AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
For the hydrolysis of methyl acetate in
aqueous solution the above
tabulated results were obtained:
(a) Show that it follow pseudo first order reaction, as the concentration of water
remains constant.
(b) Calculate the average rate of
reaction between the time interval 10 to
20 seconds.
(Given : log 2=0.3010, log 4 =0.6021)
\begin{tabular}{|c|c|c|c|}
\hline \( \mathrm{t} / \mathrm{s} \) & 0 & 10 & 20 \\
\hline \( \mathrm{r} \mathrm{CH}_{3} \mathrm{COOH}_{3} \mathrm{J} / \mathrm{moll}^{-1} \) & 0.10 & 0.05 & 0.025 \\
\hline
\end{tabular}
Subject: Maths
Domain of the function is \( \boldsymbol{y}= \)
\( \frac{\sqrt{\cos x-1 / 2}}{\sqrt{6+35 x-6 x^{2}}} \)
\( \mathbf{A} \cdot \therefore D_{1} \cap D_{2}=[0, \pi / 6] \cup[5 \pi / 3,6] \)
B \( \ldots D_{1} \cap D_{2}=[0, \pi / 3] \cup[5 \pi / 3,6] \)
\( \mathrm{c} \cdot \therefore D_{1} \cap D_{2}=[0, \pi / 3] \cup[5 \pi / 6,6] \)
D. \( \therefore D_{1} \cap D_{2}=[0, \pi / 2] \cup[5 \pi / 3,6] \)
Subject: Physics
A concave lens of focal length \( \boldsymbol{f} \) produces an image \( (1 / n) \) times the size of the object. The distance of the object from the lens is
A \( \cdot(n+1) f \)
в. \( \frac{(n-1)}{n} f \)
c. \( \frac{(n+1)}{n} f \)
D. \( (n-1) f \)
Subject: Chemistry
Which of the following represents the
correct decreasing order of acidity of
the following compounds?
(i)
(ii)
(iii)
(iv)
\( A \cdot i i>i>i i i>i v \)
\( \mathbf{B} \). \( i \mathbf{v}> \) iii \( > \) ii \( >i \)
\( \mathbf{C} \cdot \) iii \( >i v>i>i \)
D. iv \( > \) iii \( >i> \) ii
Subject: Maths
Solve: \( \frac{x^{2}-(y-z)^{2}}{(x+z)^{2}-y^{2}}+\frac{y^{2}-(x-z)^{2}}{(x+y)^{2}-z^{2}}+ \)
\( \frac{z^{2}-(x-y)^{2}}{(y+z)^{2}-x^{2}}= \)
\( A \)
B.
\( c \cdot 1 \)
\( D \)
Subject: Chemistry
Assertion
\( N H_{3} \) is a Lewis base.
Reason
Ammonia can accept a proton.
A. Both Assertion and Reason are correct and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason
is not the correct explanation of the Assertion
C. The Assertion is correct but the Reason is incorrect
D. The Assertion is incorrect and the Reason is correct
Subject: Maths
If \( y=\frac{x^{4}-x^{2}+1}{x^{2}+\sqrt{3} x+1} \) and \( \frac{d y}{d x}=a x+b \)
then the value of \( a+b \) is equal to
A \( \cdot \cot \frac{5 \pi}{8} \)
B. \( \cot \frac{5 \pi}{12} \)
c. \( \tan \frac{5 \pi}{12} \)
D. \( \tan \frac{5 \pi}{8} \)
Subject: Maths
The plane \( X O Z \) divides the join of
(1,-1,5) and (2,3,4) in the ratio \( \lambda: 1 \)
then \( \lambda \) is
A . -3
в. \( \frac{1}{4} \)
\( c \cdot 3 \)
D. \( \frac{1}{3} \)
Subject: Chemistry
The following substances were
all dissolved in 100 grams of water at \( 290 \mathrm{K} \) to produce saturated solutions.lf the solution is
heated to \( 310 \mathrm{K} \), which substance will have a decrease in its solubility:
\( \mathbf{A} \cdot N a C I \)
в. \( K I \)
c. \( \mathrm{CaCl}_{2} \)
D. \( H C I \)
E . \( K N O_{3} \)
Subject: Chemistry
Paramagnetic behaviour is observed in
out of \( \boldsymbol{O}_{3}, \boldsymbol{O}_{2}, \boldsymbol{N} \boldsymbol{O} \) and
\( N O_{2} \)
This question has multiple correct options
\( A \cdot O_{3} \)
в. \( O_{2} \)
c. \( N O \)
D. \( N O_{2} \)
Subject: Maths
Suppose that \( f(x)=x^{3}-3 x^{2}-4 x+12 \)
\( \operatorname{and} h(x)=\left\{\begin{array}{ll}\frac{f(x)}{x-3} & x \neq 3 \\ K & x=3\end{array}, \) then \right.
