AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A charged oil drop is suspended in
uniform field of \( 3 \times 10^{4} V / m \) so that it
neither falls nor rises. The charge on the drop will be: (take the mass of the
charge \( =\mathbf{9 . 9} \times \mathbf{1 0}^{-15} \mathbf{k g} \) and \( \mathbf{g}= \)
\( \left.10 m / s^{2}\right) \)
A . \( 3.3 \times 10^{-18} \mathrm{C} \)
в. \( 3.2 \times 10^{-18} \mathrm{C} \)
c. \( 1.6 \times 10^{-18} \mathrm{C} \)
D. \( 4.8 \times 10^{-18} \mathrm{C} \)
Subject: Maths
\( f(x)=\tan ^{-1}(\sin x+\cos x) \) is an
increasing function in This question has multiple correct options
A \( \cdot\left(0, \frac{\pi}{4}\right) \)
В \( \cdot\left(0, \frac{\pi}{2}\right) \)
c. \( \left(\frac{-\pi}{4}, \frac{\pi}{4}\right) \)
D. None of these
Subject: Maths
A rectangular block of wood has
dimensions \( 24 \mathrm{cm} \) by \( 8 \mathrm{cm} \) by \( 7 \mathrm{cm} . \) It is cut up into children's bricks.
Each brick is a cube of side \( 3 \mathrm{cm} \)
Find the volume of wood that is left.
Subject: Physics
Assertion
If a light body and a heavy body possess the same momentum, the lighter body
will possess more kinetic energy.
Reason
The kinetic energy of a body varies as
the square of its velocity.
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
Find the sum of the following vectors:
\( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=2 \hat{\hat{\boldsymbol{j}}}-\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\boldsymbol{2} \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
\( \mathbf{2} \hat{\boldsymbol{k}} \)
Subject: Chemistry
Consider a reaction \( a G+b H \longrightarrow \)
Products. When the concentration of
both the reactants \( G \) and \( H \) are
doubled, the rate increases by eight times. However, when the concentration
of \( G \) is doubled keeping the
concentration of \( \boldsymbol{H} \) fixed, the rate is
doubled. The overall order of reaction is:
A . 0
B. 1
c. 2
D. 3
Subject: Maths
\( p_{1}, p_{2} \) are the lengths of the
perpendiculars from any point on \( 2 x+ \)
\( 11 y=5 \) upon the lines \( 24 x+7 y= \)
\( \mathbf{2 0}, \mathbf{4 x}-\mathbf{3 y}=\mathbf{2}, \) then \( \boldsymbol{p}_{\mathbf{1}}= \)
\( A \cdot p_{2} \)
B . \( 2 \mathrm{p}_{2} \)
c. \( \frac{1}{2} p_{2} \)
D. \( \frac{1}{3} p_{2} \)
Subject: Physics
Starting from rest, the acceleration of a
particle is \( a=2(t-1) . \) The velocity of
the particle at \( t=5 s \) is:
A. \( 15 \mathrm{m} / \mathrm{s} \)
B. \( 25 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 5 m / s \)
D. None of these
Subject: Chemistry
An equilibrium mixture in a vessel of capacity 100 litre contain
1 mol \( N_{2}, 2 \) mol \( O_{2} \) and
3 mol NO.No. of moles of \( 0_{2} \) to be
added so that at new equilibrium the conc. of NO is found to be 0.04 mol/lit :
A \( .(101 / 18) \)
B. (101/9)
c. (202/9)
D. None of these
Subject: Physics
Assertion
It is possible to accelerate even if you are travelling at constant speed.
Reason
In the uniform circular motion, even if the particle has the constant speed, it
has an acceleration.
