AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( (A): \int e^{x}\left(\log x+x^{-2}\right) d x= \)
\( e^{x}\left(\log x-\frac{1}{x}\right)+c \)
\( (\mathrm{R}): \int e^{x}\left[\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}^{\prime}(\boldsymbol{x})\right] \boldsymbol{d} \boldsymbol{x}=\boldsymbol{e}^{\boldsymbol{x}} \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{c} \)
A. Both A and R are true and R is the correct explanation
of
B. Both A and R are true but R is not correct explanation of
c. \( A \) is true but \( R \) is false
D. A is false but R is true
Subject: Chemistry
Two half-cells have potentials -0.44 and 0.799 volt respectively. These two are coupled to make a galvanic cell. Which of the following will be true?
A. Electrode of half-cell potential \( -0.44 \mathrm{V} \) V will act as anode
B. Electrode of half-cell potential -0.44 V will act as cathode
c. Electrode of half-cell potential \( 0.799 \mathrm{V} \) will act as anode
D. Electrode of half-cell potential \( -0.44 \mathrm{V} \) will act as a positive terminal
Subject: Chemistry
In three test tubes \( P, Q, \) and \( R \) iron
nails, water, oil and anhydrous calcium
chloride is taken. Among these test
tubes, in which test tubes corrosion of
nails will not take place?
\( A \cdot P, Q \) and \( R \)
B. \( P \) and \( R \)
\( c . P \) and \( Q \)
D. \( Q \) and \( R \)
Subject: Chemistry
Assertion
The ratio weights of carbon and oxygen
in \( C O_{2} \) is 3: 8 and it is a constant.
Reason

The atomic weights of carbon and
oxygen are constant.
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
For the zero order reaction \( \boldsymbol{A} \rightarrow \mathbf{2} \boldsymbol{B} \), the
rate constant is \( 2 \times 10^{-6} M \) min\( ^{-1} \). The
reaction is started with \( 10 M A \)
(i) What will be the concentration of \( A \)
after 2 days (ii) What is the initial halflife of the reaction
(iii) In what time, the reaction will
complete?
Subject: Chemistry
Which of the following condition favours the reduction of a metal oxide to metal?
A. \( \Delta H=+v e, T \Delta S=+v e \) at low temperature
B. \( \Delta H=+v e, T \Delta S=-v e \) at any temperature
C. \( \Delta H=-v e, T \Delta S=-v e \) at high temperature
D. \( \Delta H=-v e, T \Delta S=+v e \) at any temperature
Subject: Physics
Angle of minimum deviation for a prism of refractive index \( 1.5, \) is equal to the
angle of the prism. Then the angle of the
prism is : (Given \( \left.\cos 41^{\circ}=0.75\right) \)
\( \mathbf{A} \cdot 62^{\circ} \)
B . 41
\( c \cdot 82 \)
D. 31
Subject: Chemistry
Match the following:
Name of the sugar Hydrolysis
products
A) Sucrose
i) Glucose + Fructose Galactose
B) Lactose
ii) Glucose + Fructose
c) Maltose
iii) Glucose + Galactose
D) Raffinose
iv) Glucose + Glucose
A. A-iii, B- ii, C-i, D-iv.
B. A-ii, B- iii, C-i, D-iv
c. A- ii, B- iii, C- iv, D-i
D. A- ii, B- iv, C- iii, D-i
Subject: Chemistry
The white solid compound \( A \) decomposes quite rapidly on heating in the presence of a black substance \( X \) to form a solid compound \( \mathrm{B} \) and a gas \( \mathrm{C} \) When an aqueous solution of compound \( \mathrm{B} \) is reacted with silver nitrate solution,
then a white precipitate of silver chloride is obtained along with potassium nitrate solution. Gas C does not burn itself but helps to burn other things.
What is compound A?
Subject: Physics
If the string is burnt, find the angle
between \( A B \) and the vertical at
equilibrium position
\( A \)
B. \( \tan ^{-1}\left(\frac{1}{4}\right) \)
\( c \cdot \tan ^{-1}(3) \)
' \( \quad \tan ^{-1}\left(\frac{1}{2}\right) \)
Subject: Chemistry
Which of the following is chemical formula of Oleum?
