AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
\( H_{2} O_{2} \) solution of \( 0.2 \mathrm{N} \) is prepared and
after 5 hours it is titrated with \( K M n O_{4} \)
solution. If the volume of the \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
solution taken is half of the volume of
\( K M n O_{4} \) used (in acidic medium), find
the molarity of \( K M n O_{4} \) solution?
\( \mathbf{A} \cdot 0.4 \mathrm{M} \)
в. 0.01 М
c. 0.02 М
D. 0.2 M
Subject: Physics
The distance of two planets from the Sun are \( 10^{13} \) and \( 10^{12} \mathrm{m}, \) respectively. The ratio
of time periods of these two planets is
A. \( \frac{1}{\sqrt{10}} \)
B. 100
c. \( \frac{10}{\sqrt{10}} \)
D. \( \sqrt{10} \)
Subject: Physics
The output of the combination of the
gates shown in the figure is
\( \mathbf{A} \cdot A+A \cdot B \)
B . \( (A+B) A+\bar{B} \)
c. \( (A . B)+(\bar{A} . \bar{B}) \)
D. \( (A+B)(\overline{A . B}) \)
Subject: Physics
An object is placed on the principal axis of a concave mirror at a distance of 60
\( \mathrm{cm} . \) If the focal length of the concave mirror is \( 40 \mathrm{cm} \) then determine the magnification of the obtained image.
\( A \cdot 4 \)
B. - -
\( c \cdot-4 \)
\( D \cdot+2 \)
Subject: Maths
If
\( \log _{10} 2, \log _{10}\left(2^{x}-1\right) \) and \( \log _{10}\left(2^{x}+3\right) \)
be three consecutive terms of an A.P.,
then
\( \mathbf{A} \cdot x=0 \)
B. \( x=1 \)
C \( . x=\log _{2} 5 \)
D. \( x=\log _{10} 2 \)
Subject: Chemistry
The oxidation number of phosphorus in
\( \boldsymbol{P O}_{4}^{3-}, \boldsymbol{P}_{4} \boldsymbol{O}_{10} \) and \( \boldsymbol{P}_{2} \boldsymbol{O}_{7}^{4-} \) is:
\( A \cdot+3 \)
\( B \cdot+2 \)
\( c \cdot-3 \)
\( D \cdot+5 \)
Subject: Maths
Assertion
Let \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x} \)
Statement I \( \boldsymbol{f} \) is not a polynomial
function
Reason
Statement II \( n \) th derivative of \( f(x), \) w.r.t.
\( x \) is not a zero function for any positive
integer \( n \)
A. Statement I is true,Statement II is also true; Statement II is the correct explanation of Statement
B. Statement I is true,Statement II is also true; Statement II is not the correct explanation of Statement
c. Statement l is true,Statement II is false
D. Statement I is false,Statement II is true
Subject: Maths
Consider the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}2 \boldsymbol{x}-\mathbf{1}, & \boldsymbol{0} \leq \boldsymbol{x}<\mathbf{2} \\ \boldsymbol{x}+\boldsymbol{a} & \boldsymbol{2} \leq \boldsymbol{x} \leq \mathbf{4} \\ \boldsymbol{3} \boldsymbol{x}+\boldsymbol{b} & \boldsymbol{4}<\boldsymbol{x} \leq \mathbf{6}\end{array}\right. \)
(i) Find \( f(2-) \) and \( f(2+) \)
(ii) Find \( a \) if \( f \) is continuous at \( x=2 \)
(iii) Find \( b \) if \( f \) is continuous on [0,6]
Subject: Chemistry
When 280 gm of ethylene polymerises to polyethene according to the equation.
\( \boldsymbol{n} \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \longrightarrow-\left(\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}\right)_{n} \)
The weight and mole of polyethylene formed will be:
A \( .280,10 n \)
в. \( \frac{280}{n}, \) n
c. \( \frac{280}{n}, \) 280
D. \( 280, \frac{10}{n} \)
Subject: Maths
Solve :
\( \cot ^{-1}\left(\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}\right) \)
A \( \cdot_{\pi}-\frac{x}{2} \)
в. \( _{\pi+\frac{x}{2}} \)
c. \( \frac{x}{2} \)
D . \( 2 \pi \)
Subject: Physics
A body with area \( A \) at a material
temperature \( \boldsymbol{T} \) and emissivity \( \boldsymbol{e}=\mathbf{0 . 6} \) is kept inside a spherical black body. what will be the maximum energy radiated
per second?