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
Prove the following by using the principle of mathematical induction for all \( \boldsymbol{n} \in \boldsymbol{N}: \mathbf{1} . \mathbf{2 . 3}+\mathbf{2 . 3 . 4}+\ldots \ldots+ \)
\( \boldsymbol{n}(\boldsymbol{n}+\mathbf{1})(\boldsymbol{n}+\mathbf{2})= \)
\( \frac{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})(\boldsymbol{n}+\mathbf{2})(\boldsymbol{n}+\mathbf{3})}{\mathbf{4}} \)
Subject: Maths
Which term of the GP \( 2,8,32, \dots \) is
\( \mathbf{1 3 1 0 7 2} ? \)
\( \mathbf{A} \cdot 6^{t h} \)
B. \( 7^{\text {th }} \)
\( c \cdot 8^{t h} \)
\( \mathbf{D} \cdot 9^{t h} \)
Subject: Physics
Q Type your question
figure. The arcs \( B C \) (radius \( =b \) ) and \( D A \)
(radius \( =a \) ) of the loop are joined by
two straight wires \( A B \) and \( C D . A \)
steady current \( I \) is flowing in the loop.
Angle made by \( A B \) and \( C D \) at the
origin \( O \) is \( 30^{\circ} . \) Another straight thin
wire with steady current \( I_{1} \) flowing out of the plane of the paper is kept at the origin. The magnitude of the magnetic field due to the loop \( A B C D \) at the
origin \( (O) \) is:
A . zero
B. \( \frac{\mu_{0} \mathrm{I}(\mathrm{b}-\mathrm{a})}{24 \mathrm{ab}} \)
c. \( \frac{\mu_{0} \mathrm{I}}{4 \pi}\left[\frac{\mathrm{b}-\mathrm{a}}{\mathrm{ab}}\right] \)
D. \( \frac{\mu_{0} I}{4 \pi}\left[2(b-a)+\frac{\pi}{3}(a+b)\right] \)
Subject: Maths
The probabilities of three events \( A, B, C \) are events such that \( P(A)= \) \( \mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4}, \boldsymbol{P}(\boldsymbol{C})=\mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \boldsymbol{B})=\mathbf{0 . 0 8}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{C})=\mathbf{0 . 2 8}, \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \boldsymbol{B} \cap \boldsymbol{C})=\mathbf{0 . 0 9 .} \) If \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B} \cup \boldsymbol{C}) \geq \mathbf{0 . 7 5} \)
Show that \( P(B \cap C) \) lies in the
interval [0.23,0.48]
Subject: Maths
The value of \( \int \frac{\left(a x^{2}-b\right) d x}{x \sqrt{c^{2} x^{2}-\left(a x^{2}+b\right)^{2}}} \) is
equal to
A \( \cdot \frac{1}{c} \sin ^{-1}\left(a x+\frac{b}{x}\right)+k \)
B. \( \operatorname{csin}^{-1}\left(a+\frac{b}{x}\right)+k \)
c. \( \sin ^{-1}\left(\frac{a x+\frac{b}{x}}{c}\right)+k \)
D. none of these
Subject: Chemistry
Select the correct order of polarity of the
bond for the following molecules:
\( \mathbf{A} \cdot N H_{3}<S b H_{3}<A s H_{3}<P H_{3} \)
B. \( N H_{3}<P H_{3}<S b H_{3}<A s H_{3} \)
\( \mathbf{c} \cdot N H_{3}<P H_{3}<A s H_{3}<S b H_{3} \)
\( \mathbf{D} \cdot N H_{3}>S b H_{3}>A s H_{3}>P H_{3} \)
Subject: Physics
\( (\Delta l) \) of a wire of length \( 1 \mathrm{m} \) suspended
from the top of a . roof at one end and
with a load W connected to the other
end. If the cross-sectional area of the
wire is \( 10^{-6} m^{2}, \) calculate the Young's
modulus of the material of the wire.
A \( \cdot 2 \times 10^{11} N / m^{2} \)
B . \( 2 \times 10^{-11} N / m^{2} \)
\( \mathbf{C} \cdot 3 \times 10^{-12} N / m^{2} \)
D \( \cdot 2 \times 10^{-13} N / m^{2} \)
Subject: Chemistry
If \( 10 \mathrm{ml} \) of \( \mathrm{H}_{2} \mathrm{O}_{2} \) solution requires \( 25 \mathrm{m} \) of \( \frac{\mathbf{N}}{\mathbf{2 0}} \mathbf{K M n O}_{4} \) for complete oxidation in acidic medium, then the mass (in g)
of available \( O_{2} \) per litre present in the solution is:
A . 1
B. 2
\( c .3 \)
D. 4
Subject: Chemistry
Which of the following statement is
correct?