\( A \cdot H_{2} S_{2} O_{8} \)
в. \( \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{5} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{4} \)
D. \( \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)
Subject: Physics
Unpolarised light is incident from air on
a plane surface of a material of
refractive index' \( \mu^{\prime} . \) At a particular
angle of incidence \( ^{\prime} \boldsymbol{i}^{\prime}, \) it is found that the reflected and refracted rays are
perpendicular to each other. Which of the following options is correct for this situation?
A \( \cdot i=\sin ^{-1}\left(\frac{1}{\mu}\right) \)
B. Reflected light is polarised with its electric vector parallel to the plane of incidence
C. Reflected light is polarised with its electric vector perpendicular to the plane of incidence
D. \( i=\tan ^{-1}\left(\frac{1}{\mu}\right) \)
Subject: Biology
Observe the given figures of three
different plant tissues and select the correct option.
28
A. 'a' and 'b' consist of living cells while 'c' consits of dead cells
B. Cytoplasm is present in cells of 'a' while it is absent in cells of 'b' and 'c'.'
C. Cell walls of 'a' 'b' and 'c' bear uniform tickening of suberin
D. 'a' provides mechanical strength to the plant while 'b' and 'c' serve as storage tissues.
Subject: Maths
If the the hyperbola \( \frac{x^{2}}{4}-\frac{y^{2}}{b^{2}}=1 \)
passses though (4,3)
\( \mathbf{A} \cdot b^{2}=3 \)
B. \( b^{2}=9 \)
\( \mathbf{c} \cdot b^{2}=4 \)
D. \( b^{2}=100 \)
Subject: Chemistry
A 0.001 molal solution of
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{4}\right] \) in water has a freezing
point depression of \( 0.0054^{0} C . \) If \( K_{f} \) for water is \( 1.80, \) the correct formulation of
the above molecule is:
\( \mathbf{A} \cdot\left[P t\left(N H_{3}\right)_{4} C l_{3}\right] C l \)
B . \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \)
c. \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] C l_{3} \)
D \( \cdot\left[P t\left(N H_{3}\right)_{4} C l_{4}\right] \)
Subject: Chemistry
Assertion
The solubility of Ammonium chloride increases with increase in temperature
Reason In case of substances whose solubility increases with increase in temperature is due to the dissolution process being endothermic.
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 \( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{3}), \boldsymbol{B}=(\mathbf{2}, \mathbf{1 0}, \mathbf{1}), \boldsymbol{Q} \) are
collinear points and \( Q_{x}=-1, \) then
\( \boldsymbol{Q}_{z}= \)
A . -3
B. 7
\( c \cdot-14 \)
D. -
Subject: Chemistry
The oxide that gives \( H_{2} O_{2} \) on treatment
with dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is:
\( \mathbf{A} \cdot P b O_{2} \)
в. \( B a O_{2} .8 H_{2} O \)
c. \( M n O_{2} \)
D. \( T i O_{2} \)
Subject: Chemistry
Calculate the minimum number of
balloons each of volume 82.1 L required to lift a mass of \( 1 \mathrm{kg} \) to a height of 831
\( \mathbf{m} \)
Given: molar mass of air \( =29 \mathrm{g} / \mathrm{mol} \), the temperature is constant at \( 290 \mathrm{K} \) and mass of each balloon is 40 g. \( \left[\text { Use } e^{-01}=0.9, \text { pressure at sea level }=1\right. \) atm, acceleration due to gravity \( (g)=10 \) \( \left.\mathrm{m} / \mathrm{s}^{2}\right] \)
A . 10
в. 20
\( c \cdot 25 \)
D. 50
Subject: Physics
A piston of cross-sectional area \( 100 \mathrm{cm}^{2} \) is used in a hydraulic press to exert a force of \( 10^{7} \) dyne on the water. The cross-sectional area of the other piston
which supports an object having a mass of \( 2000 \mathrm{kg} \) is :
A \( \cdot 100 \mathrm{cm}^{2} \)
B. \( 10^{9} \mathrm{cm}^{2} \)
c. \( 2 \times 10^{4} c m^{2} \)
D. \( 2 \times 10^{10} \mathrm{cm}^{2} \)
Subject: Maths
Find the area of the semicircle with
diameter \( 6 \mathrm{cm} \)
A . \( 3.5 \pi \) sq.units
в. \( 4.5 \pi \) sq.units
\( \mathrm{c} .5 .5 \pi \) sq.units
D. \( 6.5 \pi \) sq.units
Subject: Chemistry
According to Bohr theory, the electronic
energy of hydrogen atom in the \( n \) th Bohr orbit is given by,
\[
\boldsymbol{E}_{\boldsymbol{n}}=-\frac{\boldsymbol{2} \mathbf{1} . \boldsymbol{7} \boldsymbol{6} \times \mathbf{1 0}^{-19}}{\boldsymbol{n}^{2}} \boldsymbol{J}
\]
Calculate the longest wavelength of light that will be needed to remove an electron from the 2 nd orbit of \( L i^{2+} \) ion.