\( \mathbf{A} \cdot 0.60 \sigma \mathrm{AT}^{4} \)
B . \( 1.00 \sigma \) AT \( ^{4} \)
c. \( 0.80 \sigma \) АТ \( ^{4} \)
D. \( 0.40 \sigma \) АТ \( ^{4} \)
Subject: Physics
A spherical mirror has radius of curvature equal to \( 50 \mathrm{cm} \). Find the value
of focal length.
\( \mathbf{A} \cdot 50 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
\( \mathrm{c} \cdot 25 \mathrm{cm} \)
D. \( 100 \mathrm{cm} \)
Subject: Physics
A carbon resistance has a following
colour code. What is the value of the
resistance?
A \( .1 .64 M \Omega \pm 5 \% \)
B. \( 530 k \Omega \pm 5 \% \)
\( c \cdot 64 k \Omega \pm 10 \% \)
D. \( 5.3 M \Omega \pm 5 \% \)
Subject: Physics
A rope, under a tension of \( 200 N \) and
fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by \( : \boldsymbol{y}=\mathbf{0 . 1} \sin \left(\frac{\pi x}{2}\right) \sin 12 \pi t \)
Where \( x=0 \) at one end of the rope, \( x \) is in meters and \( t \) is in seconds. The length
of the rope is
Subject: Physics
Consider a planet in some system
which has a mass double the mass of
the earth and density equal to the average density of the earth. If an object weighs \( \mathrm{W} \) on the earth, then its weight on the planet is:
\( \mathbf{A} \cdot W \)
в. \( 2 W \)
c. \( \frac{w}{2} \)
D. \( 2^{1 / 3} W \)
Subject: Chemistry
Statement (1) : Composition and molecular structure of the reactants
can be changed by having a chemica
change
BECAUSE
Statement (2): It is said to be a
chemical reaction when new
substances and new bonds are formed
and old bonds are broken.
\( A \cdot(1) \) is true
(2) is true, (2) is the correct explanation of
(1)
B. (1) is false, (2) is true
c. (1) is true,
(2) is true
D. (1) is false,
(2) is false
\( E .(1) \) is true,
(2) is false
Subject: Chemistry
Assertion
Glycerol is purified by distillation under
reduced pressure.
Reason
Method of distillation under reduced
pressure is used to purify liquids having very high boiling points and those, which decompose at or below their boiling point.
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
Assertion: Zinc is coated on the iron to
prevent corrosion in a process called galvanization. Reason: Zinc is a stronger reducing agent than iron and is more easily oxidized than iron.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Physics
A cyclist moves in such a way that he
takes \( 72^{\circ} \) turn towards left after
travelling \( 200 \mathrm{m} \) in straight line. What is the displacement when he takes just takes fourth turn?
A. zero
B. 600 \( m \)
c. \( 400 \mathrm{m} \)
D. 200 \( \mathrm{m} \)
Subject: Chemistry
Magnetic moment \( 2.84 B M \) is given by
(Atomic numbers : \( \boldsymbol{N} \boldsymbol{i}=\mathbf{2 8}, \boldsymbol{T} \boldsymbol{i}= \)
\( \mathbf{2 2}, \mathbf{C r}=\mathbf{2 4}, \mathbf{C o}=\mathbf{2 7}) \)
A \( \cdot C r^{2} \)
в. \( C o^{2} \)
c. \( N i^{2} \)
D. \( T i^{3} \)
Subject: Maths
Find the range of \( \boldsymbol{f}(\boldsymbol{x})= \) \( \cos ^{-1} \sqrt{\log _{[x]} \frac{|x|}{x}}, \) where [.]denotes the
greatest integer.
A \( \cdot\left\{\frac{\pi}{2}\right\} \)
в. \( \left\{\frac{\pi}{4}\right\} \)
\( c \cdot\left\{\frac{\pi}{6}\right\} \)
D. \( \left\{\frac{\pi}{8}\right\} \)
Subject: Chemistry
Assertion
The purple colour of \( K M n O_{4} \) is due to
the charge transfer transition.