A. Allotropy of sulphur arises partly because of the great variety of molecular forms that can be achieved by -SS- catenation and partly because of the numerous ways in which the molecules so formed can be arranged within the crystal
B. Both rhombic and monoclinic sulphur have \( S_{8} \)
molecules and therefore, possess same value of specific gravities
C. Ozone on reaction with KI solution buffered with a borate buffer (pH 9.2) yields potassium iodate
D. The ozone layer protects the earth's surface from an excessive concentration of mainly infrared (IR) radiations
Subject: Physics
A fixed container is filled with a liquid of
density \( \rho \) up to a height \( 4 m . \) A horizontal
slit of small width but of area \( =0.5 \mathrm{m}^{2} \) is
made a height of \( 2 m \) from bottom. The
speed of top surface of the water level is Area of top surface of container is \( 4 m^{2} \)
and \( g=10 m / s^{2} \) ).
A \( \cdot \sqrt{\frac{20}{63}} \mathrm{m} / \mathrm{sec} \)
в. \( \sqrt{\frac{40}{63}} \) m/sec
c. \( \sqrt{\frac{80}{63}} \mathrm{m} / \mathrm{sec} \)
D. None of these
Subject: Chemistry
Assertion
On adding \( H_{2} S O_{4} \) to water, the
resulting aqueous solution get corrosive.
Reason
Hydronium ions are responsible for
corrosive action.
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: Chemistry
For the galvanic cell pictured below, determine the electrochemical
potential for the system at \( 25^{\circ} \mathrm{C} \)
Note: \( \boldsymbol{C u}_{(a q)}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}_{(s)} \boldsymbol{E}^{\circ}= \)
\( \mathbf{0 . 3 3 7} \mathbf{V} \)
\( Z n_{(a q)}^{2+}+2 e^{-} \rightarrow Z n_{(s)} E^{\circ}=-0.763 V \)
A. \( -0.426 V \)
В. \( -1.10 v \)
\( \mathbf{c} .+0.426 V \)
D. \( +1.10 v \)
Subject: Maths
The coefficient of the middle term in the
expansion of \( (1+x)^{2 n} \) is
This question has multiple correct options
A \( \cdot 2^{n} C_{n} \)
в. \( \frac{1.3 .5 \ldots \ldots(2 n-1)}{n !} 2^{\text {। }} \)
c. \( 2.6 \ldots(4 n-2) \)
D \( \cdot 2.4 \ldots \ldots . .2 n \)
Subject: Chemistry
Which statements are correct about
sucrose?
This question has multiple correct options
A. IUPAC name of sucrose is \( \alpha \) -D-glucopyranosyl- \( \beta \) -Dfructofuranside
B. IUPAC name of sucrose is \( \beta \) -D-fructofuranosyl- \( \alpha \) -Dglucopyranoside
C. It is hydrolysed both by emulsin and amylase
D. On hydrolysis, the solution is laevorotatory
Subject: Chemistry
werner ploneerea the rıeld or coordination chemistry in the late
nineteenth century. At that time, a number of compounds of cobalt (III) chloride with ammonia were known,
with general formula \( C o C l_{3} . x N H_{3} \)
\( \boldsymbol{x}=\mathbf{3} \) to \( \mathbf{6} \)
Treatment of these compounds with aqueous HCl acid did not remove the ammonia. However, treatment of the
compounds with excess of \( A g N O_{3} \) at
\( 273 \mathrm{K} \) gave white precipitate of AgCl in varying ratio depending on the structure. Also each complex had electrical conductivity of varying
nature.
There is no reaction of the compound with aqueous HCl indicating that there
is no free \( N H_{3} \). Thus, \( N H_{3} \) ligand is bonded to cobalt(III) by
A. Primary valency
B. Secondary valency
c. Both of these.