find the value of \( \mathrm{K} \) that makes
h' continuous at \( x=3 \)
Subject: Physics
Assuming the mass of Earth to be ten times the mass of Mars, its radius to be
twice the radius of Mars and the
acceleration due to gravity on the
surface of Earth is \( 10 \mathrm{m} / \mathrm{s}^{2} \). Then the
acceleration due to gravity on the surface of Mars is given by.
A \( \cdot 0.2 m / s^{2} \)
B. \( 0.4 m / s^{2} \)
c. \( 2 m / s^{2} \)
D. \( 4 m / s^{2} \)
E \( .5 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Chemistry
Predict the direction of the reaction
from the comparison of \( Q_{c}, K_{c} . \) Mark the
incorrect statement.
A \( \cdot \) If \( Q_{c}<K_{c} \), reaction goes from left to right.
B. If \( Q_{c}=K_{c} \), reaction goes from right to left
\( \mathrm{c} \cdot \) If \( Q_{c}>K_{c} \), net reaction goes from right to left
D. If \( Q_{c}=K_{c} \), reactants and products are at equilibrium.
Subject: Chemistry
The structure of the compound with
molecular formula \( C_{8} H_{14} \) that has 12
secondary and 2 tertiary H atoms is:
A. Bicyclo [2.2.2] octane
B. 1,2-Dimethyl cyclohexane
c. Bicyclo [3.2.1] octane
D. Tricyclo [2.2.2.0] octane
Subject: Chemistry
For the reaction \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \)
the unit of \( \boldsymbol{K}_{c} \)
A. litre/mole
B. mol/litre
c. \( \left(\text {mol litre}^{-1} \text {) }^{-1}\right. \)
D \cdot (litre mole \( ^{-1} \) ) \( ^{2} \)
Subject: Physics
If Young's modulus of iron be \( 2 \times 10^{11} \)
\( \mathrm{N} / \mathrm{m}^{-2} \) and interatomic distance be \( 3 \mathrm{x} \)
\( 10^{-10} \mathrm{m}, \) the interatomic force constant
will be :
\( \mathbf{A} .60 N / m \)
в. \( 120 N / m \)
\( c .30 N / m \)
D. \( 180 N / m \)
Subject: Maths
If \( \angle A \) and \( \angle B \) are complementary
angles and \( m \angle A \) is \( x^{o}, \) which equation
can be used to find \( m \angle B \) which is
denoted by \( y ? \)
A. \( y=(90+x)^{\circ} \)
в. \( y=(90-x)^{\circ} \)
c. \( y=(180 x)^{\circ} \)
D. \( y=(x+180)^{\circ} \)
Subject: Physics
The displacement of \( x \) of a particle moving in one dimension is related to time by the equation \( t=(\sqrt{x}+3) \)
where \( x \) is in \( m \) and \( t \) in \( s . \) The