Reason
The intense colour in most of the
transition metal complexes is due to
\( \boldsymbol{d}-\boldsymbol{d} \) transition.
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 flat, square surface with sides of length L is described by the equations. \( \boldsymbol{x}=\boldsymbol{L}, \mathbf{0} \leq \boldsymbol{y} \leq \boldsymbol{L}, \mathbf{0} \leq \boldsymbol{z} \leq \boldsymbol{L} \)
The electric flux through the square due to a positive point charge q located at the origin( \( x=0, y=0, z=0 \) ) is
A. \( \frac{q}{4 \varepsilon_{o}} \)
в. \( \frac{q}{6 \varepsilon_{o}} \)
c. \( \frac{q}{24 \varepsilon_{o}} \)
D. \( \frac{q}{48 \varepsilon_{o}} \)
Subject: Physics
Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0. What is the maximum
tension,that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed \( 6.9 \times 10^{7} \) pa ?
Assume that each rivet is to carry onequarter of the load
\( A \cdot 3 \)
в. 2.5
\( c \cdot 4 \)
D. 5
Subject: Physics
Two particles \( A \) and \( B \) are placed as
shown in figure. The particle A on the
top of a tower of height H is projected horizontally with a velocity u and the particle B is projected along the horizontal surface towards the foot of
the tower, simultaneously. When particle A reaches at ground, it simultaneously hits particle B. Then the speed of projected particle B is:(neglect any type of friction)
A \( \cdot d \sqrt{\frac{g}{2 H}} \)
B. \( d \sqrt{\frac{g}{2 H}}-u \)
\( c \)
\[
\sqrt[d]{\frac{g}{2 H}+u}
\]
D.
Subject: Chemistry
The molar conductivity of \( N a C l, H C l \)
and \( C H_{3} C O O N a \) at infinite dilution
are 126.45,426.16 and \( 91 S c m^{2} m o l^{-1} \)
respectively. The molar conductivity of
\( C H_{3} C O O H \) at infinite dilution is:
A \( .201 .28 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
B. \( 698.28 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
c. \( 390.71 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
D. \( 540.48 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
Subject: Physics
At what temperature the linear kinetic energy of a gas molecule will be equal to that of an electron accelerated through a potential difference of 10 volt?
A . \( 77.3 \times 10^{3} \mathrm{K} \)
B. 38.65 x 10 \( ^{3} \) к
c. \( 19 . \times 10^{3} \mathrm{K} \)
D. 273 K
Subject: Physics
Which of the following represent the number 300,000,000
\( A \cdot 3 \times 10^{6} \)
B . \( 3 \times 10^{7} \)
\( c \cdot 3 \times 10^{8} \)
D. \( 3 \times 10^{9} \)
E . \( 3 \times 10^{-9} \)
Subject: Biology
\( \boldsymbol{K}_{(\boldsymbol{5})} \boldsymbol{C}_{\boldsymbol{5}} \boldsymbol{A}_{(\infty)} \boldsymbol{G}_{(\boldsymbol{5}-\infty)} \) floral formula is
related is to which of the following
family?
A. Liliaceae
B. Malvaceae
c. cruciferae
D. Leguminosae
Subject: Chemistry
Assertion
With \( B r_{2}-H_{2} O, \) phenol give \( s 2,4,6 \)
tribromophenol but with \( B r-C S_{2}, \) it
gives 4 -bromophenol as the major
product.
Reason
In water ionization of phenol is
enhanced but in \( C S_{2}, \) it is greatly
suppressed.