D. None of these
Subject: Physics
With the one slit \( 25 \mathrm{mm} \) from the
biprism and the other \( 16 \mathrm{mm} \) and using light of wavelength \( 1200 \mathrm{nm} \), fringes were formed on a screen \( 0.5 \mathrm{m} \) from the single slit.The fringe width is
A. \( 0.03 \mathrm{cm} \)
B. \( 0.03 \mathrm{mm} \)
\( c \cdot 0.3 \mathrm{cm} \)
D. \( 0.3 \mathrm{m} \)
Subject: Chemistry
In acidic medium, \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) changes
\( C r_{2} O_{7}^{-2} \) to \( C r O_{5} \) which has two \( (-O- \)
\( O-) \) bonds oxidation state of \( C r \) in
\( \boldsymbol{C r} \boldsymbol{O}_{5} \) is:
\( A \cdot+5 \)
\( B \cdot+3 \)
\( c \cdot+6 \)
D. -10
Subject: Physics
The electric potential energy between a proton and an electron is given by \( U= \) \( U_{0} l n \frac{r}{r_{0}}, \) where \( r_{0} \) is a constant.
Assuming Bohr's model to be
applicable, write the variation of \( ^{\prime} \boldsymbol{r}^{\prime} \)
with \( n, n \) being the principal quantum number.
\( \mathbf{A} \cdot r_{n} \propto n \)
\( \mathbf{B} \cdot r_{n} \propto 1 / n \)
c. \( r_{n} \propto n^{2} \)
D. \( r_{n} \propto 1 / n^{2} \)
Subject: Physics
A particle travels in a straight line, such that for a short time \( 2 s \leq t \leq 6 s \), its motion is described by \( \mathrm{v}=(4 / \mathrm{a}) \mathrm{m} / \mathrm{s} \)
where a is in \( m / s^{2} . \) If \( v=6 \mathrm{m} / \mathrm{s} \) when \( t= \)
2s, determine the particle's acceleration when \( t=3 s \)
Subject: Biology
The correct match for functions of
nematocysts is
A. Stenotele
(i) Paralysing
B. Volvent
(ii) Capturing
C. Large glutinant
(iii) Attachment
D. Small glutinant
(iv) Locomotion
A. A- (ii), B- (i), C- (iii), D- (iv)
B. A- (i), B- (ii), C- (iii), D- (iv)
C. \( A- \) (iv), \( B- \) (iii), \( C- \) (ii), D- (i)
D. A- (iv), B- (i), C- (ii), D- (iii)
Subject: Chemistry
Equilibrium constants \( \boldsymbol{K}_{1} \) and \( \boldsymbol{K}_{2} \) for
the following equilibria are related as:
\( N O(g)+\frac{1}{2} O_{2} \stackrel{K_{1}}{=} N O_{2}(g) \)
\( \mathbf{2} N O_{2}(\boldsymbol{g}) \stackrel{\boldsymbol{K}_{2}}{\rightleftharpoons} \boldsymbol{2} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \)
\( ^{\mathrm{A}} \cdot_{K_{2}}=\frac{1}{K_{1}} \)
B. \( K_{2}=K_{1}^{2} \)
c. \( _{K_{2}=} \frac{K_{1}}{2} \)
D. \( _{K_{2}}=\frac{1}{K_{1}^{2}} \)
Subject: Maths
To construct a \( \triangle A B C \) in which \( B C=10 \)
\( \mathrm{cm} \) and \( \mathrm{B}=60^{\circ} \) and \( \mathrm{AB}+\mathrm{AC}=14 \mathrm{cm}, \) then
the length of BD used for construction
A. \( 7 \mathrm{cm} \)
B. \( 14 \mathrm{cm} \)
\( c .20 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Physics
Magnetic field due to a toroid inside its
turns is given by ( \( n \) is thenumber of
turns per unit length of the toroid and \( \boldsymbol{I} \) is the current in the loop)
\( \mathbf{A} \cdot B=\mu_{o} n I \)
В. \( B=\epsilon_{o} n I \)
\( \mathbf{c} \cdot B=\frac{\mu_{o}}{4 \pi} n I \)
D. None of these
Subject: Physics
The molecules of a given mass of a gas have root mean square speeds of \( 100 \mathrm{m} \)
\( s^{-1} \) at \( 27^{\circ} C \) and 1 atmospheric
pressure. The root mean square speeds
of the molecules of the gas at \( 127^{\circ} \mathrm{C} \)
and 2 atmospheric pressure is?