displacement, when velocity is zero, is
\( \mathbf{A} \cdot 1 m \)
B. \( 2 m \)
\( c .4 m \)
D. zero
Subject: Chemistry
Which of the following will be most stable diazonium salt \( \boldsymbol{R} \boldsymbol{N}_{2}^{+} \boldsymbol{X}^{-} ? \)
A \( \cdot C H_{3} N_{2}^{+} X^{-} \)
B . \( C_{6} H_{5} N_{2}^{+} X^{-} \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{N}_{2}^{+} \mathrm{X}^{-} \)
D. \( C_{6} H_{5} C H_{2} N_{2}^{+} X^{-} \)
Subject: Maths
A biased coin with probability \( \boldsymbol{p}, \boldsymbol{0}< \) \( p<1, \) of heads is tossed until a head
appears for the first time. If the probability that the number of tosses required is even is \( 2 / 5, \) then \( p=\dots \)
A. \( 2 / 5 \)
B. \( 2 / 3 \)
c. \( 1 / 3 \)
D. \( 3 / 5 \)
Subject: Physics
A particle of mass mm sides. The magnitude of impulse applied at each corner of the polygon is:
A \( \cdot 2 m v \sin \frac{\pi}{2 n} \)
B. \( m v \sin \frac{\pi}{2 n} \)
\( ^{\mathrm{c}} \cdot 2 m v \cos \frac{\pi}{2 n} \)
D. \( m v \cos \frac{\pi}{2 n} \)
Subject: Chemistry
The difference in angular momentums associated with an electronic transition
in hydrogen atom is equal to \( 3 h / 2 \pi . \) The atom contains only \( \mathrm{K}, \mathrm{L}, \mathrm{M} \) and \( \mathrm{N} \) shells. Calculate the energies and radii associated with the orbits.
A. -13.6 ev and 0.314 Angstrom, 0.08 eV and 8.48 Angstrom
B. -13.6 eV and 0.529 Angstrom, - 0.08 eV and 8.48 Angstrom
c. 13.6 ev and 0.529 Angstrom, 0.08 eV and 8.48 Angstromm
D. 27.2 eV and 0.529 Angstrom, 0.08 eV and 8.48 Angstrom
Subject: Physics
The ring \( B \) is coaxial with a solenoid \( A \)
as shown in figure. As the switch \( S \) is
closed at \( t=0, \) the ring \( B \)
A. is attracted towards \( A \)
B. is repelled by \( A \)
C. is initially repelled and then attracted
D. is initially attracted and then repelled
Subject: Physics
A conductor of resistance \( 3 \Omega \) is
stretched uniformly till its length is doubled. The wire now is bent in the
form of an equilateral triangle. The effective resistance between the ends of
any side of the triangle in ohms is :
A \( \cdot \frac{9}{2} \)
B. \( \frac{8}{3} \)
\( c \cdot 2 \)
D.