Read the above assertion and reason
and choose the correct option regarding
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. Assertion is incorrect but Reason is correct
Subject: Chemistry
The standard electrode potentials
\( \left(\boldsymbol{E}_{\boldsymbol{M}^{+} / M}^{o}\right) \) of four metals \( \mathbf{A}, \mathbf{B}, \mathbf{C} \) and \( \mathbf{D} \)
are \( -1.2 \vee, 0.6 \vee, 0.85 \mathrm{V} \) and \( -0.76 \mathrm{V} \)
respectively. The increasing sequence of deposition of metals on applying potential is :
\( A \cdot A, C, B, D \)
B. B, D, C, A
c. \( c, B, D, A \)
D. D, A, B, C
Subject: Physics
n the circuit shown \( E, F, G \) and \( H \) are cells of e.m.f. \( 2 V, 1 V, 3 V \) and \( 1 V \) respectively and their resistances are \( 2 \Omega, 1 \Omega, 3 \Omega \) and \( 1 \Omega \) respectively. Then
choose the correct alternative
A \( \cdot V_{D}-V_{B}=-2 / 13 \mathrm{V} \)
B . \( V_{D}-V_{B}=2 / 13 \mathrm{V} \)
c. \( V_{G}=21 / 13 \) V
Subject: Physics
The radius and density of two
artificial satellites are \( \boldsymbol{R}_{1}, \boldsymbol{R}_{2} \) and \( \boldsymbol{\rho}_{1} \)
\( \rho_{2} \) respectively. The ratio of
accelerations due to gravity on them will be:
\( \mathbf{A} \cdot \frac{R_{2} \rho_{2}}{R_{1} \rho_{1}} \)
в. \( \frac{R_{1} \rho_{2}}{R_{2} \rho_{1}} \)
c. \( \frac{R_{1} \rho_{1}}{R_{2} \rho_{2}} \)
D. \( \frac{R_{2} \rho_{1}}{R_{1} \rho_{2}} \)
Subject: Chemistry
The number of protons, neutrons and
orbital electrons in particles form
letters \( A \) to \( F \) are given in the following
table.
\begin{tabular}{llll} 
Particle & Protons & Neutrons & Electrons \\
\( A \) & 3 & 4 & 2 \\
\( B \) & 9 & 10 & 10 \\
\( C \) & 12 & 12 & 12 \\
\( E \) & 17 & 20 & 17 \\
\( F \) & 18 & 22 & 18 \\
\hline
\end{tabular} Choose from the table the letters that
represent an atom of inert gas.
\( \mathbf{A} \cdot B \) and \( F \)
B. \( F \)
\( \mathbf{c} \cdot A \) and \( B \)
D. \( A \)
Subject: Maths
If \( a x+b\left(\sec \left(\tan ^{-1} x\right)\right)=c \) and \( a y+ \)
\( b\left(\sec \left(\tan ^{-1} y\right)\right)=c, \) then the value of
\( \frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{1}-\boldsymbol{x} \boldsymbol{y}} \) is,
A \( \cdot \frac{2 a b}{a^{2}-c^{2}} \)
в. \( \frac{2 a c}{a^{2}-c^{2}} \)
c. \( \frac{c^{2}-b^{2}}{a^{2}+b^{2}} \)
D. none of these
Subject: Physics
In an AC generator, a coil with \( N \) turns,
all of the same area \( A \) and total
resistance \( \boldsymbol{R}, \) rotates with frequency in
a magnetic field \( B \). The maximum
value of emf generated in the coil is:
\( \mathbf{A} . N . A . B \)
в. \( N . A . B . R \)
\( ^{\mathbf{C}} \cdot \frac{1}{10} N \cdot A \cdot B \)
D. \( \frac{1}{10} N . A . B . R \)
Subject: Chemistry
A single electron orbits around a stationary nucleus of charge +Ze where \( \mathrm{Z} \) is atomic number and 'e' is the
magnitude of the electric charge. The hydrogen like species required 47.2eV to excite the electron from the second Boh
orbit to the third Bohr orbit. Find
(i) the value of \( Z \) and give the hydrogen like species formed.
(ii) the kinetic energy and potential energy of the electron in the first Bohr
orbit.
Subject: Maths
If the projections of the line segment \( A B \) on the coordinate axes are 2,3,6
then the square of the sine of the angle made by \( \boldsymbol{A B} \) with \( \boldsymbol{x}=\mathbf{0}, \) is
A \( \cdot \frac{3}{7} \)
B. \( \frac{3}{49} \)
\( c \cdot \frac{4}{7} \)
D. \( \frac{40}{49} \)
Subject: Chemistry
Assertion
\( K, R b \) and \( C s \) form superoxides.
