AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \operatorname{Let} f(x)=\left(\frac{\tan \left(\frac{\pi}{4}-x\right)}{\cot 2 x}\right)\left(x \neq \frac{\pi}{4}\right) \)
The value which should be assigned to at \( \frac{\pi}{4} \) so that it is continuous
everywhere, is
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot 2 \)
D. None of these
Subject: Maths
The difference between the outer and
the inner curved surface areas of an
open cylinder is \( 88 \mathrm{cm}^{2} \). If its length is \( 14 \mathrm{cm} \) and volume of the material in it
is \( 176 \mathrm{cm}^{3}, \) find the inner diameter of
the cylinder.
A. \( 3 \mathrm{cm} \)
в. \( 4 \mathrm{cm} \)
\( c \cdot 2 \mathrm{cm} \)
D. \( 1 \mathrm{cm} \)
Subject: Chemistry
\( 20 \mathrm{ml} \) of \( 0.2 \mathrm{M} A l_{2}\left(S O_{4}\right)_{3} \) is mixed with
\( 20 \mathrm{ml} \) of \( 6.6 \mathrm{M} \mathrm{BaCl}_{2} \), the concentration
of \( C l^{-} \) in solution is:
A. \( 0.2 \mathrm{M} \)
B. 6.6 \( M \)
c. \( 0.02 \mathrm{M} \)
D. 0.06 м
Subject: Chemistry
Amongst the following, the most stable
complex is:
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{3} \)
B . \( \left[F e\left(N H_{3}\right)_{6}\right]^{3+} \)
c. \( \left[F e\left(C_{2} O_{4}\right)_{3}\right]^{3} \)
D. \( \left[F e C l_{6}\right]^{3} \)
Subject: Maths
The foci of an ellipse are located at the points (2,4) and \( (2,-2) . \) The points (4,2) lies on the ellipse. If \( a \) and \( b \)
represent the lengths of the semi-major and semi-minor axes respectively, then
the value of \( (a b)^{2} \) is equal to
A. \( 68+22 \sqrt{10} \)
В. \( 6+22 \sqrt{10} \)
c. \( 26+10 \sqrt{10} \)
Subject: Biology
Every 20 minutes, one bacterium divides into two. How many bacteria will
be produced after two hours, if one starts with 10 bacteria?
A \( \cdot 2^{5} \times 10 \)
B . \( 2^{5} \times 10^{5} \)
c. \( 2^{6} \times 10 \)
D. \( 2^{6} \times 10^{6} \)
Subject: Physics
The energy released during the fission of \( 1 \mathrm{kg} \) of uranium:
A \( .9 \times 10^{20} \) ergs
B. \( 9.0 \times 10^{10} \) ergs
c. \( 9.0 \times 10^{18} \) ergs
D. \( 9.0 \times 10^{8} \) ergs
Subject: Physics
The dimensions of two wires \( A \) and \( B \)
are the same. But their materials are
different, Their load- extension
graphs are shown. If \( Y_{A} \) and \( Y_{B} \) are the
values of Young's modulus of elasticity
of \( A \) and \( B \) respectively then :
A. \( Y_{A}>Y_{B} \)
В. \( Y_{A}<Y_{B} \)
\( \mathbf{c} \cdot Y_{A}=Y_{B} \)
\( \mathbf{D} \cdot Y_{B}=2 Y_{A} \)
Subject: Chemistry
The total number of possible isomers for square-planar
\( \left[\boldsymbol{P t}(\boldsymbol{C l})\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)(\boldsymbol{S} \boldsymbol{C} \boldsymbol{N})\right]^{2-} \) is:
A . 16
B. 12
\( c \cdot 8 \)
D. 24
Subject: Physics
A steel wire of length \( 2 \mathrm{m} \) is hanging from a rigid horizontal support. How much energy is stored in it when a load
of 5 kg is suspended on it? If the load is
increased to 10 kg then by how much the energy stored will increase? \( (Y= \)
\( 2 \times 10^{11} N / m^{2}, \) area of cross-section \( = \)
\( \left.10^{-6} m^{2}\right) \)
Subject: Maths
An equation for the line that passes
through (10,-1) and is perpendicular to \( y=\frac{x^{2}}{4}-2 \) is
A. \( 4 x+y=39 \)
в. \( 2 x+y=19 \)
c. \( x+y=9 \)
D. \( x+2 y=8 \)
Subject: Physics
Two long straight wires of length \( l \) lie parallel to one another and carry currents opposite to one another of
magnitudes \( i_{1} \) and \( i_{2} \) respectively.
