AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A wire when connected to \( 220 \mathrm{V} \) mains
supply has power dissipation \( P_{1} . \) Now
the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this
case is \( P_{2} \). Then \( P_{2}: P_{1} \) is
\( A \)
B. 4
\( c \cdot 2 \)
D. 3
Subject: Maths
A quadratc function in x has the value
10 when \( x=1 \) and has minimum value 1
when \( x=-2 \) the function is
\( A \cdot 2 x^{2}+3 x+5 \)
B. \( 3 x^{2}+2 x+5 \)
c. \( x^{2}+3 x+6 \)
D. \( x^{2}+4 x+5 \)
Subject: Chemistry
The missing term in the following equation is \( 2 F e^{3+}+S n^{2+} \rightarrow 2 F e^{2+}+ \)
\( \ldots . ? \)
\( A \cdot S n^{4} \)
в. \( S n^{3} \)
\( c \cdot s n^{2} \)
D. \( S n^{+} \)
Subject: Physics
A bucket full of hot water is kept in a
room and it cools from \( 75^{\circ} \mathrm{C} \) to \( 70^{\circ} \mathrm{C} \) in
\( T_{1} \) minutes, from \( 70^{\circ} C \) to \( 65^{\circ} C \) in \( T_{2} \)
minutes and from \( 65^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in \( T_{3} \) minutes. Then
A. \( T_{1}=T_{2}=T_{3} \)
в. \( T_{1}<T_{2}<T_{3} \)
c. \( T_{1}>T_{2}>T_{3} \)
D. \( T_{1}<T_{2}>T_{3} \)
Subject: Physics
Two cars are moving with same velocity
of \( 30 k m h^{-1} \) maintaining a distance of
5 km between them. Speed of third car
moving in the opposite direction and meeting the two cars at an interval of
\( 240 s \) is
\( \mathbf{A} \cdot 45 \mathrm{km} h^{-1} \)
B. \( 30 \mathrm{km} \mathrm{h}^{-1} \)
c. \( 55 \mathrm{km} \) h \( ^{-1} \)
D. \( 35 \mathrm{km} h^{-1} \)
Subject: Physics
Some students set up the circuit shown
to investigate how a variable resistor
affects an electrical circuit.

If the variable resistance is increased:
ariable 'esistor
A. Ammeter reading - decreases Voltmeter
reading - decreases
B. Ammeter reading - decreases Voltmeter
reading - increases
C. Ammeter reading - increases Voltmeter reading decreases
D. Ammeter reading - increases Inter reading increases
Subject: Physics
At a depth of \( 1000 \mathrm{m} \) in the ocean,what
is the gauge pressure when density of sea water is given \( 1.03 \times 10^{3} \mathrm{kgm}^{-3} \) ?
Take \( \boldsymbol{g}=\mathbf{1 0 m s}^{-\mathbf{2}} \)
A. 675 atm
B. 103 atm
c. 203 atm
D. 244 atm
Subject: Maths
In the following, determine the value of
\( k \) for which the given value is a solution
of the equation.
\( \mathbf{3} \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{k} \boldsymbol{x}-\mathbf{3}=\mathbf{0}, \boldsymbol{x}=-\frac{\mathbf{1}}{\mathbf{2}} \)
Subject: Chemistry
An organic compound contains \( 90 \% \) carbon and \( 10 \% \) hydrogen by mass. Its empirical formula is:
A. \( C_{2} H_{4} \)
в. \( C_{3} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{6} \)
D. \( C_{3} H_{4} \)
Subject: Physics
A ball weighing \( 10 g \) hits a hard surface
vertically with a speed of \( 5 m / \)sec and rebounds with the same speed. The ball remains in contact with the surface for
\( 1 / 100 s e c . \) The average force exerted by the surface on the ball is
\( \mathbf{A} \cdot 100 N \)
в. \( 10 N \)
\( c \cdot 1 N \)
D. \( 0.1 N \)
Subject: Maths
Which one of the following relations on
\( R \) is equivalence relation
A. \( x R_{1} y \Leftrightarrow|x|=\mid y \)
В. \( x R_{2} y \Leftrightarrow x \geq y \)
c. \( x R_{3} y \Leftrightarrow x \mid y \)
D. \( x R_{4} y \Leftrightarrow x<y \)
Subject: Chemistry
A gas is expanded from volume \( V_{0} \) to
\( 2 V_{0} \) under three different processes.
