AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( f(x)=x^{4}-2 x^{3}+3 x^{2}-a x+b \) is a
polynomial such that when it is divide by \( (x-1) \) and \( (x+1) \) the remainders
are 5 and 19 respectively the remainder when \( f(x) \) is divisible by \( (x-2) \) is
\( A \cdot 7 \)
B. 8
c. 9
D. 10
Subject: Chemistry
Arrange the following in increasing
order of their acidic strength.
\( \mathbf{A} \cdot I I I<I<I V<I I \)
В . \( I I<I<I V<I I I \)
\( \mathbf{c} \cdot I<I I I<I V<I I \)
D . \( I I<I I I<I<I V \)
Subject: Physics
When the light of frequency \( 2 v_{0} \) (where
\( v_{0} \) is threshold frequency), is incident
on a metal plate, the maximum velocity
of electrons emitted is \( v_{1} \). When the
frequency of the incident radiation is
increased to \( 5 v_{0}, \) the maximum velocity
of electrons emitted from the same
plate is \( v_{2} \). The ratio of \( v_{1} \) to \( v_{2} \) is?
A . 4: 1
B. 1: 2
c. 2: 1
D. 1: 4
Subject: Physics
The moment \( P\left(\text { in } k g m s^{-1}\right) \) of a particle
is varying with time \( t \) (in second) as
\( \boldsymbol{p}=\mathbf{2}+\mathbf{3} \boldsymbol{t}^{2} . \) The force acting on the
particle at \( t=3 s \) will be
\( A \cdot 18 N \)
B. 54
\( c \cdot 9 N \)
D. 15 N
Subject: Physics
A 10 meter long thick rubber pipe is suspended from one of its ends. The extension produced in the pipe under its own weight will be \( :(Y=5 \times \)
\( 10^{6} N / m^{2} \) and density of rubber \( = \)
\( \left.1500 k g / m^{3}\right) \)
\( \mathbf{A} \cdot 1.5 m \)
B. \( 0.15 \mathrm{m} \)
\( \mathrm{c} .0 .015 \mathrm{m} \)
D. \( 0.0015 \mathrm{m} \)
Subject: Maths
If \( |z|=\max \{|z-1|,|z+1|\} \) then
A \( \cdot|z+\bar{z}|=\frac{1}{2} \)
B. \( z+\bar{z}=1 \)
c. \( |z+\bar{z}|=1 \)
D. None of these
Subject: Maths
\( \left|\begin{array}{ccc}x^{2}+x & x+1 & x-2 \\ 2 x^{2}+3 x-1 & 3 x & 3 x-3 \\ x^{2}+2 x+3 & 2 x-1 & 2 x-1\end{array}\right|= \)
\( A x+B \) then
A. A and B are independent of \( x \)
B. A and B are dependent of \( x \)
C. A dependent on x but B does not depend on x
D. B depends on x but A does not depend on x
Subject: Chemistry
Calculate \( \Delta G \) for the following cell
reaction.
\( \boldsymbol{Z} \boldsymbol{n}_{(s)}+\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{O}_{(s)}+\boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \rightarrow \boldsymbol{Z} \boldsymbol{n}_{(a q)}^{2+}+ \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g}_{(s)}+\mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
\( \boldsymbol{E}_{A \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}}^{0}=+\mathbf{0 . 8 0} \boldsymbol{V} \) and \( \boldsymbol{E}_{\boldsymbol{Z n}^{+2} / Z \boldsymbol{n}}^{0}= \)
\( -0.76 V \)
A . -305 k \( J / \operatorname{mol} \)
в. \( -301 k J / \) mol
c. \( 305 k J / \) mol
D. 301 kJ/mol
Subject: Maths
If \( \sum_{i=1}^{2 n} \sin ^{-1} x_{i}=n \pi, \) then \( \sum_{i=1}^{2 n} x_{i} \) is equal
to
A \( . n \)
B. \( 2 n \)
c. \( \frac{n(n+1)}{2} \)
D. None of these
Subject: Maths
If the function \( f(x)=x^{3}-6 a x^{2}+5 x \)
satisfies the conditions of Lagrange's mean theorem for the interval [1,2] and the tangent to the curve \( y=f(x) \) at
\( \boldsymbol{x}=\mathbf{7} / \mathbf{4} \) is parallel to the chord joining
the points of intersection of the curve
with the ordinates \( x=1 \) and \( x=2 \)
Then the value of a is?
