AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A parallel beam of diameter \( d \) is
incident on air-glass interface as shown in figure. The diameter of refracted light
beam is:
\( \left(\boldsymbol{d}=\mathbf{3} \boldsymbol{m} \boldsymbol{m}, \boldsymbol{\theta}=\mathbf{4} \mathbf{5}^{\mathbf{0}} \text { and } \frac{\boldsymbol{n}_{\boldsymbol{g} \operatorname{lass}}}{\boldsymbol{n}_{\boldsymbol{a} i \boldsymbol{r}}}=\frac{\boldsymbol{3}}{\boldsymbol{2}}\right) \)
\( A \cdot \sqrt{12} m m \)
В. \( \sqrt{14} \) тт
\( c \cdot \sqrt{6} m m \)
D. \( 4.5 \mathrm{mm} \)
Subject: Physics
A force acts on a \( 20 g \) particle in such a
way that the position of the particle as a function of time is given by \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}- \)
\( 4 t^{2}+t^{3}, \) where \( x \) is in meters and \( t \) is in
seconds. The work done during the first \( 4 \sec \) is:
A . \( -1.6 .5 \)
в. \( -1600 J \)
c. 2.6 .5
D. \( 1600 J \)
Subject: Physics
In a situation, a board is moving with a
velocity \( v \) with respect to earth, while a
man A and man B are running with a
velocity \( 2 v \) with respect to earth and
both men are running from the opposite
ends of the board at the same time, as
shown. Length of the board is \( L \). If they
meet after time \( \boldsymbol{T}, \) then
This question has multiple correct options
A. value of \( \mathrm{T} \) is \( \mathrm{L} / 4 \mathrm{v} \)
B. value of \( T \) is \( L / 2 v \)
C. Displacement of man B with respect to board in time \( T \) is \( 3 L / 4 \)
D. Displacement of man A with respect to board in time \( T \) is L/4
Subject: Maths
The solution of the D.E. \( \left(x^{3}-\right. \)
\( \left.\mathbf{3} \boldsymbol{x} \boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{x}=\left(\boldsymbol{y}^{3}-\boldsymbol{3} \boldsymbol{x}^{2} \boldsymbol{y}\right) \boldsymbol{d} \boldsymbol{y}, \) is:
A \( \cdot y^{2}-x^{2}=c\left(y^{2}+x^{2}\right)^{2} \)
B . \( y^{2}-x^{2}=\left(y^{2}+x^{2}\right)^{2} \)
C \( \cdot y^{2}+x^{2}=c\left(y^{2}-x^{2}\right)^{2} \)
D. \( c\left(y^{2}+x^{2}\right)=\left(y^{2}-x^{2}\right)^{2} \)
Subject: Maths
Resolve \( \frac{x}{(1+x)\left(1+x^{2}\right)^{2}} \) into partial
fractions.
A \( \cdot \frac{-1}{4(1+x)}+\frac{(x-1)}{4\left(1+x^{2}\right)}+\frac{(x+1)}{2\left(1+x^{2}\right)^{2}} \)
B. \( \frac{1}{4(1+x)}+\frac{(x-1)}{4\left(1+x^{2}\right)}+\frac{(x+1)}{\left(1+x^{2}\right)^{2}} \)
C \( \frac{1}{2(1+x)}+\frac{(x-1)}{2\left(1+x^{2}\right)}+\frac{(x+1)}{2\left(1+x^{2}\right)^{2}} \)
D \( \frac{1}{4(1+x)}-\frac{(x-1)}{4\left(1+x^{2}\right)}+\frac{(x+1)}{2\left(1+x^{2}\right)^{2}} \)
Subject: Maths
Suppose \( f^{\prime}(x) \) exists for each \( x \) and
\( \boldsymbol{h}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{x})-(\boldsymbol{f}(\boldsymbol{x}))^{2}+(\boldsymbol{f}(\boldsymbol{x}))^{3} \) for
every real number \( x \). Then
This question has multiple correct options
A. \( h \) is increasing whenever fis increasing
B. \( h \) is increasing whenever fis decreasing
c. \( h \) is decreasing whenever fis decreasing
D. nothing can be said in general.
Subject: Physics
Assertion
A particle is moving along x-axis. The resultant force \( \boldsymbol{F} \) acting on it at
position \( x \) is given by \( F=-a x-b \)
Where \( a \) and \( b \) are both positive constants. The motion of this particle is
not SHM
Reason
In SHM, restoring force must be proportional to the displacement from mean position.