Reason
The stability of the superxides
increases from ' \( K^{\prime} \) to \( ^{\prime} C s^{\prime} \) due to
decrease in lattice 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. Both Assertion and Reason are incorrect
Subject: Physics
Mass per unit area of a disc of inner radius 'a' and outer radius 'b' is given by \( \left(\frac{\sigma_{0}}{r}\right), r \) distance from center. Its radius of gyration w.r.t. axis of rotation passing through center and perpendicular to plane is
A. \( \sqrt{\frac{b^{4}-a^{4}}{3\left(b^{2}-a^{2}\right.}} \)
B. \( \sqrt{\frac{b^{3}-a^{3}}{3(b-a)}} \)
c. \( \sqrt{\frac{b^{3}-a^{3}}{5(b-a)}} \)
D. \( \sqrt{\frac{b^{4}-a^{4}}{5\left(b^{2}-a^{2}\right.}} \)
Subject: Maths
Find the value of \( \theta \) if \( \frac{(3+2 i \sin \theta)}{(1-2 i \sin \theta)} \) is
purely real or purely imaginary.
A \( \cdot \theta=n \pi \pm \frac{\pi}{6}, n \in Z \)
в. \( \theta=n \pi \pm \frac{\pi}{2}, n \in Z \)
c. \( \theta=n \pi \pm \frac{\pi}{3}, n \in Z \)
D. \( \theta=n \pi \pm \frac{\pi}{4}, n \in Z \)
Subject: Maths
The area of an equilateral triangle of
side ' \( a^{\prime} \) feet is increasing at the rate of 4 sq. ft./ sec. The rate at which the perimeter is increasing is
A \( \cdot \frac{3 \sqrt{8}}{2} \)
B. \( \frac{8 \sqrt{3}}{a} \)
c. \( \frac{\sqrt{3}}{a} \)
D. \( \frac{2 \sqrt{3}}{a} \)
Subject: Chemistry
What is the value of electron gain
enthalpy of \( N a^{+} \) if \( I E_{1} \) of \( N A=5.1 e V \)
\( ? \)
A. \( -5.1 e V \)
В. \( -10.2 e V \)
\( \mathbf{c} .+2.55 e V \)
D. \( +10.2 e V \)
Subject: Physics
The circuit given below is for the operation of an industrial fan. The resistance of the fan is 3 ohm. The
regulator provided with the fan is a
fixed resistor and a variable resistor in
parallel. Under what value of the variable resistance given, power transferred to the fans will be
maximum? The power source of the fan
is a dc source with internal resistance
of 6ohm
A . \( 3 \Omega \)
B.
\( c \cdot \alpha \)
D. 6.9
Subject: Maths
If \( D=\left|\begin{array}{cc}3 \sqrt{5} & 6 \\ 5 & m\end{array}\right|=0 \)
Find the value of \( \boldsymbol{m} \)
A . \( \sqrt{5} \)
B. \( 4 \sqrt{5} \)
\( c \cdot \sqrt{3} \)
D. \( 2 \sqrt{5} \)
Subject: Maths
If the line joining \( \boldsymbol{A}(\mathbf{1}, \mathbf{3}, \mathbf{4}) \) and \( \boldsymbol{B} \) is divided by the point (-2,3,5) in the ratio \( 1: 3, \) then \( B \) is
A. (-11,3,8)
(年) (-1,3,8)
в. (-11,3,-8)
D. (13,6,-13)
Subject: Maths
If \( \boldsymbol{\alpha}=\boldsymbol{2} \boldsymbol{s} \boldsymbol{i} \boldsymbol{n}^{-1}(\boldsymbol{2} / \boldsymbol{3}) \) and \( \boldsymbol{\beta}=\boldsymbol{2} \boldsymbol{t} \boldsymbol{a} \boldsymbol{n}^{-1} \boldsymbol{9} \)
then \( 80 \operatorname{cosec}^{2} \alpha+81 \operatorname{cosec}^{2} \beta \) is equal
to
Subject: Maths
Dividing \( f(z) \) by \( z-i, \) we obtain the
remainder \( i \) and dividing it by \( z+i, \) we
get the remainder \( 1+i, \) then remainder
upon the division of \( f(z) \) by \( z^{2}+1 \) is
A \( \cdot \frac{1}{2}(z+1)+i \)
B \( \cdot \frac{1}{2}(i z+1)+i \)
c. \( \frac{1}{2}(i z-1)+i \)
D \( \cdot \frac{1}{2}(z+i)+1 \)
Subject: Physics
Find the speed of the proton at the final
point.