The force experienced by each of the straight wires is \( (r \) is the distance of
their separation)
A . repulsive and equal to \( \left(\mu_{0} / 2 \pi\right)\left(i_{1} i_{2} l / r\right) \)
B. attractive and equal to ( \( \left.\mu_{0} / 2 \pi\right)\left(i_{1} i_{2} l^{2} / r\right) \)
c. repulsive and equal to \( \left(\mu_{0} / 2 \pi\right)\left(i_{1} i_{2} l^{2} / r\right) \)
D. attractive and equal to \( \left(\mu_{0} / 2 \pi\right)\left(i_{1} i_{2} l / r\right) \)
Subject: Maths
A circle touches the \( y \) -axis at (0,2) and has an intercept of 4 units on the positive side of the \( x \) -axis. Then the equation of the circle is?
A \( \cdot x^{2}+y^{2}-4(\sqrt{2} x+y)+4=0 \)
B . \( x^{2}+y^{2}-4(x+\sqrt{2} y)+4=0 \)
C \( \cdot x^{2}+y^{2}-2(\sqrt{2} x+y)+4=0 \)
D. none of these
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\sec ^{2} \boldsymbol{x}+\operatorname{cosec}^{2} \boldsymbol{x}\right)= \)
\( \mathbf{A} \cdot-4 \sec x \cdot \tan x \cdot \cos e c x \cdot \cot x \)
B. \( 4 \sec x \cdot \cos \) ec \( x \)
c. \( 2 \sec x \cdot \tan x-2 \cos e c x \cdot \cot x \)
D. \( 2 \sec ^{2} \cdot \tan x-2 \operatorname{cosec}^{2} x \cdot \cot x \)
Subject: Chemistry
In a reaction, \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C}, \mathbf{2 . 0} \) mole of
\( A 3.0 \) mole of \( B \) and 2.0 mole of \( C \) are
placed in a \( 2.0 L \) flask and the
equilibrium concentration of \( \boldsymbol{C} \) is 0.5 mole \( / L . \) The equilibrium constant
\( K \) for the reaction is
\( \mathbf{A} \cdot 0.073 \)
B. 0.147
\( c .0 .05 \)
D. 0.026
Subject: Physics
Two blocks of mass 5 kg and 10 kg are kept on a rough horizontal surface as
shown in figure A force \( F \) is applied on
upper block of mass 10 kg Now choose
the correct statement(s) regarding the
system
This question has multiple correct options
A. If magnitude of applied force is \( 2 \mathrm{N} \) then frictional force between the blocks is also 2 N
B. The acceleration of 10 kg block is 2 \( m / s^{2} \) when applied force is \( 30 \mathrm{N} \)
C. The minimum value of F for which 5 kg block begin to slide if coefficient of friction between blocks is
changed to 0.5 is \( 45 \mathrm{N} \)
D. 5 kg block will never move on the ground for any value of F if coefficient of friction between blocks is 0.1 and
between block and surface is 0.3
Subject: Maths
Solve the equation for \( x, y, z \) and \( t \) if \( \mathbf{2}\left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{z} \\ \boldsymbol{y} & \boldsymbol{t}\end{array}\right]+\mathbf{3}\left[\begin{array}{cc}\mathbf{1} & -\mathbf{1} \\ \mathbf{0} & \mathbf{2}\end{array}\right]=\mathbf{3}\left[\begin{array}{ll}\mathbf{3} & \mathbf{5} \\ \mathbf{4} & \mathbf{6}\end{array}\right] \)
Subject: Biology
Select the correct match of the
following pair with respect to type of
coelom exhibited by them.