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 parallel beam of monochromatic light is incident on one face of an equilateral
prism the angle of incidence being \( 55^{\circ} \)
The angle of emergence of the beam
from the other face is \( 46^{\circ} . \) The angle of
minimum deviation is :
\( \mathbf{A} \cdot<41^{\circ} \)
B. equal to \( 41^{\circ} \)
\( \mathbf{c} \cdot>41^{\circ} \)
\( \mathrm{D} \cdot \geq 41^{\circ} \)
Subject: Maths
If \( a x^{2}+b x+6=0 \) does not have two
distinct real roots, where \( \boldsymbol{a} \in \boldsymbol{R}, \boldsymbol{b} \in \boldsymbol{R} \)
then the least value of \( 3 a+b \) is
A .4
B. - 1
\( c .1 \)
D. - 2
Subject: Biology
Assertion
In imbricate aestivation, out of five
petals, one is completely internal, one is completely external and in each of the
remaining three petals, one margin is
internal and the other is external.
Reason

Ascending imbricate aestivation is found in Cassia and Gulmohur.
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
Let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}]^{2}+[\boldsymbol{x}+\mathbf{1}]-\boldsymbol{3}, \) where \( [\boldsymbol{x}] \)
is greatest integer less than or equal to
\( x, \) then
This question has multiple correct options
A. \( f(x) \) is a many one and into function
B. \( f(x)=0 \) for infinite number of values of \( x \)
c. \( f(x)=0 \) for only two real values
D. None of these
Subject: Physics
Consider a compound slab consisting of two different materials having equal thicknesses and thermal conductivities
\( K \) and \( 2 K, \) respectively.The equivalent thermal conductivity of the slab is
A \( \cdot 2 / 6 K \)
B. \( \sqrt{2} \) к
\( c .3 K \)
D. \( 4 / 3 K \)
Subject: Maths
The annual salaries of employees in a large company are approximately normally distributed with a mean of \( \mathbf{5 0}, \mathbf{0 0 0} \) and a standard deviation of \( 20,000 . \) What percent of people earn
between 45,000 and \( 65,000 ? \)
A . \( 56.23 \% \) \%
B . \( 47.4 \% \)
c. \( 37.2 \% \)
D. 38.56\%
Subject: Maths
The curved surface area of a
hemisphere of diameter 2 r is
\( \begin{array}{l}\text { A } 2 \pi r^{2} \\ ^{2}+2 r r^{2} \\ ^{2}\end{array}^{2} \)
В. \( 3 \pi r^{2} \)
\( \mathbf{c} \cdot 4 \pi r^{2} \)
D. \( 8 \pi r^{2} \)
Subject: Physics
A mass is suspended from the end of a
spring. When the system is oscillating the amplitude of oscillation is \( 4 \mathrm{cm} \) and the maximum kinetic energy of
oscillation of the system is 1 joule.