Subject: Physics
Match the column
\( \begin{array}{lll} & \text { । } & \text { ॥ } \\ \text { A } & \text { Force } & \text { erg } \\ \text { B } & \text { Pressure } & \text { Kgm } / s^{2} \\ \text { C } & \text { Power } & J s^{-1} \\ \text {D } & \text { Energy } & \text { Nm }^{-2}\end{array} \)
Subject: Chemistry
The number of oxygen atoms in 6.4 g of
oxygen are :
A. \( 6.023 \times 10^{23} \)
3 \( 3.02 \times 10^{3} \times 10^{-63} \)
В. \( 6.023 \times 10^{22} \)
c. \( 1.2046 \times 10^{23} \)
D. \( 1.2046 \times 10^{22} \)
Subject: Physics
A pipe's lower end is immersed in water such that the length of air column from
the top open end has a certain length
\( 25 \mathrm{cm} . \) The speed of sound in air is
\( 350 m / s . \) The air column is found to
resonate with a tuning fork of frequency
\( 1750 H z . \) By what minimum distance
should the pipe be raised in order to make the air column resonate again
with the same tuning fork?
\( \mathbf{A} \cdot 7 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
c. \( 35 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Maths
Assertion
If \( \vec{u} \) and \( \vec{v} \) are unit vectors inclined at
an angle \( \alpha \) and \( \vec{x} \) is a unit vector
bisecting then angle between them, then \( \vec{x}=\frac{\vec{u}+\vec{v}}{\sqrt{2}} \)
Reason
If \( A B C \) be an isosceles triangle with
\( A B=A C, \) then vector representing
bisector of angle \( \boldsymbol{A} \) is given by \( \overrightarrow{\boldsymbol{A D}}= \) \( \frac{\overrightarrow{\boldsymbol{A B}}+\overrightarrow{\boldsymbol{A C}}}{2} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Chemistry
In the reaction, \( C(s)+C O_{2}(g) \leftrightharpoons \)
\( 2 C O(g), \) the equilibrium pressure is 12
atm. If \( 50 \% \) of \( C O_{2} \) reacts, calculate \( K_{p} \)
A. 1.6 atm
B. 0.16 atm
\( c \cdot 16 \operatorname{atm} \)
D. 160 atm
Subject: Physics
A second harmonic has to be generated in a string if length I stretched between two rigid supports. The points where the string has to be plucked and touched are respectively
A \( \cdot \frac{l}{4}, \frac{l}{2} \)
в. \( \frac{l}{4}, \frac{3 l}{4} \)
c. \( \frac{l}{2}, \frac{l}{2} \)
D. \( \frac{l}{2}, \frac{3 l}{4} \)
Subject: Physics
The maximum angular deflection of the
rod from the vertical after the collision
is
\( ^{\mathbf{A}} \cdot_{\theta}=\cos ^{-1}\left(1-\frac{5 v_{0}^{2}}{16 g l}\right) \)
B. \( \quad \theta=\sin ^{-1}\left(1-\frac{3 v_{0}^{2}}{16 g l}\right) \)
\( \mathbf{c} \cdot_{\theta}=\cos ^{-1}\left(1-\frac{3 v_{0}^{2}}{16 g l}\right) \)
D \( \quad \theta=\sin ^{-1}\left(1-\frac{5 v_{0}^{2}}{16 g l}\right) \)
Subject: Maths
If \( f(x)=\sin ^{-1}\left(\frac{2 \times 3^{x}}{1+9^{x}}\right), \) then \( f^{\prime}\left(-\frac{1}{2}\right) \)
\( ^{\mathrm{A}} \cdot \frac{-\sqrt{3}}{2} \log _{e} \sqrt{3} \)
B. \( \frac{\sqrt{3}}{2} \log _{e} \sqrt{3} \)
c. \( -\sqrt{3} \log _{e} 3 \)
D. \( \sqrt{3} \log _{e} 3 \)
Subject: Chemistry
2,4-hexadiyne \( \left(C_{6} H_{6}\right) \) is allowed to
react with \( L i \) in \( N H_{3}(\text { liq }) . \) The product obtained is treated with 1 equivalent of \( C l_{2} C C l_{4} . \) Which of the following constitutional isomers are possible products?