A \( \cdot \frac{20}{\sqrt{3}} \)
в. \( \frac{100}{\sqrt{3}} \)
c. \( \frac{400}{3} \)
D. \( \frac{200}{3} \)
Subject: Physics
Assertion
In a 'tug-of-war' game, both teams exert force on the other through the rope.
Reason

The team that pulls the rope harder wins.
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
The time taken to assemble a car in a
certain plant is a random variable having a normal distribution of 20
hours and a standard deviation of 2
hours. What is the probability that a car can be assembled at this plant in a
period of time between 20 and 22
hours?
A . 0.3513
B. 0.3216
c. 0.3413
D. 0.3613
Subject: Maths
\[
\begin{array}{l}
\boldsymbol{A}_{\mathbf{1}}=\left[\boldsymbol{a}_{1}\right] \\
\boldsymbol{A}_{2}=\left[\begin{array}{lll}
\boldsymbol{a}_{2} & \boldsymbol{a}_{3} \\
\boldsymbol{a}_{\boldsymbol{4}} & \boldsymbol{a}_{5}
\end{array}\right] \\
\boldsymbol{A}_{\boldsymbol{3}}=\left[\begin{array}{lll}
\boldsymbol{a}_{\boldsymbol{6}} & \boldsymbol{a}_{\boldsymbol{7}} & \boldsymbol{a}_{\boldsymbol{8}} \\
\boldsymbol{a}_{\boldsymbol{9}} & \boldsymbol{a}_{\boldsymbol{1 0}} & \boldsymbol{a}_{11} \\
\boldsymbol{a}_{\boldsymbol{1 2}} & \boldsymbol{a}_{\boldsymbol{1 3}} & \boldsymbol{a}_{14}
\end{array}\right] \ldots \ldots \boldsymbol{A}_{\boldsymbol{n}}=[\ldots .]
\end{array}
\]
where \( \quad a_{r}=\left[\log _{2} r\right]([.] \) denotes
greatest integer. Then trance of \( \boldsymbol{A}_{\mathbf{1 0}} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{\alpha} & \mathbf{0} \\ \mathbf{1} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{5} & \mathbf{1}\end{array}\right], \) then
value of \( \alpha \) for which \( A^{2}=B \), is
A .
B. -
\( c \cdot 4 \)
D. No real value
Subject: Physics
A particle moving with uniform acceleration has average velocities \( \boldsymbol{v}_{1} \)
\( v_{2} \) and \( v_{3} \) over the successive intervals
of time \( t_{1}, t_{2} \) adn \( t_{3} \) respectively. teh value of \( \frac{\left(v_{1}-v_{2}\right)}{\left(v_{2}-v_{3}\right)} \) will be
A \( \cdot \frac{\left(t_{1}-t_{2}\right)}{\left(t_{2}-t_{3}\right)} \)
B . \( \frac{\left(\frac{\left(t_{1}-t_{2}\right)}{\left(t_{2}+t_{3}\right)}\right.}{)} \)
D. \( \frac{\left(\frac{\left(t_{1}+t_{2}\right)}{\left(t_{t}+3_{3}\right)}\right.}{)_{2}} \)
Subject: Chemistry
Kunal took few iron turnings and mixed them well with Sulphur powder. He could separate the iron turnings with the help of a magnet. He heated the
mixture for some time and tried to
separate the iron turnings with the magnet but he could not. Why?
A. on heating, a chemical change takes place and a new compound is formed.
B. on heating, iron becomes non-magnetic hence, it is not attracted by magnettet
c. on heating, a physical change takes place hence iron and Sulphur gets mixed up
D. on heating, iron evaporates and only sulphur is left behind
Subject: Physics
A particle is executing simple harmonic simple motion of amplitude \( 5 \mathrm{cm} \) and period 6 s. How long will it take to move from one end of its path on one side of mean position to a position \( 2.5 \mathrm{cm} \) on the same side of the mean position?
A . \( 1 \mathrm{s} \)
B. 1.5 s
\( c \cdot 3 s \)
D. 3.5
Subject: Physics
An object falls from a bridge that is
\( 45 m \) above water. It falls directly into a small boat moving with constant velocity that is \( 12 ~ m \) from the point of impact when the object was released.