Then the force constant of the spring is:
A. \( 2500 \mathrm{N} / \mathrm{m} \)
в. \( 1250 \mathrm{N} / \mathrm{m} \)
c. \( 500 \mathrm{N} / \mathrm{m} \)
D. \( 250 \mathrm{N} / \mathrm{m} \)
Subject: Physics
A wave has velocity v in medium P and velocity \( 2 v \) in medium \( Q \). If the wave is incident in medium \( \mathrm{P} \) at an angle of 30 then the angle of refraction will be
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)
Subject: Maths
Let the equation of the plane through
the points (-1,1,1) and (1,-1,1) and
perpendicular to the plane \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+ \)
\( \mathbf{2} z=\mathbf{7} \) be \( \boldsymbol{k} \boldsymbol{x}+\boldsymbol{m} \boldsymbol{y}-\boldsymbol{n} \boldsymbol{z}+\boldsymbol{p}=\mathbf{0} . \) Find
\( \boldsymbol{k}+\boldsymbol{m}+\boldsymbol{n}+\boldsymbol{p} ? \)
Subject: Maths
If the complex numbers \( z_{1}, z_{2} \) and \( z_{3} \)
denote the vertices of an isosceles
triangle, right angled at \( z_{1}, \) then \( \left(z_{1}-\right. \)
\( \left.z_{2}\right)^{2}+\left(z_{1}-z_{3}\right)^{2} \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \left(z_{2}+z_{3}\right)^{2} \)
\( c \cdot 2 \)
D. 3
E \( \cdot\left(z_{2}-z_{3}\right)^{2} \)
Subject: Chemistry
The formation of polyethylene from
calcium carbide takes places as follows
\( \boldsymbol{C a} \boldsymbol{C}_{2}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{C}_{2} \boldsymbol{H}_{2} \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{2}+\boldsymbol{H}_{2} \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{4} \)
\( \boldsymbol{n} \boldsymbol{C}_{2} \boldsymbol{H}_{4} \rightarrow\left(\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}\right)_{n} \)
The amount of polyethylene obtained
from 64 kg of \( C a C_{2} \) is :
A. \( 14 \mathrm{kg} \)
B. \( 7 \mathrm{kg} \)
c. \( 21 \mathrm{kg} \)
D. \( 28 \mathrm{kg} \)
Subject: Physics
A wooden plank of length \( 1 \mathrm{m} \) and uniform cross-section is hinged at one
end to the bottom of a tank as shown.
The tank is filled with water upto a
height of \( 0.5 \mathrm{m} . \) The specific gravity of
the plank is \( 0.5 . \) The angle \( \theta \) made by
the plank in equilibrium position is
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)
Subject: Physics
(a) List three common refractive defects
of vision. Suggest the way of correcting these defects.
(b) About 45 lac people in the developing countries are suffering from corneal blindness. About 30 lac children
below the age of 12 years suffering from this defect can be cured by replacing the defective cornea with the cornea of
a donated eye. How and why can students of your age involve themselves to create awareness about this fact
among people ?
Subject: Physics
The length of a rubber cord is \( l_{1} \) metres
when the tension in it is \( 4 N \) and \( l_{2} \)
metres when the tension is \( 5 N \). then the
length in meters when the tension is \( \mathbf{9} N \) is
A \( \cdot 3 l_{2}+4 l_{1} \)
B . \( 3 l_{2}+2 l_{1} \)
\( \mathbf{c} \cdot 5 l_{2}-4 l_{1} \)
D. \( 3 l_{2}-2 l_{1} \)
Subject: Physics
What will be the magnitude of e.m.f. induced in a 200 turns coil with cross
section area \( 0.16 m^{2} ? \) The magnetic field through the coil changes from 0.10 Wb \( m^{-2} \) to \( 0.30 \mathrm{Wb} \), at a uniform rate over a
period of \( 0.05 \mathrm{s} \)
A . \( 128 v \)
B. 130v
\( c \cdot 118 v \)
D. 1320
Subject: Physics
Magnitude of binding energy of satellite is \( \boldsymbol{E} \) and kinetic energy is \( \boldsymbol{K} \). The ratio \( \boldsymbol{E} / \boldsymbol{K} \) is :
A . \( 2 / 1 \)
B . \( 1 / 4 \)
\( c .1 \)
D. \( 1 / 2 \)
Subject: Physics
In young's experiment, the source of red light of wavelength \( 7 \times 10^{-7} \) m. When a
thin glass plate of refractive index 1.5 at this wavelength is put in the path of one of the interfering beams, the central fringe shifts by \( 10^{-3} m \) to the position previously occupied by the 5 th bright fringe. If the thickness of the plate is \( \boldsymbol{X} \boldsymbol{\mu} \boldsymbol{m} \)
Find \( X ? \)
Subject: Maths
Subtract the following:
\( \boldsymbol{p}(\boldsymbol{y})=\boldsymbol{3} \boldsymbol{y}^{7}-\boldsymbol{2} \boldsymbol{y}^{2}+\boldsymbol{3} \) and \( \boldsymbol{q}(\boldsymbol{y})=\boldsymbol{y}^{7}+ \)
\( \boldsymbol{y}^{2}+\boldsymbol{y} \)
Subject: Chemistry
In the raction \( S O_{2}+2 H_{2} S \rightarrow 3 S+ \)
\( 2 H_{2} O, \) the substance that is oxidized is
\( A \cdot S O_{2} \)
в. \( H_{2} \) О
\( c \cdot s \)
D. \( H_{2} S_{S} \)
Subject: Maths
\( f\left(\frac{1+\sin \theta-\cos \theta}{1+\sin \theta+\cos \theta}\right)^{2}= \)
\( \lambda\left(\frac{1-\cos \theta}{1+\cos \theta}\right), \) then \( \lambda \) equals
\( A \)
B. 1
\( c \cdot 2 \)
D.