\( \mathbf{A} \cdot 35 / 16 \)
B. \( 35 / 48 \)
c. \( 7 / 16 \)
D. \( 5 / 16 \)
Subject: Chemistry
Assertion
\( O_{3} \) acts as a powerful oxidising agent.
Reason
\( O_{3} \) oxidises lead sulphide to lead
sulphate and iodide ions to iodine.
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
Two unequal masses \( \left(M_{1} \text { and } M_{2}\right. \)
)are connected by a string which passes
over a frictionless pulley (Fig. 3.1). If \( \boldsymbol{M}_{\mathbf{1}} \)
\( M_{2} \) and the table are frictionless, the
acceleration of the masses would be
\( A \)
B. \( \frac{M_{1}+M_{2}}{M_{1} g} \)
c. \( \frac{M_{2} g}{M_{1}+M_{2}} \)
D. None of these
Subject: Chemistry
One litre of \( 2 M \) acetic acid and one litre
of \( 3 M \) ethyl alcohol were mixed. The
esterification takes place according to the reaction:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H} \rightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5}+\boldsymbol{H}_{2} \boldsymbol{O} \)
If each solution is diluted by one litre water, the rate would become:
A. 4 times
B. 2 times
c. 0.5 times
D. 0.25 times
Subject: Physics
\( \ln \operatorname{an} A C \) generator, a coil with \( N \) turns, all of the same area \( A \) and total
resistance \( \boldsymbol{R} \), rotates with frequency \( \boldsymbol{\omega} \)
in a magnetic field \( B \). The
maximum value of e.m.f. generated in the coil is :
A. NABR \( \omega \)
B. NAB
c. NABR
D. NAB
Subject: Physics
Assertion
An \( n- \) type semiconductor has a large
number of electrons but still it is
electrically neutral
Reason
An \( n- \) type semicondutor is obtained
by doping an intrinsic semiconductor with a pentavalent impurity.
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
Construct a trapezium \( A B C D \) in which \( \boldsymbol{A B} \| \boldsymbol{C D}, \boldsymbol{A B}=\mathbf{5} \boldsymbol{c m}, \angle \boldsymbol{B}= \)
\( \mathbf{8 0}^{\circ}, \boldsymbol{B C}=\mathbf{4} \boldsymbol{c m} \) and \( \boldsymbol{A D}=\mathbf{4 . 5} \boldsymbol{c m} \)
Subject: Chemistry
Select the correct reduction process:
This question has multiple correct options
\( \mathbf{A} \cdot 2\left[A g(C N)_{2}\right]^{-}+Z n \longrightarrow\left[Z n(C N)_{4}\right]^{2-}+2 A g \)
\( \mathbf{B} \cdot C u O+H_{2} \longrightarrow C u+H_{2} O \)
\( \mathbf{c} \cdot A l_{2} O_{3}+3 Z n \longrightarrow 2 A l+3 Z n O \)
D. \( M g O+C \frac{\text {high}}{\text {temp}} M g+C O \)
Subject: Physics
The position of a particle moving in the \( X \) -Y plane from origin at any time \( t \)
is given by \( \boldsymbol{x}=\left(\mathbf{3} \boldsymbol{t}^{2}-\mathbf{6} \boldsymbol{t}\right) \mathbf{m} ; \boldsymbol{y}=\left(\boldsymbol{t}^{2}-\right. \)
\( 2 t) \mathrm{m}, \) where \( t \) is in seconds. Select the
correct statement(s) about the moving particle from the following.
A. The acceleration of the particle is zero at \( t=0 \) second
B. The velocity of the particle is zero at \( t=0 \) second
c. The velocity of the particle is zero at \( t=1 \) second
D. The velocity and acceleration of the particle are never zero
Subject: Physics
In the displacement method, a convex lens is placed in between an object and a screen. If one of the magnification is 3 and the displacement of the lens between the two positions is \( 24 \mathrm{cm}, \) then the focal length of the lens is:
A . \( 10 \mathrm{cm} \)
B. \( 9 \mathrm{cm} \)
\( c \cdot 6 \mathrm{cm} \)
D. \( 16 / 3 \mathrm{cm} \)
Subject: Physics
A monoatomic ideal gas undergoes a process in which the ratio of \( \boldsymbol{P} \) to \( \boldsymbol{V} \) at
any instant is constant and equal to unity. The molar heat capacity of gas is:
\( \mathbf{A} \cdot 1.5 R \)
B. \( 2.0 R \)
c. \( 2.5 R \)
D. 0
Subject: Maths
The perimeter of a rhombus is \( 146 \mathrm{cm} \)
and one of its diagonal is \( 55 \mathrm{cm} . \) Find the other diagonal and the area of the
rhombus.