A \( \cdot 2.7 \times 10^{-6} \mathrm{m} / \mathrm{s} \)
В. \( 3 \times 10^{8} m / s \)
c. \( 3 \times 10^{-8} m / s \)
D. \( 2.7 \times 10^{6} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
The cell,
\( Z n\left|Z n^{2+}(1 M) \| C u^{2+}(1 M)\right| C u, \) was
allowed to be completely discharged at 298 K. The relative concentration of \( Z n^{2+} \) to \( C u^{2+}\left(\frac{\left[Z n^{2+}\right]}{\left[C u^{2+}\right]}\right) \) is :
\( \left[\boldsymbol{E}_{c e l l}^{0}=\mathbf{1 . 1 0} \boldsymbol{V}\right] \)
\( \mathbf{A} \cdot 9.65 \times 10^{4} \)
B . antilog (24.08)
c. 37.3
D. \( 10^{37.3} \)
Subject: Chemistry
Assertion: \( B_{2} \) molecule is diamagnetic.
Reason: The highest occupied molecular orbital is of \( \sigma \) type.
A. Assertion and Reason are true and the Reason is a correct explanation of the Assertion
B. Assertion and Reason are true but Reason is not a correct explanation of the Assertion
c. Assertion is true but Reason is false
D. Both the Assertion and Reason are false
E. Assertion is false but the Reason is true
Subject: Physics
The figure shows the cross-section of
two long coaxial tubes carrying equal
currents \( I \) in opposite directions. If \( B_{1} \)
and \( B_{2} \) are magnetic fields at point
and \( 2, \) as shown in figure then
\( \mathbf{A} \cdot B_{1} \neq 0 ; B_{2}=0 \)
B . \( B_{1}=0 ; B_{2}=0 \)
c. \( B_{1} \neq 0 ; B_{2} \neq 0 \)
D. \( B_{1}=0 ; B_{2} \neq 0 \)
Subject: Chemistry
The following are some statements about
galvanic cell.
1) The cell reaction will be obtained by
summing up the reactions in the two half
cells.
2) \( E^{0} \) cell \( =E^{0} \) cathode \( -E_{\text {Anode }}^{0} \)
3) \( E_{C e l l}^{0}=E_{\text {reduction electrode }}^{0}-E_{\text {oxidation electrode }}^{0} \)
4) \( E^{0} \) Cell \( =E^{0}_{L . H . E}-E^{0} R . H . E \)
The correct combination is :
A. only I and III are correct
B. only I and II are correct
C. only I,II,III are correct
D. all are correct
Subject: Maths
\( A B C D \) is a trapezium in which \( A B \| \) \( D C, A B=16 \mathrm{cm} \) and \( D C=24 \mathrm{cm} . \) If
\( E \) and \( F \) are respectively the midpoints of \( A D \) and \( B C, \) then \( a r(A B F E)= \) \( \frac{9}{11} a r(E F C D) \)
A . True
B. False
Subject: Biology
Growth in human brain from new born
to adult is
A. \( 100 \mathrm{gm} \) to \( 1 \mathrm{kg} \)
B. \( 400 \mathrm{gm} \) to \( 1.4 \mathrm{kg} \)
c. \( 0.2-1.4 \mathrm{kg} \)
D. 1.4 to 2.4 kg
Subject: Maths
If \( 49 x^{2}-b=\left(7 x+\frac{1}{2}\right)\left(7 x-\frac{1}{2}\right), \) then
the value of \( b \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Maths
The solution of the equation \( \sin ^{-1}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)=\boldsymbol{x}+\boldsymbol{y} \) is
A \( \cdot \tan (x+y)+\sec (x+y)=x+C \)
B \cdot \( \tan (x+y)-\sec (x+y)=x+C \)
C \( \cdot \tan (x+y)+\sec (x+y)+x+C=0 \)
D. None of the above
Subject: Maths
If \( z_{1} \) and \( z_{2} \) are two complex number
such that \( \operatorname{lm}\left(z_{1}=z_{2}\right)=0=\operatorname{lm}\left(z_{1} z_{2}\right) \)
then
B. \( z_{1}=\bar{z}_{2} \)
\( \mathbf{c} \cdot z_{1}=-z_{2} \)
D. \( z_{1}=-\bar{z}_{2} \)
Subject: Physics
A driver takes 0.3 s to fully apply the brakes of truck. The truck moving with velocity of \( 54 \mathrm{km} / \mathrm{h} \) stops in \( 20 \mathrm{s} \) with a
deceleration of \( 6 m / s^{2} . \) Find the distance for where the driver must
apply the brakes without collision from the first obstacle?