Subject: Maths
The solution of the differential equation, \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=(\boldsymbol{x}-\boldsymbol{y})^{2}, \) when \( \boldsymbol{y}(\mathbf{1})=\mathbf{1}, \) is
\( ^{\mathrm{A}} \cdot \log _{e}\left|\frac{2-y}{2-x}\right|=2(y-1) \)
\( ^{\mathbf{B}} \cdot \log _{e}\left|\frac{2-x}{2-y}\right|=x-y \)
c. \( -\log _{e}\left|\frac{1+x-y}{1-x+y}\right|=x+y-2 \)
D. \( -\log _{e}\left|\frac{1-x+y}{1+x-y}\right|=2(x-1) \)
Subject: Maths
If \( A^{\prime} \) s income is \( 30 \% \) less than \( B^{\prime} s \)
then how much per cent is \( B^{\prime} \) s income
more than \( A^{\prime} \) s?
A \( 42 \frac{6}{7} \% \)
в. \( 32 \frac{1}{10} \% \)
c. \( 30 \% \)
D. \( 40 \% \)
Subject: Chemistry
In a 1 lit. container following equilibrium
is established with equal moles of \( N O_{2} \)
(g) \( \& N_{2} O_{4}(g) \)
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g), \) at equilibrium
\( M_{\text {avg.}}=\frac{184}{3}, \) thenratioofK_\( \{\mathrm{C}\} \$ \$ 8 \)
total initial moles is.
A. 3
B. 3/2
c. 27/4
D. 6
Subject: Maths
Equation of the ellipse in its standard form is \( \frac{\boldsymbol{x}^{2}}{\boldsymbol{a}^{2}}-\frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}=\mathbf{1} \)
A. True
B. False
c. Nither
D. Either
Subject: Maths
Let the algebraic sum of the perpendicular distance from the points (2,0)(0,2) and (1,1) to a variable straigth line be zero, then the passes through a fixed point whose coordinates
are........ Find the condition on \( a \) and \( b \)
such that the portion of thelineax \( + \)
\( b y-1=0, \) intercepted between the
line axis.
Subject: Chemistry
A sulphate salt of group 2 element of the periodic table is a white, soft substance, which can be moulded into
different shapes by making its dough.
When this compound is left in open for some time, it becomes a solid mass and cannot be used for
moulding purposes. Identify the sulphate salt.
A. White paris
B. Plaster of paris
c. Calcium hydroxide
D. Calcium carbonate
Subject: Chemistry
In the following reaction:
\( \mathbf{3} \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{6} \boldsymbol{C} \boldsymbol{O}_{3}^{2-}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \mathbf{5} \boldsymbol{B} \boldsymbol{r}^{-}+ \)
\( \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3}^{-} \)
This question has multiple correct options
A. bromine is oxidised and carbonate is reduced
B. bromine is oxidised
c. bromine is neither oxidised nor reduced
D. bromine is reduced
Subject: Chemistry
If the activation energies of the forward and backward reactions of a reversible
reaction are \( \boldsymbol{E}_{\boldsymbol{a}}(\boldsymbol{f}) \) and \( \boldsymbol{E}_{\boldsymbol{a}}(\boldsymbol{b}) \)
respectively. The \( \Delta E \) of the reaction is
A \( \cdot E_{a}(F)-E_{a}(b) \)
B . \( E_{a}(F)+E_{a}(b) \)
\( \mathbf{c} \cdot E_{a}(F)=E_{a}(b) \)
D. \( -E_{a}(F)+E_{a}(b) \)
Subject: Maths
Assertion
If \( \tan A+\tan B+\tan C=3 \sqrt{3}, \) then
triangle is equilateral
Reason
\( \ln \Delta A B C, \tan A+\tan B+\tan C= \)
\( \tan A \tan B \tan C \)
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 false but Reason is true
Subject: Chemistry
The following characteristics of a substance are given. What is the name of this substance?