A. \( 24 \mathrm{cm} 660 \mathrm{sq} . \mathrm{cm} \)
B. \( 24 \mathrm{cm} 330 \) sq. \( \mathrm{cm} \)
c. \( 48 \mathrm{cm} 660 \mathrm{sq} . \mathrm{cm} \)
D. \( 48 \mathrm{cm} 1320 \) sq. \( \mathrm{cm} \)
Subject: Chemistry
Assertion: A mixture of \( C H_{3} \) COOH
and \( C H_{3} C O O N H_{4} \) is not a buffer
solution.

Reason: An acidic buffer contains
the mixture of a weak acid and its salt
with a strong base.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both Assertion and Reason are not correct
Subject: Physics
\( A \) is singing a note and at the same
time \( B \) is also singing a note with
1 / 8 the frequency of \( A \). The energies of the two sounds are equal. The disparagement amplitude of the note if
\( \boldsymbol{B} \) is:
A. same as that of \( A \)
B. Twice that of \( A \)
c. four times that of \( A \)
D. eigth times that of \( A \)
Subject: Maths
\( \boldsymbol{A} \cap \boldsymbol{X}=\boldsymbol{B} \cap \boldsymbol{X}=\boldsymbol{\phi} \& \boldsymbol{A} \cup \boldsymbol{X}=\boldsymbol{B} \cup \boldsymbol{X} \)
prove that \( \boldsymbol{A}=\boldsymbol{B} \)
Subject: Physics
If resistance of \( 100 \Omega \) and the
inductance of 0.5 henry and capacitance of \( 10 \times 10^{6} \) farad are
connected in series through \( 50 \mathrm{Hz} \) A.C supp;y, then impedence is
A. \( 1.8765 \Omega \)
B. \( 18.76 \Omega \)
c. \( 187.6 \Omega \)
D. 101.3\Omega
Subject: Physics
Two charges when kept at a distance of \( 1 m \) apart in vacuum have some force of
repulsion. If the force of repulsion between these two charges be same, when placed in an oil of dielectric
constant \( 4, \) the distance of separation is :
\( \mathbf{A} \cdot 0.25 m \)
в. \( 0.4 m \)
\( c .0 .5 m \)
D. \( 0.6 m \)
Subject: Maths
In the figure,two 4 -digit numbers are to be formed by filling the places with digits. The number of different ways in which the places can be filled by digits so that the sum of the numbers formed
is also a 4 -digit number and in no place the addition is with carrying, is
\( \mathbf{A} \cdot 55^{4} \)
B. 220
\( c \cdot 45^{4} \)
D. none of these
Subject: Physics
Assertion
The mechanical energy between consecutive node and antinode will
remain conserved in standing wave.
Reason

The mechanical energy does not flow between node and antinode in standing
wave.
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 man standing on the edge of the terrace of a high rise building throws a stone, vertically up with a speed of 20
\( \mathrm{m} / \mathrm{s} . \) Two seconds later, an identical stone is thrown vertically downwards with the same speed of \( 20 \mathrm{m} / \mathrm{s} \). Then :
This question has multiple correct options
A. the relative velocity between the two stones remains constant till one hits the ground
B. both will have the same kinetic energy, when they hitt the ground
c. the time interval between their hitting the ground is 2 s
D. if the collision on the ground is perfectly elastic, both will rise to the same height above the ground
Subject: Chemistry
Which of the following ions does not have S-S linkage?
A. \( S_{2} O_{8}^{2} \)
B. \( S_{2} O_{6}^{2-} \)
\( \mathrm{c} \cdot S_{2} O_{5}^{2} \)
D. \( S_{2} O_{3}^{2} \)
Subject: Maths
Six boys and girls sit in a row randomly Find the probability that the six girls sit together.