A. A- Platyhelminthes, B- Nematodes, C- Annelids
B. A- Nematodes, B- Annelids, C- Platyhelminthes
C. A- Platyhelminthes, B- Annelids, C- Nematodes
D. A- Annelids, B- Platyhelminthes, C- Nematodes
Subject: Maths
\( A \) and \( B \) are two events where \( P(A)= \) 0.25 and \( P(B)=0.5 . \) The probability of
both happening together is 0.14 . The
probability of both \( A \) and \( B \) not happening is
A . 0.39
B. 0.25
c. 0.11
D. none of these
Subject: Chemistry
Assertion
Boron forms only covalent compounds.
Reason

Due to small size of boron, sum of its
first three ionization enthalpies are very
high.
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: Physics
A gas undergoes change in its state
from state \( A \) to state \( B \), via three
different paths as shown in the figure.
Select the correct alternative(s)
This question has multiple correct options
A. Change in internal energy in all the three paths is
equa
B. In all the three paths heat is absorbed by the gas
C. Heat absorbed / released by the gas is maximum in path (1)
D. Temperature of the gas first increases and then decreases continuously in path (1)
Subject: Chemistry
Which of the following reactions have
\( \boldsymbol{K}_{\boldsymbol{p}}<\boldsymbol{K}_{\boldsymbol{c}} \)
This question has multiple correct options
A \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
в. \( C O(g)+C l_{2}(g) \rightleftharpoons C O C l_{2}(g) \)
c. \( 2 B r C l(g) \rightleftharpoons B r_{2}(g)+C l_{2}(g) \)
D. \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
Subject: Chemistry
Antibiotics kill or inhibits bacteria. The
real revolution in antibacterial therapy began with the discovery of Alexander Fleming. Antibiotics have either bactericidal effect or a
bacteriostatic effect on microbes. The
antibiotic given orally in case of
typhoid, dysentry, acute fever, etc. is:
A. penicillin
B. chloramphenicol
c. ofloxacin
D. ampicillin
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3}, \) then find
\( \frac{\boldsymbol{f}(\boldsymbol{x}+\boldsymbol{h})-\boldsymbol{f}(\boldsymbol{x}-\boldsymbol{h})}{\boldsymbol{h}}, \boldsymbol{h} \neq \mathbf{0} \)
Subject: Physics
In the following diagram if \( V_{2}>V_{1} \) then
\( \mathbf{A} \cdot \lambda_{1}=\sqrt{\lambda_{2}} \)
B \( \cdot \lambda_{1}<\lambda_{2} \)
\( c \cdot \lambda_{1}=\lambda_{2} \)
D. \( \lambda_{1}>\lambda_{2} \)
Subject: Physics
Two separate monochromatic light beams \( A \) and \( B \) of the same intensity
are falling normally on a unit area of a metallic surface. Their wavelengths are
\( \boldsymbol{\lambda}_{A} \) and \( \boldsymbol{\lambda}_{B}, \) respectively. Assuming that
all the incident light is used in ejecting the photoelectrons, the ratio of the number of photoelectrons from beam \( \boldsymbol{A} \)
to that from \( B \) is:
A. \( \frac{\lambda_{A}}{\lambda_{B}} \)
в. \( \frac{\lambda_{B}}{\lambda_{A}} \)
\( ^{c}\left(\frac{\lambda_{B}}{\lambda_{A}}\right)^{2} \)
\( ^{\mathrm{D}}\left(\frac{\lambda_{A}}{\lambda_{B}}\right)^{2} \)
Subject: Physics
If 'S' is stress and 'Y' is Young's modulus of a wire material, then energy stored in the wire per unit volume, is?