(i) It is used as an abrasive for cutting glass.
(ii) It is used as a tip of deep boring drills.
(iii) It is used for making dies for
drawing wires.
(iv) It is used in generating laser beams in electronics.
A. Diamond
B. Buckminister fullerene
c. Lampblack
D. Graphite
Subject: Maths
If \( n \geq 2 \) then the number of surjections
that can be defined from \( \{1,2,3, \dots n\} \) onto \{1,2\} is
A \( \cdot n^{2}-n \)
B \( \cdot n^{2} \)
\( c \cdot 2^{n} \)
D. \( 2^{n}-2 \)
Subject: Chemistry
Balance the following equation in basic medium by ion-electron method and oxidation number methods and identify
the oxidising agent and the reducing
agent
\( \boldsymbol{C l}_{2} \boldsymbol{O}_{7}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{C l O}_{2}^{-}(\boldsymbol{a q})+ \)
\( \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}^{+} \)
Subject: Physics
The values of \( n_{1} \) and \( n_{2} \) for Pfund's
series are
A \( \cdot n_{1}=5, n_{2}=6,7 \)
В . \( n_{1}=4, n_{2}=5,6,7 . . . \)
C \( . n_{1}=3, n_{2}=4,5,6 \dots \)
D. \( n_{1}=2, n_{2}=3,4,5 \dots \)
Subject: Maths
Find the interval in which \( \boldsymbol{f}(\boldsymbol{x})=\int_{-1}^{x}\left(\boldsymbol{e}^{t}-\mathbf{1}\right)(\mathbf{2}-\boldsymbol{t}) \boldsymbol{d t},(\boldsymbol{x}>\mathbf{1}) \)
is
increasing
\( A \cdot[3,5] \)
B . [1,3]
\( \mathbf{c} \cdot[0,3] \)
D. [0,2]
Subject: Chemistry
Which set of figures will be obtained after rounding up the following upto three significant figures? 34.216,0.04597,10.4107
A . 34.3,0.0461,10.4
B. 34.2, 0.0460, 10.4
c. 34.20,0.460,10.40
D. 34.21, 4.597, 1.04
Subject: Maths
The area of the parallelogram formed by
the lines \( 3 x-4 y+1=0,3 x-4 y+ \)
\( \mathbf{3}=\mathbf{0}, \mathbf{4} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}-\mathbf{1}=\mathbf{0} \) and \( \mathbf{4} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}- \)
\( \mathbf{2}=\mathbf{0}, \) is
A \( \cdot \frac{1}{6} \) sq.units
B. \( \frac{2}{7} \) sq.units
c. \( \frac{3}{8} \) sq.units
D. none of the above
Subject: Chemistry
In which of the following systems, doubling the volume of the container causes a shift to right?