A \( \cdot p=\frac{1}{95040} \)
B. \( _{p}=\frac{1}{132} \)
c. \( _{p}=\frac{1}{924} \)
D. \( p=\frac{1}{66} \)
Subject: Chemistry
The boiling points of methane, ethane,
propane and butane are given
compound
\( \begin{array}{ll}\boldsymbol{C H}_{4} & \boldsymbol{C H}_{3} \boldsymbol{C H}_{3}\end{array} \)
boiling \( \quad 112 \quad 185 \) point \( / K \)
Which statement explains the increase in boiling point from methane to
butane?
A. closer packing of molecules results in stronger van der Waals' forces
B. More covalent bonds are present and therefore more energy is required to break the bonds
c. More electrons in the molecules results in stronger van der Waals' forces
D. More hydrogen atoms in the molecules results in stronger hydrogen bonding
Subject: Chemistry
Which of the following is nucleophilic
addition reaction?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C O C l \frac{C H_{3} M g B r(1 e q)}{ } C H_{3} C O C H_{3} \)
\( \mathbf{B} \cdot C H_{3} C O C H_{3} \frac{I_{2} / O H^{-} / \Delta}{\longrightarrow} C H_{3} C O O^{-}+C H I_{3} \)
\( \mathbf{c} \cdot \operatorname{Ph} C H O \frac{K C N / H^{\oplus}}{\longrightarrow} \operatorname{Ph} C H(O H)(C N) \)
\( \mathbf{D} \cdot C H_{3} C \equiv C M g B r \frac{C H_{3} B r}{\longrightarrow} C H_{3} C \equiv C C H_{3} \)
Subject: Maths
Solve \( \int \frac{e^{x}(x-1)}{(x+1)^{3}} d x \)
A \( \cdot \frac{-e^{x}}{(x+1)^{2}}+c \)
в. \( \frac{e^{x}}{(x+1)^{2}}+c \)
c. \( \frac{e^{x}}{(x+1)^{3}}+c \)
D. \( \frac{-e^{x}}{(x+1)^{3}}+c \)
Subject: Physics
An old man and a boy are walking
towards
each other and a bird is flying over them as shown in the figure. Find the
velocity of bird as seen by the boy.
A \( .12 \hat{j} \)
B. \( 16 \hat{j} \)
\( c .-12 \hat{j} \)
D. \( -16 \hat{j} \)
Subject: Physics
In a series resonant \( L C R \) circuit, the
voltage across \( \boldsymbol{R} \) is 100 volts and \( \boldsymbol{R}= \)
\( 1 k \Omega \) with \( C=2 \mu F . \) The resonant
frequency is 200 rad/s. At resonance
the voltage across \( L \) is
A. \( 4 \times 10^{-3} V \)
В. \( 2.5 \times 10^{-2} V \)
c. \( 40 V \)
D. 250 V
Subject: Biology
Chemiosmosis is a universal
mechanism by which organisms
harvest and store energy.
Which of the following best describes
the process?
A. It is the process of whereby a proton gradient drives an energy-requiring reaction.
B. It is the process used to move protons up a concentration gradient for subsequent production of ATP
C. It is the process that uses pumps to drive chemicals across the membrane
D. It is the movement of specific chemicals against its gradient coupled to the flow of protons down its concentration gradient.
Subject: Maths
The value of \( 2 \int \sin x \operatorname{cosec} 4 x d x \) is
equal to:
\( ^{\mathbf{A}} \cdot \frac{1}{2 \sqrt{2}} \ln \left|\frac{1+\sqrt{2} \sin x}{1-\sqrt{2} \sin x}\right|-\frac{1}{4} \ln \left|\frac{1+\sin x}{1-\sin x}\right|+c \)
\( \frac{1}{2 \sqrt{2}} \ln \left|\frac{1+\sqrt{2} \sin x}{1-\sqrt{2} \sin x}\right|-\frac{1}{2} \ln \left|\frac{1+\sin x}{\cos x}\right|+c \)
\( \frac{1}{2 \sqrt{2}} \ln \left|\frac{1-\sqrt{2} \sin x}{1+\sqrt{2} \sin x}\right|-\frac{1}{4} \ln \left|\frac{1+\sin x}{1-\sin x}\right|+c \)
\( \frac{1}{2 \sqrt{2}} \ln \left|\frac{1-\sqrt{2} \sin x}{1+\sqrt{2} \sin x}\right|+\frac{1}{2} \ln \left|\frac{1+\sin x}{\cos x}\right|+c \)
Subject: Maths
The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})= \)
\( x^{2}, \forall x \in R \) is
A. Injection but not surjection
B. Surjection but not injection
c. Injection as well as surjection
D. Neither injection nor surjection
Subject: Physics
If \( \vec{A}=\hat{i}+2 \hat{j}+3 \hat{k} \& \vec{B}=3 \hat{i}-2 \hat{j}+\hat{k} \)
then the area of parallelogram formed with \( \vec{A} \) and \( \vec{B} \) as the sides of the
parallelogram is :
A. \( \sqrt{3} \)
B. \( 8 \sqrt{3} \)
\( c \cdot 64 \)
D.
