. Potassium hexacyanidoferrate(II)
B. Potassium hexacyanidoferrate(III)
c. Potassium hexacyanidoiron(II)
D. Tripotassium hexacyanidoiron(II)
Subject: Chemistry
Acetic acid dimerises in vapour phase
at \( 437 K \) as \( 2 C H_{3} C O O H(g) \rightleftharpoons \)
\( \left(C H_{3} C O O H\right)_{2}(g) . A \) mass of \( 0.0519 g \)
of acetic acid was found to have
764.3 \( m m \) pressure at \( 437 K \) in a container of \( 21.45 \mathrm{cm}^{3} . \) Calculate degree
of dimerisation for acetic acid
dimerisation.