A . I and II
B. II and II
c. I and IV
D. I and III
Subject: Maths
\begin{tabular}{|ccc} 
If \( \boldsymbol{f}(\boldsymbol{x})= \) & \\
\( \mathbf{1} \) & \( \boldsymbol{x} \) & \( \boldsymbol{x} \) \\
\( \boldsymbol{2} \boldsymbol{x} \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( (\boldsymbol{x}-1) \) \\
\( \boldsymbol{3} \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2}) \) & \( (\boldsymbol{x}+\mathbf{1}) \)
\end{tabular}
then \( f(100) \) is equal to
A.
B.
\( c \cdot 100 \)
D. -100
Subject: Chemistry
An ideal gas whose adiabatic exponent is \( \gamma \) is expanded so that the amount of heat transferred to the gas is equal to the decrease of its internal energy. Molar heat capacity of the gas for this
process is
A \( \cdot \frac{R}{1-\gamma} \)
B. \( \frac{R}{\gamma-1} \)
c. \( R \)
D. \( \frac{n}{2} \)
Subject: Maths
If \( y=A \sin (\omega t-k x), \) then the value of \( \frac{d y}{d x} \)
is
A. \( A \cos (\omega t-k x) \)
B. \( -A \omega \cos (\omega t-k x) \)
c. \( A k \cos (\omega t-k x) \)
D. \( -A k \cos (\omega t-k x) \)
Subject: Maths
The area of a sector of a circle of radius
\( \mathbf{7} \mathrm{cm} \) and central angle \( 120^{\circ} \) is
A \( \cdot 152 \mathrm{cm}^{2} \)
B. \( \frac{154}{3} \mathrm{cm}^{2} \)
c. \( \frac{128}{3} \mathrm{cm}^{2} \)
D. \( 128 \mathrm{cm}^{2} \)
Subject: Maths
At the point \( x=1, \) the function \( f(x)= \)
\( \left\{\begin{array}{ll}x^{3}-1, & 1<x<\infty \\ x-1, & -\infty<x \leq 1\end{array}\right. \)
A. continuous and differentiable
B. Continuous and not differentiable
c. Discontinuous and differentiable
D. Discontinuous and not differentiable
Subject: Chemistry
\( \boldsymbol{p} \boldsymbol{K}_{a} \) values of two acids \( \boldsymbol{A} \) and \( \boldsymbol{B} \) are \( \boldsymbol{4} \)
and \( 5 . \) The strengths of these two acids are related as:
A. acid A is 10 times stronger than acid B
B. strength of acid A : strength of acid \( B=4: 5 \)
c. strength of two acids cannot be compared
D. acid B is 10 times stronger than acid A
Subject: Physics
Mass of the earth has been determined
through
A \( \cdot \) use of Kepler's \( \frac{T^{2}}{R^{3}} \) constancy law
B. sampling the density of earth's crust and using earth's radius.
C. Cavendish's determination of G and using earth's radius and \( g \) at its surface.
D. use of periods of satellites at different heights above earth's surface.
Subject: Maths
What must be added to \( x^{3}+3 x-8 \) to
\( \operatorname{get} 3 x^{3}+x^{2}+6 ? \)
A \( \cdot 2 x^{3}+x^{2}-3 x+14 \)
B \( \cdot 2 x^{2}+x^{2}+14 \)
c. \( 2 x^{3}+x^{2}-6 x-14 \)
D. None of these
Subject: Chemistry
If standard entropies of \( N_{2}, H_{2} \) and
\( N H_{3} \) are \( 60,40,50 J /(K . m o l) \)
respectively and enthalpy of formation of \( N H_{3} \) is \( -30 k J . m o l^{-1}, \) then the
temperature at which reaction for formation of ammonia will be at
equilibrium is:
\( \mathbf{A} \cdot 227^{\circ} C \)
В. \( 477^{\circ} \mathrm{C} \)
c. \( 750^{\circ} \mathrm{C} \)
D. \( 900^{\circ} \mathrm{C} \)
Subject: Maths
The I.F of \( \left(x+2 y^{3}\right) \frac{d y}{d x}=y^{2} \) is
A \( \cdot e^{1 / y} \)
B . \( e^{-1 / y} \)
\( c \cdot y \)
D. \( -1 / y \)
Subject: Physics
A heat engine is supplied with \( 250 \mathrm{kJ} / \mathrm{s} \) of heat at a constant fixed temperature of \( 227^{0} C ; \) the heat is rejected at \( 27^{0} C \)
the cycle is reversible, then what amount of heat is rejected?
A . 24kJ/s
B. 223kJ/s
c. \( 150 k J / \)
D. none of the above
Subject: Chemistry
Assertion
\( H C l \rightarrow H^{+}+C l^{-} \) is an ionization
Reason
The electron is initially shared between both atoms, thus the dissociation event
into ions involves the transfer of an
electron from one atom to the other.
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
The Coefficient of \( x^{n} \) in the expansion of
\( (1+x)(1-x)^{n} \) is
A. \( (n-1) \)
B \( \cdot(-1)^{n-1} n \)
C \( \cdot(-1)^{n-1}(n-1)^{2} \)
D・ \( (-1)^{n}(1-n) \)
Subject: Physics
A conic surface is placed in a uniform electric field \( E \) as shown in Fig. such
that the field is perpendicular to the
surface on the side \( A B \). The base of the
cone is of radius \( R, \) and the height of the
cone is h. The angle of the cone is \( \theta \). Find
the magnitude of the flux that enters
the cone's curved surface from the left
side. Do not count the outgoing flux
\( \left(\theta<45^{\circ}\right) \)
A \( . E R[h \cos \theta+\pi(R / 2) \sin \theta \)
B. \( E R[h \sin \theta+\pi R / 2 \cos \theta] \)
c. \( E R[h \cos \theta+\pi R \sin \theta \)
D. none of these
Subject: Maths
State whether the given statement is
True or False \( \int_{0}^{2} e^{x} d x \) can be represented as
\( 2 \lim _{n \rightarrow \infty} \frac{1}{n}\left[e^{0}+e^{\frac{2}{n}}+e^{\frac{4}{n}}+\ldots \ldots+e^{\frac{2(n-1)}{n}}\right] \)
A. True
B. False
Subject: Chemistry
What is the number of molecules
present in 0.5 mole of hydrogen?
A. \( 3.011 \times 10^{22} \) molecules
B. \( 3.011 \times 10^{23} \) molecules
c. \( 6.022 \times 10^{23} \) molecules
D. \( 3.011 \times 10^{33} \) molecules
Subject: Chemistry
Which of the following statements are
correct for \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \) molecule?