Subject: Maths
Express a in terms of b if the function defined by \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{a} \boldsymbol{x}+\mathbf{1} & , \boldsymbol{x} \leq \mathbf{3} \\ \boldsymbol{b} \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}>\mathbf{3}\end{array}\right\} \)
is continuous at \( x=3 \)
Subject: Maths
Find the \( 15^{t h} \) term of the G.P. 3,12,48
\( 192, \ldots \)
A \( \cdot 3 \times 4^{15} \)
B . \( 3 \times 4^{14} \)
\( \mathrm{c} \cdot 3 \times 4^{16} \)
D. \( 3^{15} \)
Subject: Maths
If \( \frac{2 x+A}{(x-3)(x+2)}=\frac{9}{5(x-3)}+ \)
\( \frac{B}{(x+2)}, \) then
This question has multiple correct options
\( \mathbf{A} \cdot A=3 \)
B. \( B=5 \)
c. \( _{A}=\frac{1}{3} \)
D. \( B=\frac{1}{5} \)
Subject: Physics
A concave mirror forms an erect image of an object placed at a distance of 10 \( \mathrm{cm} \) from it. The size of the image is double that of the object. Where is the image formed?
A. 20 cm behind the mirror
B. 20 cm in front of the mirror
c. \( 40 \mathrm{cm} \) behind the mirror
D. \( 40 \mathrm{cm} \) in front of the mirror
Subject: Chemistry
In the process of extraction of gold, the following reaction takes place:
Roasted gold ore \( +\boldsymbol{C} \boldsymbol{N}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( [\boldsymbol{X}]+\boldsymbol{O H}^{-} \)
\( [\boldsymbol{X}]+\boldsymbol{Z} \boldsymbol{n} \rightarrow[\boldsymbol{Y}]+\boldsymbol{A} \boldsymbol{u} \)
Identify the compounds \( [\mathrm{X}] \) and \( [\mathrm{Y}] \)
A \( \cdot[X]=\left[A u(C N)_{2}\right]^{-},[Y]=\left[Z n(C N)_{4}\right]^{2-} \)
B . \( [X]=\left[A u(C N)_{4}\right]^{3-},[Y]=\left[Z n(C N)_{4}\right]^{2-} \)
C \( \cdot[X]=\left[A u(C N)_{2}\right]^{-},[Y]=\left[Z n(C N)_{6}\right]^{4} \)
D \( \cdot[X]=\left[A u(C N)_{4}\right]^{-},[Y]=\left[Z n(C N)_{6}\right]^{2} \)
Subject: Maths
Evaluate: \( \int \sqrt[9]{x^{-8}} d x \)
A \( \cdot 9 x^{\frac{1}{9}}+c \)
\( c \)
B \( .9 x^{8}+c \)
c. \( x^{\frac{1}{9}}+c \)
D. \( x^{\frac{8}{9}}+c \)
Subject: Maths
f \( a, b, c \) are in G.P., then
A \( \cdot a\left(b^{2}+a^{2}\right)=c\left(b^{2}+c^{2}\right) \)
B . \( a\left(a^{2}+c^{2}\right)=c\left(a^{2}+b^{2}\right) \)
C \( \cdot a^{2}(b+c)=c^{2}(a+b) \)
D. None of these
Subject: Biology
Match the lists and find the correct
option.