A \( \cdot H_{2}(g)+I_{2}(g) \leftrightharpoons 2 H I(g) \)
B . \( 2 C O(g)+O_{2}(g) \leftrightharpoons 2 C O_{2}(g) \)
C \( . N_{2}(g)+3 H_{2}(g) \leftrightharpoons 2 N H_{3}(g) \)
D. \( P C l_{5}(g) \leftrightharpoons P C l_{3}(g)+C l_{2}(g) \)
Subject: Maths
What is the greatest value of \( \theta \) lying between \( 0^{0} \) and \( 720^{0} \) whose tangent is \( -\frac{1}{\sqrt{3}} ? \)
A \( \cdot 690^{\circ} \)
\( ^{0} \)
в. \( 510^{\circ} \)
c. \( 330^{\circ} \)
D. \( 150^{\circ} \)
Subject: Chemistry
From the following sequence calculate the lattice energy of \( A B(s) \) \( \boldsymbol{A}(\boldsymbol{s}) \rightarrow \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{e} ; \quad \boldsymbol{6} 1 \boldsymbol{0} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{e} \rightarrow \boldsymbol{B}(\boldsymbol{g}) ; \quad-\boldsymbol{2 6 0} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{A}(s)+\boldsymbol{B}(\boldsymbol{g}) \rightarrow \boldsymbol{A} \boldsymbol{B}(s) \)
\( -569 k J m o l^{-1} \)
\( \mathbf{A} \cdot-219 \)
в. -919
\( \mathbf{c} \cdot+1539 \)
D. +301
Subject: Chemistry
Rutherfords alpha particle scattering experiment, which established the nuclear model of the
atom, used a beam of:
A. alpha particles, which impinged on a metal foil and got scattered
B. beta particles, which impinged on a metal foil and got absorbed
c. helium atoms, which impinged on a metal foil and got scattered
D. helium nucleus, which impinged on a metal foil and ejected electrons
Subject: Physics
India's Mangalyan was sent to the Mars
by launching it into a transfer orbit EOM around the sun. It leaves the earth at \( \mathrm{E} \)
and meets Mars at M. If the semi-major
axis of Earth's orbit is \( a_{e}=1.5 \times \)
\( 10^{11} m, \) that of Mars's orbit \( a_{m}= \)
\( 2.28 \times 10^{11} m, \) taken Kepler's laws, the
estimate of time of Mangalyan to reach
Mars from Earth to be close to
A. 500 days
B. 320 days
c. 260 days
D. 220 days
Subject: Physics
A string of length \( 0.4 \mathrm{m} \& \operatorname{mass} 10^{2} \mathrm{kg} \)
is tightly clamped at its ends. The tension in the string is 1.6 N. Identical wave pulses are produced at one end at equal intervals of time, \( \Delta \) t. The minimum value of \( \Delta t \) which allows
constructive interference between
successive pulses is:
A . \( 0.05 \mathrm{s} \)
B. 0.10 s
c. \( 0.20 \mathrm{s} \)
D. 0.40 s
Subject: Physics
A source of wave vibrates with a
frequency \( 500 H z . \) The wave travels 33
\( \mathrm{m} \) in \( 0.1 s . \) How far does the waves
travels when the source executes 150
vibrations?
A . \( 11 m \)
B. \( 99 m \)
\( c .66 m \)
\( \mathbf{D} \cdot 128 m \)
Subject: Physics
if force \( \overrightarrow{\boldsymbol{F}}=(\hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}) \boldsymbol{N} \) acts on a body
at a point whose distance from the axis of rotation is given by \( \vec{r}=(3 \hat{i}+\hat{j}) N \) then torque acting on the body is:
\( \mathbf{A} \cdot 9 N m \)
B. \( 8 N m \)
\( \mathbf{c} .6 N m \)
D. \( 1 N m \)
Subject: Chemistry
Dissociation of water takes place in two
steps:
\( \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{H}^{+}+\boldsymbol{O} \boldsymbol{H}^{-} ; \boldsymbol{\Delta} \boldsymbol{H}=+497.8 \mathrm{kJ} \)
\( O H^{-} \rightarrow H^{+}+O^{2-} ; \Delta H=+428.5 \mathrm{kJ} \)
What is the bond energy of \( 0-H \) bond?
A . \( 463.15 \mathrm{kJ} \mathrm{mol}^{-1} \)
В. 428.5 k \( \mathrm{mol}^{-1} \)
c. \( 69.3 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 926.3 kJ \( m o l^{-1} \)
Subject: Chemistry
\( K_{a} \) for the reaction; \( F e^{3+}(a q .)+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightleftharpoons \boldsymbol{F} \boldsymbol{e}(\boldsymbol{O} \boldsymbol{H})^{2+}(\boldsymbol{a} \boldsymbol{q} \cdot)+ \)
\( H_{3} O^{+}(a q .) \) is \( 6.5 \times 10^{-3} . \) What is the
maximum \( p H \) value which could be
used do that at least \( 80 \% \) of the total
ion \( (I I I) \) in a dilute solution exists as
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \boldsymbol{?} \)
A . 2
B. 2.41
c. 2.79
D. 0.59
Subject: Physics
Electrons at rest are accelerated by a potential of \( V \) volt. These electrons enter the region of space having a uniform, perpendicular magnetic induction field