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{4}\end{array}\right] \) then \( \boldsymbol{A}- \)
\( \boldsymbol{B}= \)
\( \mathbf{A} \cdot\left[\begin{array}{ll}-2 & -2\end{array}\right] \)
B. \( \left[\begin{array}{ll}2 & 2\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{ll}-3 & -1\end{array}\right] \)
D. None of these
Subject: Chemistry
Hydrogen combines with oxygen in a 1: 8 weight ratio to form water. If every molecule of water contains two atoms
of hydrogen and one atom of oxygen, an atom of oxygen must weigh:
A. 8 times the mass of a hydrogen atom
B. 16 times the mass of a hydrogen atom
c. \( 1 / 16 \) times the mass of a hydrogen atom
D. \( 1 / 8 \) times the mass of a hydrogen atom
Subject: Maths
A line with direction cosines
proportional to 2,1,2 meets each of the line \( \boldsymbol{x}=\boldsymbol{y}+\boldsymbol{a}=\boldsymbol{z} \) and \( \boldsymbol{x}+\boldsymbol{a}=\boldsymbol{2} \boldsymbol{y}= \)
2 \( z \). The co-ordinates of each of the
points of intersection are given by:
A. \( (3 a, 3 a, 3 a),(a, a, a) \)
в. \( (3 a, 2 a, 3 a),(a, a, a) \)
c. \( (3 a, 2 a, 3 a),(a, a, 2 a) \)
D. \( (2 a, 3 a, 3 a),(2 a, a, a) \)
Subject: Chemistry
\( \begin{array}{cc}C_{4} H_{6} O_{4} \stackrel{\Delta}{\longrightarrow} C_{3} H_{6} O_{2} \frac{\text {sodalime}}{\Delta} & C \\ A & B\end{array} \)
Compound ' \( C^{\prime} \) is a hydrocarbon,
occupying approx \( 0.75 L \) volume per
gram. Identify \( ^{\prime} A^{\prime} \) and \( ^{\prime} B^{\prime} \)
A. tartaric acid, propanoic acid
B. Succinic acid, succinic anhydride
C . Maleic anhydride, maleic acid
D. Methyl malonic acid, propanoic acid
Subject: Maths
Period of \( \boldsymbol{f}(\boldsymbol{x})=\{\boldsymbol{x}\}+\left\{\boldsymbol{x}+\frac{1}{3}\right\}+ \)
\( \left\{x+\frac{2}{3}\right\} \) is equal to (where \( \{.\} \) denotes fraction part function
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{2} \)
D.
Subject: Chemistry
Increase in the pressure on the following gaseous equilibrium will:
\( \mathbf{2} \boldsymbol{A}+\mathbf{3} \boldsymbol{B} \leftrightharpoons \mathbf{3} \boldsymbol{C}+\mathbf{2} \boldsymbol{D} \)
A. favour forward reaction
B. favour backward reaction
c. have no effect
D. favour forward and backward reaction
Subject: Physics
Suppose a current carrying wire has a
cross-sectional area that gradually
become smaller along the wire has the
shape of a very long cone as shown in figure.Then:
This question has multiple correct options
A. electric current is different in different portions of wire
B. electric current is same everywhere.
C. drift speed of electrons at point \( A \) is lesser than that of at point B.
D. drift speed of electrons at point \( A \) is same as that of at point B.
Subject: Chemistry
Which one of the following is not correct order of boiling points of the alkyl/aryl halides?
A. \( C H C l_{3}>C H_{2} C l_{2} \)
B. \( C H_{3}\left(C H_{2}\right)_{3} C l>C H_{3}\left(C H_{2}\right)_{2} C l \)
c. \( \left(C H_{3}\right)_{3} C C l>\left(C H_{3}\right)_{2} C H C H_{2} C l \)
D. \( C H_{3}\left(C H_{2}\right)_{3} C l>C H_{3} C H_{2} C H C l C H_{3} \)
Subject: Physics
The escape velocity for a body projected vertically upwards from the surface of earth is \( 11 \mathrm{km} / \mathrm{s} \). If the body is projected
at an angle of \( 45^{0} \) with the vertical, the escape velocity will be
A. \( 11 \sqrt{2 \mathrm{km} / \mathrm{s}} \)
.
B. 22 km/s
c. \( 11 \mathrm{km} / \mathrm{s} \)
D. \( 11 / \sqrt{2 \mathrm{m}} / \mathrm{s} \)
Subject: Biology
Three of the following pairs of the human skeletal parts are correctly matched with their respective inclusive skeletal category and one pair is not matched. Identify the non-matching pair.