Subject: Physics
In Young's double slit experiment the distance d between the slits \( S_{1} \) and \( S_{2} \)
is \( 1 \mathrm{mm} \). What should the width of each
slit be \( \operatorname{so~as~to~obtain~} 10^{t h} \) maxima of
the double slit pattern within the central maximum of the single slit
pattern?
A. \( 0.9 \mathrm{mm} \)
B. 0.8 mm
\( c .0 .2 \mathrm{mm} \)
D. 0.6 mm
Subject: Maths
If the points \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right) \) and \( \left(x_{3}, y_{3}\right) \) are collinear, show that \( \sum\left(\frac{\boldsymbol{y}_{1}-\boldsymbol{y}_{2}}{\boldsymbol{x}_{1} \boldsymbol{x}_{2}}\right)=\mathbf{0}, \) i.e
\( \frac{\boldsymbol{y}_{1}-\boldsymbol{y}_{2}}{\boldsymbol{x}_{1} \boldsymbol{x}_{2}}+\frac{\boldsymbol{y}_{2}-\boldsymbol{y}_{3}}{\boldsymbol{x}_{2} \boldsymbol{x}_{3}}+\frac{\boldsymbol{y}_{3}-\boldsymbol{y}_{1}}{\boldsymbol{x}_{3} \boldsymbol{x}_{1}}=0 \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{x-2}{x^{2}-3 x+2} & x \in R-\{1,2\} \\ 2 & x=1 \\ 1 & x=2\end{array}\right. \)
then \( \lim _{x \rightarrow 2} \frac{f(x)-f(2)}{x-2} \) is
\( A \)
B.
c. 1
\( D \cdot-\frac{1}{2} \)
Subject: Maths
A lot of contains 20 articles. The
probability that the lot contains exactly
2 defective articles is 0.4 and the
probability that the lot contains exactly 3 defective articles is \( 0.6 . \) Articles are
drawn from the lot at random one by one without replacement and are tested till all defective articles are found. What is
the probability that the testing procedure ends at the twelfth testing?
A \( \cdot \frac{99}{1900} \)
в. \( \frac{99}{950} \)
c. \( \frac{198}{1900} \)
D. \( \frac{99}{1000} \)
Subject: Physics
A wheel of mass \( 10 k g \) and radius \( 0.2 m \)
is rotating at an angular speed of 100rpm, when the motion is turned off Neglecting the friction at the axis, the force that must be applied tangentially to the wheel to bring it to rest in 10 rev is approximately o. \( x N \). Find \( x \). Assume
wheel to be a disc.
Subject: Physics
From a disc of radius \( R \) and mass \( M, \) a
circular hole of diameter \( R \), whose rim
passes through the centre is cut. What is the moment of inertia of the
remaining part of the disc about a perpendicular axis, passing through the centre?
\( ^{A} \cdot \frac{9 M R^{2}}{32} \)
в. \( \frac{15 M R^{2}}{32} \)
c. \( \frac{13 M R^{2}}{32} \)
D. \( \frac{11 M R^{2}}{32} \)
Subject: Physics
A swimmer's speed in the direction of
flow of river is \( 16 k m h^{-1} . \) Against the
direction of flow of river, the swimmer's
speed is \( 8 k m h^{-1} \) Calculate the
swimmer's speed in still water and the velocity of flow of the river.
\( \mathbf{A} \cdot 12 k m / h, 4 k m / h \)
B. \( 10 k m / h, 3 k m / h \)
c. \( 10 k m / h, 4 k m / h \)
D. \( 12 k m / h, 3 k m / h \)