The speed of the boat is
A. \( 3 m / s \)
B. \( 4 \mathrm{m} / \mathrm{s} \)
c. \( 5 m / s \)
D. \( 6 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
On increasing temperature from \( 200 \mathrm{K} \) to \( 220 \mathrm{K} \) rate of reaction \( \boldsymbol{A} \) increases by
3 times and rate of reaction \( B \)
increases by 9 times then correct relationship between activation energy of \( A \) and \( B \) is:
A. \( E_{A}=3 E_{B} \)
B \( .3 E_{A}=E_{B} \)
\( \mathbf{c} \cdot E_{B}=2 E_{A} \)
D. \( E_{A}=2 E_{B} \)
Subject: Maths
\( \triangle A B C \) and \( \triangle D B C \) are two iosceles
triangle on the same base \( B C \) and
vertices \( A \) and \( D \) are on the same sides
of \( B C . \) If \( A D \) is exerted to intersect \( B C \)
at \( P \), show that
\( \triangle \boldsymbol{A B P} \cong \)
triangleACP
Subject: Physics
A magnetic field of flux density \( 10 T \)
acts normal to a coil of 50 turns having
\( 100 \mathrm{cm}^{2} \) area. The e.m.f. induced if the
coil is removed from magnetic field in
0.1 second is
A . \( 50 V \)
в. \( 60 V \)
c. \( 80 V \)
D. \( 40 V \)
Subject: Physics
Find the fractional decrement of its
volume
A \( \cdot \frac{\Delta V}{V}=-\frac{3 p}{E}(1-2 \mu) \)
B. \( \frac{\Delta V}{V}=-\frac{3 p}{E}(1+2 \mu) \)
c. \( \frac{\Delta V}{V}=\frac{2 p}{E}(1+3 \mu) \)
D. None of these
Subject: Chemistry
Two liquids \( H N O_{3}(A) \) and water \( (B) \)
form a maximum boiling azeotrope
when mixed in the ratio of \( 68 \% \) and \( 32 \% \)
respectively. It means:
A. A-B interactions are stronger than \( A \) -A and B-B interactions
B. A-B interactions are weaker than A-A and B-B interactions
c. vapour pressure of solution is more than the pure components
D. vapour pressure of solution is less since only one component vaporises
Subject: Maths
The equation of the line passing
through the point \( P(1,2) \) and cutting
the lines \( x+y-5=0 \) and \( 2 x-y=7 \)
at \( A \) and \( B \) respectively such that the
harmonic mean of \( \boldsymbol{P} \boldsymbol{A} \) and \( \boldsymbol{P} \boldsymbol{B} \) is \( \mathbf{1 0} \), is
A \( \cdot y-2=\tan \left(\cos ^{-1} \frac{11}{\sqrt{146}}-\cos ^{-1} \frac{14}{5 \sqrt{146}}\right)(x-1) \)
в. \( y+2=\tan \left(\cos ^{-1} \frac{11}{\sqrt{146}}+\cos ^{-1} \frac{14}{5 \sqrt{146}}\right)(x+1) \)
c. \( y-2=\tan \left(\cos ^{-1} \frac{11}{\sqrt{146}}+\cos ^{-1} \frac{14}{5 \sqrt{146}}\right)(x-1) \)
D. None of the above
Subject: Chemistry
The equilibrium constant for the reaction:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \Leftrightarrow 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \) is \( 64, \) at
certain temperature.The equilibrium
concentrations of \( H_{2} \) and \( H I \) are 2 and
16 mollit\( ^{-1} \) respectively. The
equilibrium concentration (in molLit \( ^{-1} \)
of \( I_{2} \) is ?