Process 1 is isobaric process, process 2 is isothermal and process 3 is
adiabatic. Let \( \Delta U_{1}, \Delta U_{2} \) and \( \Delta U_{3} \) be
the change in internal energy of the gas in these three process. Then
A \( \cdot \Delta U_{1}>\Delta U_{2}>\Delta U_{3} \)
в. \( \Delta U_{1}<\Delta U_{2}<\Delta U_{3} \)
c. \( \Delta U_{2}<\Delta U_{1}<\Delta U_{3} \)
D. \( \Delta U_{2}<\Delta U_{3}<\Delta U_{1} \)
Subject: Maths
The sum of the series \( 1+2(1+1 / n)+3 \)
\( (1+1 / n)^{2}+\ldots . \infty \quad \) is given \( b y \)
A \( \cdot n^{2}+1 \)
the 1
B \( \cdot n(n+1) \)
c. \( n(1+1 / n)^{2} \)
\( \mathbf{D} \cdot n^{2} \)
Subject: Physics
A point positive charge of \( Q \) ' unit is moved round another positive charge of \( \mathrm{Q} \) unit on a circular path. If the radius of the circle is \( r, \) the work done on the charge \( Q \)
in making one complete revolution is:
\( ^{A} \cdot \frac{Q}{4 \pi \epsilon_{0} r} \)
в. \( \frac{Q Q^{\prime}}{4 \pi \epsilon_{0} r} \)
c. \( \frac{Q^{\prime}}{4 \pi \epsilon_{0} r} \)
D. 0
Subject: Chemistry
An organic compund contains \( \boldsymbol{C}= \) \( \mathbf{4 0 \%}, \boldsymbol{H}=\mathbf{1 3 . 3 3 \%} \) and \( \boldsymbol{N}=\mathbf{4 6 . 6 7 \%} . \) Its
emperical formula is:
A. \( C_{2} H_{2} N \)
в. \( C_{3} H_{7} N \)
c. \( C H_{4} N \)
D. \( C H N \)
Subject: Physics
A planet of mass \( M=2.4 \times 10^{14} k g \) is
orbiting a star in time \( \boldsymbol{T}=\boldsymbol{3} \times \mathbf{1 0}^{4} \boldsymbol{s} \)
sweeps an area of \( \boldsymbol{A}=\mathbf{6 . 9} \times \mathbf{1 0}^{\mathbf{8}} \boldsymbol{m}^{\mathbf{2}} \)
Calculate Angular Momentum of Planet
Subject: Chemistry
Q Type your question-
alternatives given:
Chlorobenzene can be converted into
phenol by heating in aqueous sodium hydroxide solution at a temperature of
\( 623 \mathrm{K} \) and a pressure of 300 atm. However, the rate of reaction can be
increased by the presence of certain
groups in the benzene ring.

What will be the order of reactivity of following compounds towards the above
substitution reaction?