This question has multiple correct options
A. Two \( N \) -bonds are perpendicular to each other
B. Lone pair lying in the orbital which is perpendicular to both \( N \) -bonds
C. The dipole moment value is non zero
D. The direction of dipole moment is from \( N \) to \( H \) -atom
Subject: Maths
Compare the modal ages of two groups
of students appearing for an entrance
test:
\( \begin{array}{llll}\text { Age } & \mathbf{1 6}- & \mathbf{1 8}- & \mathbf{2 0}- & \mathbf{2 2}- \\ \text { (in } & \mathbf{1 8} & \mathbf{2 0} & \mathbf{2 2} & \mathbf{2 4} \\ \text { years) } & & & \end{array} \)
\begin{tabular}{lcccc} 
Group A: & 50 & 78 & 46 & 28 \\
Group B: & 54 & 89 & 40 & 25 \\
\hline
\end{tabular}
Subject: Physics
The moment of inertia of a rod about its
perpendicular bisector is I. When the temperature of the rod is increased by \( \triangle T, \) the increase in the moment of
inertia of the rod about the same axis is
(Here, \( \alpha \) is the coefficient of linear
expansion of the rod)
\( \mathbf{A} \cdot \alpha I \Delta T \)
в. \( 2 \alpha I \Delta T \)
c. \( \frac{\alpha I \Delta T}{2} \)
D. \( \frac{2 I \triangle T}{\alpha} \)
Subject: Chemistry
The correct relationship between free energy change in a reaction and the
corresponding equilibrium constant, \( \boldsymbol{K} \)
is:
A \( \cdot \Delta G^{o}=-R T \ln K \)
В. \( \Delta G=R T l n K \)
c. \( \Delta G=-R T \ln K \)
D. \( \Delta G^{o}= \) R TlnK
Subject: Physics
Consider a jet traveling at \( 1000 \mathrm{km} / \mathrm{hr} \). If the jet shoots a laser in the same direction it is traveling, how fast will the laser be traveling relative to the ground?
A. \( 300,000 \mathrm{km} / \mathrm{sec} \)
B. 300,000 km/sec plus 1000 km/hr
c. \( 300,000 \mathrm{km} / \mathrm{sec} \) minus \( 1000 \mathrm{km} / \mathrm{hr} \)
D. 1000 km/hr minus 300,000 km/sec
E. cannot be determined with information providede
Subject: Biology
Which of the following is translated completely?
I. AUG, UGA, UUA, AAG, AAA
II. AUG, AUA, UUG, CCC, UGA
III. \( A G U, U C C, A G A, C U C, U A A \)
IV. AUG, UAC, AGU, AAC, UAG
A. I and II
B. II and IV
c. I and IV
D. II and III
Subject: Chemistry
The degree of dissociation of water at \( 25^{\circ} \mathrm{C} \) is \( 1.8 \times 10^{-7} \% \) and density is
\( 1.0 g c m^{-3} . \) The ionic constant for water
is:
A \( \cdot 1.0 \times 10^{-14} \)
В. \( 2.0 \times 10^{-16} \)
c. \( 1.0 \times 10^{-16} \)
D. \( 1.0 \times 10^{-8} \)
Subject: Physics
symmetrical container. Four pistons of
equal area \( A \) are used at the four
openings to keep the water in
equilibrium. Now an additional force \( \boldsymbol{F} \)
is applied at each piston. The increase
in the pressure at the center of the
container due to this addition is
Fig. 4.191
\( A \cdot F \)
\( \bar{A} \)
B. \( \underline{2 F} \)
\( \bar{A} \)
c. \( \frac{4 F}{A} \)
\( D \)
Subject: Chemistry
An amount of 0.2 mole of \( A O_{3}^{-} \) gains 1.2
mole of electron in a process. Assuming that there is no change in oxidation state of oxygen, determine the oxidation state of 'A' in product:
\( A \cdot+1 \)
B. -
\( c \cdot 0 \)
\( D \cdot+6 \)
Subject: Maths
In a right triangle having angles of \( 30^{\circ} \)
and \( 60^{\circ}, \) the \( 60^{\circ} \) angle is bisected. What
is the ratio of the segments into which the angle bisector divides the opposite leg?