A. Sternum and ribs - Axial skeleton
B. Clavicle and glenoid cavity - Pelvic girdle
c. Humerus and ulna - Appendicular skeleton
D. Malleus and stapes - Ear ossicles
Subject: Physics
A ball is thrown vertically up. If the ball reached at maximum height in \( 3 s \) Assume air resistance is negligible. The initial velocity of the ball is most nearly
A. \( 10 \mathrm{m} / \mathrm{s} \)
в. \( 15 \mathrm{m} / \mathrm{s} \)
c. \( 30 m / s \)
D. \( 45 \mathrm{m} / \mathrm{s} \)
E . \( 60 \mathrm{m} / \mathrm{s} \)
Subject: Physics
For the Paschen series the values of \( n_{1} \)
and \( n_{2} \) in the expression \( \Delta E= \) \( \boldsymbol{R h c}\left(\frac{1}{\boldsymbol{n}_{1}^{2}}-\frac{1}{\boldsymbol{n}_{2}^{2}}\right) \) are
\( \mathbf{A} \cdot n_{1}=1, n_{2}=2,3,4, \ldots \)
B \( \cdot n_{1}=2, n_{2}=3,4,5, \ldots \)
c \( \cdot n_{1}=3, n_{2}=4,5,6, \dots \)
D. \( n_{1}=4, n_{2}=5,6,7, \ldots \)
Subject: Physics
While a collector to emitter voltage is constant in a transistor, the collector
current changes by \( 8.2 m A \) when the
emitter current changes by \( 8.3 m A \). The
value of forward current ratio \( \boldsymbol{h}_{f e}(\text { or } \boldsymbol{\alpha}) \)
is
A .0 .9879
B. 8.30
c. 8.2158
D. 8.0123
Subject: Physics
A body of mass \( 2 k g \) is on an inclined
plane inclined at \( 30^{0} \) to the horizontal.
The force applied on it parallel to the plane so that it moves up that slope with the acceleration of \( 2 m s^{-2} \) against
a frictional force of \( 5 N \) is:
A . \( 5 N \)
B. \( 9.8 N \)
c. \( 14.2 N \)
D. 18.81N
Subject: Maths
In the figure \( , \boldsymbol{A B}= \)
\( A C \quad \) and \( \quad \angle B A C=20^{\circ} . \) The points \( D \)
on \( A B \) and \( E \) on \( A C \) are such that
\( A D=D E=E C . \) Then \( \angle B D C \) equals.
\( 4 \cdot 10^{\circ} \)
B . \( 20^{\circ} \)
\( c \cdot 30 \)
D. \( 80^{\circ} \)
Subject: Physics
A ball of mass \( 400 \mathrm{gm} \) is dropped from a height of \( 5 \mathrm{m} \). A boy on the ground hits the ball vertically upwards with a bat with an average force of \( 100 \mathrm{N} \) so that it attains a vertical height of \( 20 \mathrm{m} . \) The time for which the ball remains in
contact with the bat is:
\( \left[\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right] \)
A. \( 0.12 s \)
B. \( 0.08 s \)
c. \( 0.04 s \)
D. 12
Subject: Biology
The figure given above shows three
velocity-substrate concentration curves
for an enzyme reaction. What do the
curves 1,2 and 3 depict respectively?
A. 1 - Normal enzyme reaction, 2 - competitive inhibition
3- Non-competitive inhibition
B. 1 - Enzyme with an allosteric modulator added, 2 Normal enzyme activity, 3 - Competitive inhibition
C. 1 - competitive inhibition added,
2 - Enzyme with allosteric substance
3 - Normal enzyme reaction
D. 1 - Normal enzyme reaction
2 - Non-competitive inhibitor added, 3 - Allosteric inhibitor added
Subject: Chemistry
Towards catalytic hydrogenation, the least reactive compound is:
A \( \cdot C H_{2}=C H_{2} \)
в. \( C H_{3}-C H=C H_{2} \)
c. \( H_{3} C-C H=C H-C H_{3} \)
D. \( \left(C H_{3}\right)_{2} C=C\left(C H_{3}\right)_{2} \)
Subject: Physics
Assertio
A block of mass \( m \) starts moving on a
rough horizontal surface with a velocity
\( v . \) It stops due to friction between the
block and the surface after moving through a certain distance. The surface
is now tilted to an angle of \( 30^{\circ} \) with the horizontal and the same block is made
to go up on the surface with the same
initial velocity \( v \). The decrease in the
mechanical energy in the second situation is smaller than that in the
first situation.