A. iii \( > \) ii \( >i \)
B. ii > iii > i
\( \mathbf{C} \cdot \mathbf{i}>\mathbf{i} \mathbf{i}>\mathbf{i} \) ii
D. i > iii > ii
Subject: Physics
When a neutron collides with a quasi
free proton, it loses half of its energy on the average in the every collission. How many collisions, on the average, are required to reduce a 2 MeV neutron to a thermal energy df \( 0.04 \mathrm{eV} \)
A . 30
B. 22
\( c .35 \)
D. 26
Subject: Maths
In each of the exercises 1 to 3 , form a
differential equation representing the given family of curves by eliminating arbitrary constants \( a \) and \( b \)
1. \( \frac{x}{a}+\frac{y}{b}=1 \)
2. \( y^{2}=a\left(b^{2}-x^{2}\right) \)
3. \( \boldsymbol{y}=\boldsymbol{a} e^{3 x}+\boldsymbol{b} e^{2 x} \)
Subject: Maths
If the points of local extremum of
\( f(x)=x^{3}-3 a x^{2}+3\left(a^{2}-1\right) x+1 \)
lies between \( -2 \& 4, \) then \( ^{\prime} a^{\prime} \) belongs to
A. (-2,2)
B \( \cdot(-\infty,-1) \cup(3, \infty) \)
c. (-1,3)
\( D \cdot(3, \infty) \)
Subject: Physics
To get an output of 1. from the circuit
shown in figure the input must be
\( \mathbf{A} \cdot a=0, b=0, c=1 \)
B \( . a=1, b=0, c=0 \)
\( \mathbf{c} \cdot a=1, b=0, c=1 \)
D . \( a=0, b=1, c=0 \)
Subject: Physics
If a straight wire carrying a current \( \boldsymbol{i}_{1} \) amp runs along the axis of a circular
current carrying loop having current \( i_{2} \) amp, then the force of interaction
between the two current carrying conductors is
A. zero
B. Infinity
c. \( \frac{2 i_{1} i_{2}}{r} N m^{-1} \)
D. \( \frac{\mu_{0}}{4 \pi} \frac{2 i_{1} i_{2}}{r} N m^{-1} \)
Subject: Physics
Two identical magnetic dipoles are
placed, as shown separated by distance
d. The magnetic field, mid way between
the dipoles, is :
\( A \)
\[
\frac{\mu_{0} M \sqrt{2}}{4 \pi d^{3}}
\]
B.
\[
\frac{\mu_{0} M \sqrt{5}}{4 \pi d^{3}}
\]
\( c \)
\[
\frac{2 \mu_{0} M \sqrt{5}}{\pi d^{3}}
\]
D. none of these
Subject: Chemistry
The \( K_{s p} \) value for \( G d(O H)_{3} \) is \( 2.8 \times \) \( 10^{-23}, \) the \( p H \) at which \( G d(O H)_{3} \)
begins to precipitate is:
A . 6.08
B. 5.08
c. 8.47
D. 4.08
Subject: Chemistry
Which of the following is not correctly
matched with its IUPAC name?
\( \mathbf{A} \cdot C H F_{2} C B r C l F: 1- \) Bromo- 1 -chloro- \( 1,2,2- \) trifluoroethane
B. \( \left(C C l_{3}\right)_{3} C C l \) : 2-(Trichloromethyl)-1,1,1,2,3,3, 3 heptachioropropane
\( \mathbf{c} \cdot C H_{3} C\left(p-C l C_{6} H_{4}\right)_{2} C H(B r) C H_{3}: 2-\mathrm{Bromo}-3,3- \)
bis(4-chlorophenyl) butane
D \( \cdot o-B r C_{6} H_{4} C H\left(C H_{3}\right) C H_{2} C H_{3}: \) 2-Bromo-1-
methylpropylbenzene
Subject: Physics
Two lamps one rated \( 60 \mathrm{W}, 220 \mathrm{V} \) and the other \( 40 \mathrm{W}, 220 \mathrm{V} \) are connected in
parallel to a \( 220 \mathrm{V} \) electric supply mains. What is the total current drawn from the
electric mains if the voltage of electric supply is \( 220 \mathrm{V} ? \)
Subject: Physics
quantıties for the pictured circult. What is the current flowing through the
resistor \( 3 ? \)
Battery Terminal Voltage \( \quad 16.0 \mathrm{v} \)
Voltmeter 1 Reading
Ammeter 1 Reading