A . 2: 3
B. 3:
\( c \cdot 1: 2 \)
D. 3:
E. 2: 5
Subject: Maths
The solutions set of inequality \( \cos ^{-1} x<\sin ^{-1} x \) is
A \( \cdot[-1,1] \)
B. \( \left[\frac{1}{\sqrt{2}}, 1\right] \)
c. [0,1]
D. \( \left(\frac{1}{\sqrt{2}}, 1\right] \)
Subject: Maths
Length of the common chord of the
\( \operatorname{circles}(x-1)^{2}+(y+1)^{2}= \)
\( c^{2} \) and \( (x+1)^{2}+(y-1)^{2}=c^{2} \) is
A \( \cdot \frac{1}{2} \sqrt{c^{2}-2} \)
B. \( \sqrt{c^{2}-2} \)
c. \( 2 \sqrt{c^{2}-2} \)
D. \( (c+2) \)
Subject: Physics
A glass of refractive index 1.5 is coated
with a thin layer of thickness of \( t \) of
refractive index 1.8 light of wavelength
\( \lambda \) tavelling at the upper and the lower
surfaes of the layer and the two reflected rays interfere. If \( \boldsymbol{\lambda}=\mathbf{6 4 8 n m} \)
obtain the least value of \( t\left(\operatorname{in} 10^{-8} m\right) \) for
which the rays interfere constructively.
Subject: Physics
A cycle wheel with 64 spokes is rotating with \( \mathrm{N} \) rotations per second at right angles to horizontal component of magnetic field. The induced emf generated between its axle and rim is E. If the number of spokes is reduced to 32 then the value of induced emf will be :
\( A \cdot E \)
B . 2E
c. \( \frac{E}{2} \)
D. \( \frac{E}{4} \)
Subject: Physics
One mole of an ideal monatomic gas undergoes the following four reversible
processes:
Step1 - it is first compressed adiabatically from volume \( 8.0 m^{3} \) to
\( 1.0 m^{3} \)
Step 2 - then expanded isothermally at temperature \( T_{1} \) to volume \( 10.0 m^{3} \)
Step3 - then expanded adiabatically to
volume \( 80.0 m^{3} \)
Step 4 - then compressed isothermally
at temperature \( T_{2} \) to volume \( 8.0 m^{3} \)
Then \( \boldsymbol{T}_{\mathbf{1}} / \boldsymbol{T}_{\mathbf{2}} \) is
A .2
B. 4
\( c .6 \)
D.
Subject: Maths
Let \( \boldsymbol{y}=\sin ^{-1} \boldsymbol{x}, \) then find \( \left(\mathbf{1}-\boldsymbol{x}^{2}\right) \boldsymbol{y}_{2} \)
\( \boldsymbol{x} \boldsymbol{y}_{1} \)
Where \( y_{1} \) and \( y_{2} \) denote the first and
second order derivatives respectively.
\( \mathbf{A} \cdot \mathbf{1} \)
в. - 1
c. 0
D.
Subject: Maths
\( \int \sqrt{\frac{x}{x-1}} d x, x \in(0, \pi / 2) \) equals
A \( \cdot \sqrt{x(x-1)}+\log (\sqrt{x}+\sqrt{x-1})+c \)
B . \( \sqrt{x(x-1)}-\log (\sqrt{x}+\sqrt{x-1})+c \)
c. \( \sqrt{x(x-1)}+\log (\sqrt{x}-\sqrt{x-1})+c \)
D. \( \sqrt{x(x+1)}-\log (\sqrt{x}-\sqrt{x+1})+c \)
Subject: Chemistry
The maximum amount of sulphur is
given by:
\( \mathbf{A} \cdot A g S\left(K_{s p}=6 \times 10^{-29}\right) \)
B. \( C u S\left(K_{s p}=4 \times 10^{-27}\right) \)
C. \( P b S\left(K_{s p}=8 \times 10^{-28}\right) \)
D. \( Z n S\left(K_{s p}=8 \times 10^{-30}\right) \)
Subject: Chemistry
The fraction of collisions that posses
the energy \( \boldsymbol{E}_{\boldsymbol{a}} \) is given by:
A \( \cdot f=e^{\frac{-E q}{R T}} \)
B . \( f=e^{\frac{E}{m}} \)
C . \( f=e^{-E a . R T} \)
D. \( f=e^{\text {Ea. } R T} \)
Subject: Physics
The primary winding of transformer has 500 turns whereas its secondary has \( \mathbf{5 0 0 0} \) turns. The primary is connected to an A.C supply of \( 20 V, 50 H z \). The secondary will have an output of
A. \( 2 V, 5 H z \)
в. \( 200 V, 500 H z \)
\( \mathbf{c} \cdot 2 V, 50 H z \)
D. \( 200 V, 50 H z \)