Reason
The coefficient of friction between the
block and the surface decreases with
the increase in the angle of inclination
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 freely falling body covers half of its journey from the top of a tower in \( 0.5 s \)
What is the height of the tower?
A \( .4 .9 m \)
B. \( 2.45 m \)
\( \mathrm{c} .9 .8 \mathrm{m} \)
D. \( 9 m \)
Subject: Physics
Specific heat capacity of substance \( \boldsymbol{A} \)
is \( 3.8 J g^{-1} K^{-1} \) whereas the Specific
heat capacity of substance \( B \) is
\( \mathbf{0 . 4} \boldsymbol{J} \boldsymbol{g}^{-1} \boldsymbol{K}^{-1} \)
(i) Which of the two is a good conductor of heat?
(ii) How is one led to the above
conclusion?
(iii) If substances \( A \) and \( B \) are liquids then which one would be more useful in
car radiators?
Subject: Chemistry
In the commercial electrochemical
process for aluminium extraction, the
electrolyte used is:
A \( \cdot A l(O H)_{3} \) in \( N a O H \) solution
B. An aqueous solution of \( A l_{2}\left(S O_{4}\right)_{3} \)
c. A molten mixture of \( A l_{2} O_{3}, N a_{3} A l F_{6} \& C a F_{2} \)
D. A molten mixture of \( A l O(O H) \) and \( A l(O H) \)
Subject: Maths
If \( A=\operatorname{diag}\left[d_{1}, d_{2}, d_{3}\right] \) then \( a^{n} \) is equal to
A \( \cdot \operatorname{diag}\left[d_{1}^{n-1}, d_{2}^{n-1}, d_{3}^{n-1}\right] \)
B. A
c. \( \operatorname{diag}\left[d_{1}^{n}, d_{2}^{n}, d_{3}^{n}\right] \)
D. none
Subject: Chemistry
The equilibrium constants for the
reaction, \( B r_{2} \rightleftharpoons 2 B r \) at \( 500 \mathrm{K} \) and 700
K are \( 1 \times 10^{-10} \) and \( 1 \times 10^{-5} \)
respectively. The reaction is:
A. endothermic
B. exothermic
\( c . \) fast
D. slow
Subject: Physics
A planet whose mass and radius are
both half of that of earth. Acceleration
due to gravity(g) at its surface should
be:
A \( \cdot 29.4 m / s e c^{2} \)
в. \( 19.6 \mathrm{m} / \mathrm{sec}^{2} \)
\( \mathrm{c} \cdot 9.8 \mathrm{m} / \mathrm{sec}^{2} \)
D. \( 4.9 \mathrm{m} / \mathrm{sec}^{2} \)
Subject: Physics
For the following nuclear disintegration process \( _{92}^{238} \boldsymbol{U} \rightarrow_{82}^{206} \boldsymbol{P b}+\boldsymbol{x}\left[_{2}^{4} \boldsymbol{H} e\right]+\left[_{-2}^{0} \boldsymbol{e}\right] \)
then value of \( x \) is
\( \mathbf{A} \cdot \mathbf{8} \)
B. 6
\( c \cdot 4 \)
D. 10
Subject: Maths
The interior of a building is in the form of a right circular cylinder of a diameter \( 4.2 \mathrm{m} \) and height \( 4 \mathrm{m}, \) surmounted by a cone. The vertical height of the cone is 2.1 \( \mathrm{m} \). Find the outer surface area and
volume of the building.(Take \( \pi=22 / 7) \)
A. Outer surface area \( =72.4 \mathrm{m}^{2} ; \) Volume \( =68.142 \mathrm{m}^{3} \)
B. Outer surface area \( =72.4 \mathrm{m}^{2} ; \) Volume \( =65.142 \mathrm{m}^{3} \)
c. outer surface a rea \( =75.4 m^{2} ; \) volume \( =68.142 m^{3} \)
D. Outer surface area \( =75.4 \mathrm{m}^{2} ; \) Volume \( =65.142 \mathrm{m}^{3} \)
Subject: Physics
\( 200 g \) of a cold ball at \( 20^{\circ} \mathrm{C} \) is dropped in
an equal amount of water at \( 80^{\circ} \mathrm{C} \). The
resulting temperature is \( 60^{\circ} \mathrm{C} \). This means that specific heat of solid is.