Ammeter 2 Reading \( 7.0 \mathrm{A} \)
\( A \cdot 8.0 A \)
B. 13.0 A
\( c \cdot 7.0 A \)
D. 16.0 A
E. 6.0
Subject: Chemistry
The chemicals used for
preparing acetophenone
are
A) \( C_{6} H_{6} \) B) \( C H_{3} C O O C H_{3} \)
3
C) \( C H_{3} C O C l \)
D) Anhydrous \( A l C l_{3} \)
\( A \cdot A, B, C \)
B. B,C,D
\( c \cdot A, C, D \)
D. A,B,D
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{a} & \boldsymbol{p} \\ \boldsymbol{b} & \boldsymbol{q} \\ \boldsymbol{c} & \boldsymbol{r}\end{array}\right]_{\mathbf{3} \times \mathbf{2}} \) then determinant
\( \left(A A^{T}\right) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( a^{2}+b^{2}+c^{2} \)
c. \( p^{2}+q^{2}+r^{2} \)
D. \( p^{2}+q^{2} \)
Subject: Maths
Consider two curves \( C_{1}: y=\frac{1}{x} \) and
\( C_{2}: y=\ln x \) on the \( x y \) plane. Let \( D_{1} \)
denotes the region surrounded by
\( C_{1}, C_{2} \) and the line \( x=1 \) and \( D_{2} \)
denotes the region surrounded by
\( C_{1}, C_{2} \) and the line \( x=a . \) If \( D_{1}=D_{2} \)
then the sum of logarithm of possible values of \( a \) is:
Subject: Chemistry
Consider the two gaseous equilibria involving \( S O_{2} \) and the corresponding equilibrium constants at \( 298 \mathrm{K} \)
\( \boldsymbol{S O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \Leftrightarrow \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) ; \boldsymbol{K}_{1} \)
\( 2 S O_{3}(g) \Leftrightarrow 2 S O_{2}(g)+O_{2}(g) ; K_{2} \)
The values of the equilibrium constants are related by:
A \( \cdot K_{1}=K_{2} \)
в. \( K_{2}=K_{1}^{2} \)
c. \( _{K_{2}=\frac{1}{K_{1}^{2}}} \)
D. \( _{K_{2}}=\frac{1}{K_{1}} \)
Subject: Chemistry
Assertion
Threshold frequency is a characteristic
for a metal.
Reason
Threshold frequency is a maximum frequency required for the ejection of electron from the metal surface.
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: Maths
If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \) and
\( \boldsymbol{f}(1)=2, f(x+y)=f(x) f(y) \) for all
\( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} . \) Then \( \boldsymbol{x}^{f(1)}+\boldsymbol{y}^{f(2)}+\boldsymbol{z}^{f(3)}- \)
\( \frac{\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}}{\boldsymbol{x}^{f(1)}+\boldsymbol{y}^{f(2)}+\boldsymbol{z}^{f(3)}} \) is equal to
\( A \cdot 0 \)
B. 1
\( c \cdot 2 \)
D. 3
Subject: Physics
The angular momentum of a disc of radius R about an axis, passing through its centre of mass perpendicular to the plane and rotating
with an angular velocity \( \omega \) will be
\( \mathbf{A} \cdot m R^{2} \omega \)
B. \( 2 m R^{2} \omega^{\text {( }} \)
\( \mathbf{c} \cdot 1 / 2 m R^{2} \omega \)
D. \( m R^{2} / 4 \omega \)
Subject: Physics
A ray of light is incident at the glass-
water interface at angle \( i, \) it emerges
finally parallel to the surface of water,
then the value of \( \mu_{g} \) would be
A \( \cdot(4 / 3) \sin (i) \)
B. \( [1 / \sin (i)] \)
\( c \cdot 4 / 3 \)
D.
Subject: Maths
Find the output order for the following
matrix multiplication \( \boldsymbol{A}_{\mathbf{4} \times \mathbf{2}} \times \boldsymbol{B}_{\mathbf{2} \times \mathbf{4}} \) ?