(a) Viroid infecting
(i) 6,500 nucleotides tomato plant
(b) \( T M V \)
(ii) \( 300-400 \) nucleotides
(iii) Two identical
(c) Polio virus \( \quad \) molecules of \( R N A \)
(d) Lentivirus
(iv) Many sided
(v) Prion
\( A \cdot(a)-(i i),(b)-(i),(c)-(i v),(d)-(i i i) \)
B. (a) - (iii), (b) - (i), (c) - (iv), (d) - (ii)
C. \( (a)-(i i),(b)-(i v),(c)-(v),(d)-(i) \)
D. \( (a)-(i),(b)-(i v),(c)-(v),(d)-(i) \)
Subject: Physics
The heat developed in a resistor \( \boldsymbol{R}_{1} \) connected to a cell is equal to the heat developed when it is connected to
another resistance, \( \boldsymbol{R}_{2} \) replacing \( \boldsymbol{R}_{1} \) for the same time. The internal resistance
of the cell will be
A. \( \frac{R_{1}+R_{2}}{2} \)
в. \( \frac{R_{1} R_{2}}{2\left(R_{1}+R_{2}\right)} \)
c. \( \frac{R_{1} R_{2}}{R_{1}+R_{2}} \)
D. \( \sqrt{R_{1} R_{2}} \)
Subject: Chemistry
Select correct statement for 50ml 0.1M
\( \boldsymbol{H}_{2} \boldsymbol{A}(\boldsymbol{a} \boldsymbol{q} .) \) solution
\( \boldsymbol{K}_{\boldsymbol{a}_{1}}=\mathbf{1 0}^{-\mathbf{5}} ; \boldsymbol{K}_{\boldsymbol{a} \mathbf{2}}=\mathbf{1 0}^{-\mathbf{8}} \)
\( \mathbf{A} \cdot\left[H^{+}\right]=2\left[A^{2-}\right] \)
B. pH of 0.1M \( H_{2} A \) solution is 3
C. In above \( H_{2} A \) solution when 5 milimoles of NaHA are added then pH increases by 2 units
D. 50ml of 0.1M NaOH required to neutralised completely 50ml of 0.1M \( H_{2} A \) solution
Subject: Chemistry
Paramagnetism of oxygen is explained on the basis of which of the following electronic configuration?
A \( \cdot\left(2 \pi^{*} p y\right)^{1}\left(2 \pi^{*} p z\right)^{1} \)
B . \( \left(2 \pi^{*} p x\right)^{1}\left(2 \pi^{*} p y\right)^{1} \)
C \( \cdot(2 \sigma p x)^{1}(2 \pi p y)^{1} \)
D. \( (2 \sigma p y)^{1}(2 \pi p y)^{1} \)
Subject: Maths
State whether the following statement
is True or False.
The current in the circuit with
inductance \( L \) and resistance \( R \) and
voltage \( \boldsymbol{E} \sin \omega \boldsymbol{t} \) is given by \( \boldsymbol{L} \frac{\boldsymbol{d} \boldsymbol{i}}{\boldsymbol{d} \boldsymbol{t}}+\boldsymbol{R} \boldsymbol{i}= \)
Esinwt.if \( i=0 \) at \( t=0 \) then,current is
given by \( i=\frac{E}{\sqrt{E^{2}+L^{2} \omega^{2}}}[\sin (\omega t- \)
\( \left.\phi)+e^{-R t / L} \sin \phi\right] \) where \( \phi= \)
\( \tan ^{-1}\left(\frac{L \omega}{R}\right) \)
A. True
B. False
Subject: Chemistry
The reactions \( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+ \)
\( C l_{2}(g) \) and \( C O C l_{2}(g) \rightleftharpoons C O(g)+ \)
\( C l_{2}(g) \) are simultaneously in
equilibrium in an equilibrium box at constant volume. A few moles of \( C O(g) \) are later introduced into the vessel.
After some time, the new equilibrium concentration of
A. \( P C l_{5} \) will remain unchanged
B. \( C l_{2} \) will be greater
c. \( P C l_{5} \) will become less
D. \( P C l_{5} \) will become greater
Subject: Maths
The line \( \mathbf{L} \) given by \( \frac{\mathbf{x}}{\mathbf{5}}+\frac{\mathbf{y}}{\mathbf{b}}=\mathbf{1} \) passes
through the point \( (13,32) . \) If the line \( \mathbf{K} \) is parallel to L and has the equation \( \frac{\mathbf{x}}{\mathbf{c}}+\frac{\mathbf{y}}{\mathbf{3}}=\mathbf{1}, \) then the distance between
\( \mathbf{L} \) and \( \mathbf{K} \) is
A. \( \sqrt{17} \)
в. \( \frac{17}{\sqrt{15}} \)
c. \( \frac{23}{\sqrt{17}} \)
D. \( \frac{23}{\sqrt{15}} \)
Subject: Biology
Select the characters which are not
applicable to the family Solanaceae.