A. One fourth of water
B. One half of water
C. Twice of water
D. Four times of water
Subject: Maths
If \( r, s \) and \( t \) are prime numbers and \( p, q \)
are positive integers such that the LCM of \( p, q \) is \( r^{2} t^{4} s^{2} \) then the number of
ordered pair \( (p, q) \) is
A . 254
B. 252
c. 225
D. 224
Subject: Physics
In a two step pulley arrangement meant
for a load \( \mathrm{W} \), the ratio between force \( \mathrm{P} \)
and \( W \) in equilibrium position, when
radii of pulleys are \( r_{1} \) and \( r_{2} \)
A \( \cdot \frac{r_{2}}{r_{1}-r_{2}} \)
B. \( \frac{r_{1}-r_{2}}{r_{2}} \)
c. \( \frac{r_{1}}{r_{2}-r_{1}} \)
D. \( \frac{r_{2}-r_{1}}{r_{1}} \)
Subject: Physics
Figure shows two long wires carrying
equal currents \( I_{1} \) and \( I_{2} \) flowing in
opposite directions.Which of the arrows
labeled \( A, B, C \) and \( D \) correctly
represents the direction of the
magnetic field due to the wires at a
point located at an equal distance \( d \)
from each wire?
A . \( A \)
B. \( B \)
c. \( C \)
\( D . D \)
Subject: Maths
The foci of the ellipse \( \frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1 \) and the hyperbola \( \frac{x^{2}}{144}-\frac{y^{2}}{81}=\frac{1}{25} \) coincide
Then, the value of \( b^{2} \) is :
A . 5
B. 7
c. 9
D.
Subject: Physics
Dielectric constant, property of an electrical insulating material (a dielectric) equal to
A. the ratio of the capacitance of a capacitor filled with the given material to the capacitance of an identical capacitor in a vacuum without the dielectric material.
B. the ratio of the capacitance of a capacitor filled with the given material to the capacitance of an identical capacitor in a vacuum with the dielectric material
c. the capacitance of a capacitor filled with the given material
D. none of the above
Subject: Chemistry
The state of hybridization of boron and oxygen atoms in boric acid \( \left(\boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3}\right) \)
respectively are:
A \( \cdot s p^{2} \) and \( s p^{2} \)
B. \( s p^{2} \) and \( s p^{3} \)
c. \( s p^{3} \) and \( s p^{2} \)
D. \( s p^{3} \) and \( s p^{3} \)
Subject: Physics
Three point charges \( +\boldsymbol{q},+\mathbf{2} \boldsymbol{q} \) and \( -\mathbf{4 q} \)
where \( \boldsymbol{q}=\mathbf{0 . 1} \boldsymbol{\mu} \boldsymbol{C}, \) are placed at the
vertices of an equilateral triangle of
side \( 10 \mathrm{cm} \) as shown in figure. The potential energy of the system is
A \( \cdot 3 \times 10^{-3} J \)
В. \( -3 \times 10^{-3} J \)
\( \mathbf{c} \cdot 9 \times 10^{-3} J \)
\( \mathbf{D} \cdot-9 \times 10^{-3} \mathbf{J} \)
Subject: Physics
A force \( \overrightarrow{\boldsymbol{F}}=4 \hat{\boldsymbol{i}}-5 \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \) is acting at a
point \( \vec{r}_{1}=\hat{i}-2 \hat{j}+3 \hat{k} . \) Find the torque acting about a point \( \vec{r}_{2}=3 \hat{i}-2 \hat{j}-3 \hat{k} \)
Subject: Physics
Two fixed charges \( -2 Q \) and \( Q \) are located at the points with coordinates \( (-3 a, 0) \) and \( (+3 a, 0), \) respectively, in the xy plane.