\( A \cdot 2 \times 4 \)
B. \( 4 \times 4 \)
\( c \cdot 4 \times 2 \)
D. Multiplication not possible
Subject: Physics
A wave train has the equation \( y= \) \( 4 \sin (30 \pi t+0.1 x) \) where \( x \) is in \( \mathrm{cm} \) and
\( t \) in seconds. What is the frequency of
the source? How much time does a
wave pulse take to reach a point \( 30 \mathrm{cm} \)
from it??
Subject: Maths
Let \( z_{1} \) and \( z_{2} \) be two roots of the
equation \( z^{2}+a z+b=0, z \) being
complex, Further, assume that the
origin \( z_{1} \) and \( z_{2} \) form an equilateral
triangle. Then,
A \( \cdot a^{2}=b \)
в. \( a^{2}=2 b \)
\( \mathbf{c} \cdot a^{2}=3 b \)
D. \( a^{2}=4 b \)
Subject: Maths
If \( y=\tan ^{-1}\left(\frac{2^{x^{\prime}}}{1+2^{2 x+1}}\right) \) then \( \frac{d y}{d x} \) at
\( \boldsymbol{x}=\mathbf{0} \) is?
A \( \cdot \frac{1}{10} \log 2 \)
в. \( \frac{1}{5} \log 2 \)
c. \( -\frac{1}{10} \log 2 \)
D. \( \log 2 \)
Subject: Physics
Two cars \( X \) and \( Y \) start off to a race on a
straight path with initial velocities of 8 \( \mathrm{m} / \mathrm{s} \) and \( 5 \mathrm{m} / \mathrm{s} \) respectively. Car \( \mathrm{X} \)
moves with uniform acceleration of \( 1 m / s^{2} \) and car \( Y \) moves with uniform acceleration of \( 1.1 \mathrm{m} / \mathrm{s}^{2} . \) If both the cars reach the winning post together find the length of the track.
A. \( 1000 \mathrm{m} \)
B. 2000
c. 2500
D. 2280
Subject: Chemistry
\( 10 \mathrm{mL} \) of water required \( 1.47 \mathrm{mg} \) of \( K_{2} C r_{2} O_{7}\left(M . w t_{.}=294\right) \) for oxidation of
dissolved organic matter in presence of acid. Then the \( C .0 . D \) of water sample is:
A. 2.44 ppm
B. 24 ppm
c. 32 ppm
D. 1.6 ppm
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \int_{\boldsymbol{f}(\boldsymbol{x})}^{\boldsymbol{g}(\boldsymbol{x})} \boldsymbol{h}(\boldsymbol{t}) \boldsymbol{d} \boldsymbol{t}= \)
A \( \cdot g^{\prime}(x) h(g(x)) \)
B. \( h(g(x))-h(f(x)) \)
c. \( h(g(x)) . g^{\prime}(x)-h(f(x)) . f^{\prime}(x) \)
D. none of these
Subject: Chemistry
What is the heat of reaction for the
above reaction given the heat of
formation, \( \Delta \boldsymbol{H}_{f} \) of \( \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \) is
\( 34 k J / \) mole and \( N_{2} O_{4}(g) \) is
\( 10 k J / \) mole?
A. \( -58 k J \)
\( J \)
в. \( -48 k J \)
c. \( 10 k J \)
D. \( 48 k J \)
E . \( 78 k J \)
Subject: Physics
Two trains \( A \) and \( B \) of length \( 400 m \)
each are moving on two parallel tracks
with a uniform speed of \( 72 \mathrm{km} \mathrm{h}^{-1} \) in
the same direction, with \( A \) ahead of \( B \)
The driver of \( B \) decides to overtake \( A \)
and accelerates by \( 1 \mathrm{m} \mathrm{s}^{-2} \). If after \( 50 \mathrm{s} \)
the guard of \( B \) just brushes past the
driver of \( A, \) what was the original
distance between them?