B. The radius of the path of the electrons inside the magnetic field is?
A \( \cdot \sqrt{(m e V) / B e} \)
B. \( \sqrt{(2 m e V) / B e} \)
\( \mathbf{c} \cdot \sqrt{(m e V) / 2 B e} \)
D. None of these
Subject: Chemistry
A reaction is spontaneous at all
temperature when
A. \( \Delta H \) is -ve and \( \Delta S \) is +ve
B. \( \Delta H \) is +ve and \( \Delta S \) is -ve
C. Both \( \Delta H \& \Delta S \) are -ve
D. Both \( \Delta H \) \& \( \Delta S \) are +ve
Subject: Maths
\( \operatorname{In} \) a trapezium \( \boldsymbol{A B C D}, \boldsymbol{A B} \| \boldsymbol{D C} \) and
\( D C=2 A B . E F \) drawn parallel to \( A B \)
cuts \( A D \) in \( F \) and \( B C \) in \( E \) such that \( \frac{B E}{E C}=\frac{3}{4} . \) Diagonal \( D B \) intersects \( E F \)
at \( G . \) Prove that \( \mathbf{7 F E}=\mathbf{1 0 A B} \)
Subject: Chemistry
The reaction, \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C}+\boldsymbol{D} \) was
studied using an initial concentration
of \( B \) which was 1.5 times that of \( A \). But
the equilibrium concentration of \( A \) and
\( C \) were found to be equal. The \( K_{c} \) for the
equilibrium is:
A .4
B. 8
\( c \cdot 6 \)
D. 0.32
Subject: Maths
Given a function \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} ; \) where \( \boldsymbol{A}= \)
\{1,2,3,4,5\} and \( B=\{6,7,8\} \)
The number of mappings of \( g(x): B \rightarrow \)
\( A \) such that \( g(i) \leq g(j) \) whenever \( i<j \)
is
A . 55
в. 140
c. 10
D. 35 5
Subject: Maths
In a random experiment, a fair die is rolled until two fours are obtained in
succession. The probability that the experiment will end in the fifth throw of the die is equal to:
A \( \cdot \frac{150}{6^{5}} \)
в. \( \frac{175}{6^{5}} \)
c. \( \frac{200}{6^{5}} \)
D. \( \frac{225}{6^{5}} \)
Subject: Chemistry
Electron transition in \( H e^{+} \) ion takes
from \( n_{2} \) to \( n_{1} \) shell such that:
\( 2 n_{2}+3 n_{1}=18 \)
\( 2 n_{2}-3 n_{1}=6 \)
What will be the total number of
photons emitted when electrons transit
to \( n_{1} \) shell?
A . 21
B . 15
c. 20
D. 10
Subject: Chemistry
The correct statement regarding \( S O_{2} \)
molecule is:
A. two \( p \pi-d \pi \) bonds
B. molecule has 2 lone pair, 2 \( \sigma \) bonds and \( 2 \pi \) bonds
c. two \( p \pi-p \pi \) bonds
D. one \( p \pi-p \pi \) bond and one \( p \pi-d \pi \) bond
Subject: Physics
A coil of inductance \( 0.1 \mathrm{H} \) is connected to
\( 50 V, 100 H z \) generator and current is found to be 0.5A. The potential
difference across resistance of the coil
is
A . \( 15 v \)
B. 20V
c. \( 25 v \)
D. 39V
Subject: Physics
Consider an expanding sphere of instantaneous radius \( R \) whose total
mass remains constant. The expansion is such that the instantaneous density
\( \rho \) remains uniform throughout the
volume. The rate of fractional change in density \( \left(\frac{1}{\rho} \frac{d p}{d t}\right) \) is constant. The
velocity \( v \) of any point on the surface of
the expanding sphere is proportional to
A \( \cdot R^{2 / 3} \)
в. \( R \)
c. \( R^{3} \)
D. \( \frac{1}{R} \)