a. Show that all points in the xy plane
where the electric potential due to the
two charges is zero lie on a circle.Find its
radius and the location of its center.
b. Give the expression \( V(x) \) at a general point on the \( x \) -axis and sketch the
function \( V(x) \) on the whole \( x \) -axis.
c. If a particle of charge +q starts from rest at the center of the circle, show by a
short quantitative argument that the
particle eventually crosses the circle. Find its speed when it does so.
Subject: Physics
A gyroscope, a uniform disc of radius \( R=5.0 \mathrm{cm} \) at the end of a rod of length
\( l=10 \mathrm{cm} \) (figure shown above), is
mounted on the floor of an elevator car
going up with a constant acceleration
\( \boldsymbol{w}=\mathbf{2 . 0} \boldsymbol{m} / \boldsymbol{s}^{2} . \) The other end of the rod
is hinged at the point \( O . \) The gyroscope
precesses with an angular velocity \( n= \)
0.5 rps. Neglecting the friction and the
mass of the rod, the proper angular
velocity of the disc in \( r a d / s \) is \( 100 x \)
Find the value of \( x \)
Subject: Maths
In the figure, if \( \angle B O C=7 x+20^{\circ} \) and
\( \angle C O A=3 x, \) then the value of \( x \) for
which \( A O B \) becomes a straight line is:
\( 4 \cdot 16^{\circ} \)
B. 14
\( c \cdot 20 \)
D. \( 21^{\circ} \)
Subject: Physics
Current 1 in a long \( 4 y- \) axis is paced through a square metal frame of side
\( 2 a \) oriented in the \( y-z \) p[lane a shown.
The linear mass density of the frame is
\( \lambda . \) A uniform magnetic field \( B \) is now
switched on along \( x- \) axis. Then the
instantaneous angular acceleration of
the frame will be:
A \( \cdot \frac{4 I B}{\lambda_{n}} \)
В. \( \frac{12 I B}{\lambda a} \)
c. \( \frac{4 I B}{3 \lambda a} \)
\( D \)
Subject: Maths
Subtract \( 4 p^{2} q-3 p q+5 p q^{2}-8 p- \)
\( 7 q-10 \) from \( 18-3 p+11 q+5 p q \)
\( 2 p q^{2}+5 p^{2} q \)
A \( \cdot p q^{2}-7 p^{2} q+8 p q+18 q+5 p+28 \)
B . \( p^{2} q-7 p q^{2}+8 p q+18 p+5 q+28 \)
C \( \cdot p q^{2}-7 p^{2} q+8 p q+18 p+5 q+28 \)
D. \( p^{2} q-7 p q^{2}+8 p q+18 q+5 p+28 \)
Subject: Chemistry
The Henry's law constant for the solubility of oxygen in water is \( 3.3 \times \)
\( 10^{-4} \) M \( / \) atm at \( 12^{\circ} \mathrm{C} \). Air is \( 21 \mathrm{mol} \% \)
oxygen. How many grams of oxygen can be dissolved in one litre of a trout
stream at \( 12^{\circ} \mathrm{C} \) at an air pressure of 1.00
atm?
A. 0.222 g
gg \( . . .222 \)
В. 0.11222 g
c. 0.333 g
D. 0.422 g