Subject: Maths
Factorize the following expression \( 9 x^{2}+y^{2}+1-6 x y+6 x-2 y \)
A \( \cdot(3 x-y+1)^{2} \)
в. \( (3 x-y+1)^{3} \)
c. \( (3 x-y-1)^{2} \)
D. None of these
Subject: Physics
Two magnetic poles each of magnetic pole strength \( 16 \mathrm{A} \mathrm{m} \) are placed at a distance of \( 2 \mathrm{m} \) apart. Find magnetic force acting on each pole.
A \( \cdot 4 \times 10^{-7} N \)
B . \( 16 \times 10^{-7} N \)
c. \( 32 \times 10^{-7} N \)
D. \( 64 \times 10^{-7} N \)
Subject: Chemistry
The rate constant for the reaction, \( \mathbf{2} N_{2} O_{5} \rightarrow 4 N O_{2}+O_{2} \) is \( 2 \times 10^{-5} s^{-1} . \)
rate of reaction is \( 1.4 \times \)
\( 10^{-5} \) mol \( L^{-1} s^{-1}, \) what will be the
concentration of \( N_{2} O_{5} \) in mol \( L^{-1} \) ?
A. 0.8
B. 0.7
c. 1.2
D.
Subject: Chemistry
Among the following which is not the \( \pi \) -
bonded organomettalic compound?
\( \mathbf{A} \cdot K\left[P t C l_{3}\left(\eta^{2}-C_{2} H_{4}\right)\right] \)
\( \mathbf{B} \cdot F e\left(\eta^{5}-C_{5} H_{5}\right)_{2} \)
\( \mathbf{c} \cdot C r\left(\eta^{6}-C_{6} H_{6}\right)_{2} \)
\( \mathbf{D} \cdot\left(C H_{3}\right)_{4} S n \)
Subject: Physics
A particle of charge \( q \) and mass \( m \) is moving through a region of space where crossed magnetic and electric fields produce a zero net force on the charge. At a later time, the Electric field is
reduced by a factor of two. What effect will this have on the motion
of the particle? Select all that apply.
A. The particle will continue to move in a circle of the same radius.
B. The particle will eventually move in a circle of twice the radius
C. The particle will eventually move in a circle of half the radius
D. The particle will eventually follow a curved-noncircular path
E. The particle will follow a straight line path.
Subject: Chemistry
In the following reaction \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightleftharpoons \boldsymbol{H} \boldsymbol{I} \)
the amount of \( \boldsymbol{H}_{2}, \boldsymbol{I}_{2} \) and \( \boldsymbol{H} \boldsymbol{I} \) are \( \boldsymbol{0} . \boldsymbol{2} \boldsymbol{g} \)
\( 9.525 g \) and \( 44.8 g \) respectively at equilibrium at a certain temperature. Calculate the equilibrium constant of
the reaction.
Subject: Chemistry
Number of non-bonding electron pairs
on \( X e \) in \( X e F_{6}, X e F_{4} \) and \( X e F_{2} \)
respectively will be:
\( \mathbf{A} \cdot 6,4,2 \)
B. 1,2,3
c. 3,2,1
D. 0,3,2
Subject: Chemistry
Which of the following molecules/species have identical bond order and same magnetic properties?