(i) Epipetalous and syngenesious anthers
(ii) Bicarpellary and synchronous ovary
(iii) Superior ovary with axile placentation
(iv) Stamens six and are arranged in
two whorls
(v) Bicarpellary, synchronous and inferior ovary
A. (ii) and (iii) only
B. (i), (iv) and (v) only
c. (ii), (iv) and (v) only
D. (i) and (iii) only
E. (iii), (iv) and (v) only
Subject: Maths
Find the following product: \( \left(x^{3}-5 x^{2}+\right. \)
\( 3 x+1) \times\left(x^{2}-3\right) \)
A \( \cdot x^{5}-5 x^{4}+16 x^{2}-9 x+3 \)
B. \( x^{5}-5 x^{4}+16 x^{2}+9 x-3 \)
c. \( x^{5}+5 x^{4}+16 x^{2}-9 x-3 \)
D. \( x^{5}-5 x^{4}+16 x^{2}-9 x-3 \)
Subject: Maths
The rectangular fence is enclosed with an area \( 16 \mathrm{cm}^{2} . \) The width of the field is
\( 6 \mathrm{cm} \) longer than the length of the fields.
What are the dimensions of the field?
A. length \( =2 \mathrm{cm}, \) width \( =6 \mathrm{cm} \)
B. length \( =1 \mathrm{cm}, \) width \( =8 \mathrm{cm} \)
c. length \( =2 \mathrm{cm}, \) width \( =8 \mathrm{cm} \)
D. length \( =3 \mathrm{cm}, \) width \( =8 \mathrm{cm} \)
Subject: Maths
The particular solution of \( \frac{d y}{d x}+ \) \( \frac{\boldsymbol{y}+\boldsymbol{2}}{\boldsymbol{x}+\boldsymbol{2}}=\boldsymbol{0} \) at (1,2) is given by
A \( . x y+2(x+y)=8 \)
B. \( x y+8(x+y)=2 \)
c. \( (x+2)+2(y+2)=8 \)
D. \( 8(x+2)+(y+2)=2 \)
Subject: Chemistry
Molar conductivity of 0.15 M solution of KCl at \( 298 \mathrm{K} \), if its conductivity is \( 0.0152 \mathrm{S} \mathrm{cm}^{-1} \) will be:
A \( \cdot 124 \Omega^{-1} \mathrm{cm}^{2} \mathrm{mol}^{-} \)
B. \( 204 \Omega^{-1} \mathrm{cm}^{2} \mathrm{mol}^{-} \)
c. \( 101 \Omega^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \)
D. \( 300 \Omega^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \)
Subject: Physics
Two short magnets with pole strengths of
\( 900 A m \) and \( 100 A m \) are placed with their
axes in the same vertical line, with
similar poles facing each other. Each magnet has a length of \( 1 \mathrm{cm} \). When
separation between the nearer poles is
\( 1 \mathrm{cm}, \) the weight of the upper magnet is
supported by the repulsive force between the magnets. If \( g=10 m s^{-2} \), then the
mass of upper magnet is \( \left(x \times 10^{-4}\right) \)
A. \( 1.6 k g \)
в. \( 2.4 k g \)
c. \( 5.5 k g \)
D. \( 4.8 k g \)
Subject: Chemistry
The rate of a reaction doubles when its
temperature changes from \( 300 K \) to
\( 310 K . \) Activation energy of such a
reaction will be : \( (\boldsymbol{R}= \)
\( \left.8.314 J K^{-1} m o 1^{-1} \text {and } \log 2=0.301\right) \)
A \( .48 .6 \mathrm{kJmol}^{-1} \)
B. 58.5 kJmol\( ^{-1} \)
\( \mathbf{c} \cdot 60.5 k J m o l^{-1} \)
D. \( 53.6 \mathrm{kJmol}^{-1} \)