A . 16
B. 4
\( c \cdot 8 \)
D. 2
Subject: Chemistry
The self ionisation constant for pure
formic acid. \( \boldsymbol{K}= \)
\( \left[\boldsymbol{H} \boldsymbol{C O O H}_{2}^{+}\right]\left[\boldsymbol{H} \boldsymbol{C O O}^{-}\right] \) has been
estimated as \( 10^{-6} \) at room
temperature. The percentage of formic
acid molecules in pure formic acid are converted to formate ion is \( 0.00 X \% \). The
density of formic acid is \( 1.22 g / c m^{3} \) Value of \( X \) is:
Subject: Chemistry
\( A t-50^{0} C, \) liquid \( N H_{3} \) has ionic
product is \( 10^{-30} \). How many amide
\( \left(N H_{2}^{-}\right) \) ions are present per \( m m^{3} \) in
pure liquid \( \left.\boldsymbol{N} \boldsymbol{H}_{3} \text { ? (take } \boldsymbol{N}_{\boldsymbol{A}}=\boldsymbol{6} \times \mathbf{1 0}^{\mathbf{2 3}}\right) \)
Subject: Physics
A battery of emf \( 15 \mathrm{V} \) and internal resistance of \( 4 \Omega \) is connected to a
resistor. If the current in the circuit is 2
A and the circuit is closed. Resistance
of the resistor and terminal voltage of the battery will be.
A \( .2 .5 \Omega, 6 \vee \)
B. \( 3.5 \Omega, 6 v \)
c. \( 2.5 \Omega, 7 v \)
D. \( 3.5 \Omega, 7 \vee \)
Subject: Maths
If \( \sin ^{-1} x=y, \) then
A. \( 0 \leq y \leq \pi \)
B. \( -\frac{\pi}{2} \leq y \leq \frac{\pi}{2} \)
c. \( 0<y<\pi \)
D. \( -\frac{\pi}{2}<y<\frac{\pi}{2} \)
Subject: Biology
Which of the following sequences is correct to initiate inspiration?
(i) The contraction of external
intercostal muscles raises the ribs and
sternum
(ii) Volume of thorax increases in the dorso-ventral axis
(iii) Intrapulmonary pressure decreases
(iv) Diaphragm contraction
(v) Air rushes into lungs
(vi) Volume of thorax increases in the
anterior-posterior axis
\( A \cdot(i),(i i),(i v),(v),(i i i),(v i) \)
B. (i), (ii), (iii), (iv), (vi), (v)
c. (i), (ii),(iv),(vi),(iii),(v)
D. (vi), (v), (i), (ii), (iii), (iv)
Subject: Biology
Refer to the given table illustrating the characteristics of the body plan of some invertebrate embryos.
Select the correct sequence which
corresponds to the phyla represented with \( P, Q, R, S, \) and \( T \)
\begin{tabular}{|c|c|c|c|c|}
\hline \( \mathrm{P} \) & \( \mathrm{Q} \) & \( \mathrm{R} \) & \( \mathrm{s} \) & \( \mathrm{T} \) \\
\hline Acoelomate & Acoelomate & Pseudocoelomate & Schizocoelom & Enterocoelom \\
\hline Diploblastic & \multicolumn{3}{|c|} { Triploblastic } \\
\hline Incomplete or blind gut & \multicolumn{2}{|c|} { Complete gut } \\
\cline { 2 - 3 } & \multicolumn{2}{|c|} { (Tube-withint-a-tube) } \\
\hline \multicolumn{2}{|c|} { Without true segmentation } & With segmentation \\
\hline
\end{tabular}
A. Cnidaria - Platyhelminthes - Nematoda Echinodermata - Annelida
B. Cnidaria - Nematoda - Platyhelminthes Echinodermata - Annelida
c. Platyhelminthes - Nematoda - Annelida Echinodermata - chordata
D. Cnidaria - Platyhelminthes - Nematoda - Annelida Echinodermata
Subject: Chemistry
The reaction of \( P_{4} \) with \( X \) leads
selectively to \( P_{4} O_{6} . \) The \( x \)
is
\( A \cdot \operatorname{Dry} O_{2} \)
B. A mixture of \( O_{2} \) and \( N_{2} \)
c. Moist \( O_{2} \)
D. \( O_{2} \) in the presence of aqueous \( N a O H \)
Subject: Chemistry
The van't Hoff factor of
\( 0.1 M L a\left(N O_{3}\right)_{3} \) solution is found to
be 2.74 , the percentage dissociation of the salt is:
A. \( 85 \% \)
в. \( 58 \% \)
c. \( 65.8 \% \)
D. \( 56.8 \% \)
Subject: Maths
The angle between the lines, whose direction ratios are 1,1,2 and \( \sqrt{3}- \) \( 1,-\sqrt{3}-1,4, \) is
A . \( 45^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)