(I) \( \boldsymbol{O}_{2}(\|) \boldsymbol{N} \boldsymbol{O}(\| \text { I }) \boldsymbol{N}_{2}^{+} \)
\( A \cdot(1),(11) \) only
B. (I) and (III) only
c. (I), (II) and (III)
D. (II) and (III) only
Subject: Chemistry
Total number of cis \( N-M n-C l \) bond
angles (that is, \( M n-N \) and \( M n-C l \)
bonds in cis position) present in a
molecule of cis \( \left[M n(e n)_{2} C l_{2}\right] \) complex
is
\( \left(e n=N H_{2} C H_{2} C H_{2} N H_{2}\right) \)
Subject: Chemistry
Give Nernst equation:
Calculate the electrode potential of the
following single electrode. \( \boldsymbol{C u}_{(a q)}^{++}(\boldsymbol{C}=\mathbf{0 . 0 1 M}) / \boldsymbol{C u} ;\left(\boldsymbol{E}^{\circ}=\right. \)
\( +0.337 V) \)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) when \( \boldsymbol{y}=\boldsymbol{x}^{\boldsymbol{x} \cos \boldsymbol{x}}+\left(\frac{\boldsymbol{x}^{2}+\mathbf{1}}{\boldsymbol{x}^{2}-\mathbf{1}}\right) \)
Subject: Maths
If \( \cos ^{2} 45-\cos ^{2} 30=x \cos 45^{\circ} \sin 45^{\circ} \)
\( \operatorname{then} x= \)
A .2
B. \( \frac{3}{2} \)
\( c \cdot \frac{-1}{2} \)
D. \( \frac{-3}{4} \)
Subject: Chemistry
\( \boldsymbol{A}_{\boldsymbol{3}(\boldsymbol{g})} \rightleftharpoons \mathbf{3} \boldsymbol{A}_{(\boldsymbol{g})} \)
In the above reaction, the initial moles
of \( A_{3} \) is "a". If \( \alpha \) is degree of
dissociation of \( A_{3} \). The total number of
moles at equilibrium will be:
A \( \cdot a-\frac{a \alpha}{3} \)
B. \( \frac{a}{3}-\alpha \)
c. \( \left(\frac{a-a \alpha}{2}\right) \)
D. None of these
Subject: Chemistry
During the adsorption of krypton on activated charcoal at low temperature:
\( \mathbf{A} \cdot \Delta H<0 \) and \( \Delta S>0 \)
B. \( \Delta H>0 \) and \( \Delta S>0 \)
c. \( \Delta H<0 \) and \( \Delta S<0 \)
D. \( \Delta H>0 \) and \( \Delta S<0 \)
Subject: Maths
For \( \boldsymbol{x} \in \boldsymbol{R}-\{\boldsymbol{n} \boldsymbol{\pi}\}, \) the graph is: \( \boldsymbol{y}= \)
\( x+\sin x \)
A. Monotonically Increasing
B. Monotonically Decreasing
c. Either \( A \) or \( B \)
D. None of these
Subject: Chemistry
A big irregular shaped vessel container water, the specific conductance of which was \( 2.56 \times 10^{-5} \mathrm{mhocm}^{-1} .500 \mathrm{g} \)
of \( N a C l \) was the added to the water and
the specific conductance after the addition of \( N a C l, \) was found to be
\( 3.10 \times 10^{-5} \mathrm{mhocm}^{-1} . \) The capacity of
the vessel if it is fulfilled with water is :
\( \left(\lambda_{\infty} N a C l=149.9\right) \)
B . \( V=2.59 \times 10^{6} \mathrm{cm}^{-3} \)
c. \( V=3.14 \times 10^{9} \mathrm{cm}^{-3} \)
D. none of the above
Subject: Maths
If \( \tan \theta, 2 \tan \theta+2,3 \tan \theta+3 \) are in
G.P, then the value of \( \frac{7-5 \cot \theta}{9+4 \sqrt{\sec ^{2} \theta-1}} \)
is
A \( \cdot \frac{12}{5} \)
в. \( \frac{-33}{28} \)
c. \( \frac{33}{100} \)
D. \( \frac{12}{13} \)
Subject: Physics
Two equal masses are attached to the
two ends of a spring of spring constant
k. The masses are pulled out.
Symmetrically to stretch the spring by a
length \( x \) over its natural length. The
work done by the spring on each mass
during the above stretching is
A \( \cdot \frac{1}{2} k x^{2} \)
B. \( -\frac{1}{2} k x^{2} \)
c. \( \frac{1}{4} k x^{2} \)
D \( \cdot-\frac{1}{4} k x^{2} \)
Subject: Chemistry
When the equation: \( C_{2} H_{6}+O_{2} \rightarrow \)
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \) is completely
balanced using the lowest whole number coefficients, the sum of
the coefficients will be :
A . 4
B. 9.
c. 19
D. 15.5
E. 1
Subject: Biology
Match the following
1
Eutrophication
I. Rise in sea level
2
II. Water hyacinth Biomagnification
III. Increase of quantity of
3. Terror of Bengal pollutant at successive trophic levels
4. Green house \( \quad \) IV. Enrichment with nutrients effect
\( A \cdot 1-1 V, 2-111,3-1,4-11 \)
B. 1- -।, 2- ||, 3- |II, 4- IV
c. \( 1- \) ॥, \( 2- \) ॥ᅵ, \( 3-1 V, 4-1 \)
D. 1- -IV, 2- |II, 3- ||, 4-1
Subject: Physics
A current I flows in a circular arc of
radius R, which subtends an angle \( \frac{\pi}{6} \) radian at the center. The magnetic induction B at the center is
\( A \cdot \frac{I_{l d}}{4 R_{D}} \)
B. \( \frac{I_{\mu}}{2_{R}} \)
c. \( \frac{I \mu_{0}}{24 R_{0}} \)
D. \( \frac{I \mu_{0}}{12 R_{R}} \)
Subject: Physics
For wave connected with proton, debroglie wavelength change by \( 0.25 \% \) if
its momentum change by \( P_{0} \) initial
momentum =
A. \( 100 P_{0} \)
в. \( \frac{P_{0}}{400} \)
c. \( 401 P_{0} \)
D. \( \frac{P_{0}}{100} \)
Subject: Maths
if the coefficient of the middle term in
the expansion of \( (1+x)^{2 n+2} \) and \( p \) and
the coefficients of middle terms in the
expansion of \( (1+x)^{2 n+1} \) are \( q \) and \( r \)
then
A \( . p+q=r \)
в. \( p+r=q \)
c. \( p=q+r \)
D. \( p+q+r=0 \)
Subject: Chemistry
Which of the following is true?
A. In an endothermic equilibrium reaction, activation energy required for a forward reaction is higher than that for a backward reaction
B. To an endothermic equilibrium reaction, activation energy required for a forward reaction is higher than that for a backward reaction
C. Activation energy required for both forward and backward reaction is same in equilibrium
D. No activation energy is required for an exothermic backward equilibrium reaction
Subject: Chemistry
The table shows some information
about elements in Group VII of the
Periodic Table.
yellow-
green \( \begin{array}{ll}\text { Name } & \begin{array}{l}\text { State at room } \\ \text { temperature }\end{array} \\ \text { Chlorine } & \text { Gas } \\ \text { Bromine } & \text { liquid } \\ \text { iodine } & \text { ? } \\ \text { Astaine } & \text { solid }\end{array} \) brown
? black
Which information about iodine
completes the table?
A. State - liquid, colour - black
B. State - liquid, colour - green
c. state - solid, colour - grey
D. State - solid, colour - yellow
Subject: Physics
A secondary cell after long use has an emf of \( 1.9 V \) and a large internal
resistance of \( 380 \Omega \). What maximum
current can be drawn from the cell?
Could the cell drive the starting motor of
a car?
\( \mathbf{A} \cdot 5 m A, \) yes
B. \( <5 m A \), Yes
\( \mathbf{c} .5 m A, \) No
\( \mathbf{D} \cdot<5 m A, \) No
Subject: Physics
Solve:
Estimate the mass of the earth, given,
radius of the earth \( =\mathbf{6 . 4} \times \mathbf{1 0}^{\mathbf{6}} \mathbf{m} \)
acceleration due to gravity \( =9.8 m / s^{2} \)
and gravitational constant \( =6.67 \times \)
\( 10^{-11} S . I . \) units.
Subject: Physics
Electric flux through a surface of area
100 \( m^{2} \) lying in the xy plane is (in \( V \) m) if \( \overrightarrow{\boldsymbol{E}}=\hat{\boldsymbol{i}}+\sqrt{\boldsymbol{2}} \hat{\boldsymbol{j}}+\sqrt{\boldsymbol{3}} \hat{\boldsymbol{k}} \)
A. 100
B. 141.4
c. 173.2
D. 200