A \( \cdot \frac{s^{2}}{2 Y} \)
в. \( \frac{2 Y}{S^{2}} \)
c. \( \frac{s}{2 Y} \)
\( \mathbf{D} \cdot 2 S^{2} Y \)
Subject: Chemistry
Which of the following is not true for \( \mathbf{1} \boldsymbol{H}^{1}, \mathbf{1} \boldsymbol{H}^{2}, \mathbf{1} \boldsymbol{H}^{3} \mathbf{?} \)
A. They are isotopes of each other
B. They have similar electronic configurations
c. They exist in the nature in the ratio of 1: 2: 3
D. Their atomic masses are in the ratio of 1: 2: 3
Subject: Maths
Two numbers \( b \) and \( c \) are chosen at
random (with replacement) from the
numbers 1,2,3,4,5,6,7,8 and \( 9 . \) The probability that \( x^{2}+b x+c>0 \) for all
\( c \in \boldsymbol{R} \) is \( \frac{\mathbf{4} k}{81} . \) Find the value of \( \boldsymbol{k} ? \)
Subject: Chemistry
Froth flotation process used for the
concentration of sulfide ore
\( \mathbf{A} \cdot \) is based on the difference in wettability of different minerals
B. uses sodium ethly xanthate, \( C_{2} H_{5} O C S_{2} N a \) as collector
C. uses \( N a C N \) as depressant in the mixture of ZnS and PbS when ZnS forms soluble complex and Pbs forms froth
D. all of the above statements are correct
Subject: Maths
n given fig. sides \( A B \) and \( A C \) of
\( \Delta A B C \) are produced to \( E \) and \( D \)
respectively. If angle bisectors \( B O \) and
\( C O \) of \( \angle C B E \) and \( \angle B C D \) meet each
other at point \( O, \) then prove that:
\( \angle B O C=90^{\circ}-\frac{\angle x}{2} \)
Subject: Chemistry
Mohr salt, \( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4} \cdot\left(\boldsymbol{N} \boldsymbol{H}_{4}\right)_{2} \cdot \boldsymbol{S} \boldsymbol{O}_{4} \)
\( 6 H_{2} O, \) is preferred over \( F e S O_{4} \cdot 7 H_{2} O \)
for standardization of \( K M n O_{4} \) solution
because:
A. Mohr's salt is a double salt wile ferrous sulphate
B. Mohr's salt is not hygroscopic but \( F e S O_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O} \) is hygroscopic.
c. Moh'sr salt contains only ferrous ions whereas ferrous sulphate contains some ferric ions
D. Mohr's salt solution can be titrated even in the absence of \( H_{2} S O_{4} \)
Subject: Chemistry
A manometer attached to flask
contains with ammonia gas have no difference in mercury level initially as shown in diagram. After sparking into the flask, ammonia is partially
dissociated as \( 2 N H_{3}(g) \rightarrow N_{2}(g)+ \)
\( 3 H_{2}(g) \) now it have difference of \( 6 \mathrm{cm} \) in
mercury level in two columns, what is
partial pressure of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) at equilibrium?
\( A \cdot 6 \mathrm{cm} \mathrm{Hg} \)
B. \( 18 \mathrm{cm} \mathrm{Hg} \)
C. \( 27 \mathrm{cm} \mathrm{Hg} \)
D. None of these
Subject: Physics
What is the final temperature of the
mixture of 300 g of water at \( 25^{\circ} \mathrm{C} \)
added to 100 of ice at \( 0^{\circ} C \)
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 1^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 2^{o} C \)
D. \( 3^{\circ} \mathrm{C} \)
Subject: Maths
\( \int_{-1}^{1} \sqrt{\left(\frac{x+2}{x-2}\right)^{2}}+\left(\frac{x-2}{x+2}\right)^{2}-2 d x \)
A \( \cdot \sin \frac{4}{3} \)
B. \( \operatorname{sln} \frac{3}{4} \)
c. \( 4 \ln \frac{4}{3} \)
\( D \)
Subject: Maths
The number of possible surjection from \( \boldsymbol{A}=\{1,2,3, \dots n\} \) to \( B=\{1,2\} \) (where
\( \boldsymbol{n} \geq \mathbf{2}) \) is \( \mathbf{6 2}, \) then \( \boldsymbol{n}= \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 6
\( c \cdot 7 \)
D.
Subject: Maths
Given \( A=\hat{i}+2 \hat{j}-3 \hat{k} . \) When a vector
\( B \) is added to \( A, \) we get a unit vector
along \( x \) -axis. Then \( B \) is
\( \mathbf{A} \cdot-2 \hat{j}+3 \hat{k} \)
В. \( -1 \hat{i}-2 \hat{j} \)
c. \( -1 \hat{i}+3 \hat{k} \)
D. 2 \( \hat{j}-3 \hat{k} \)
Subject: Physics
A sphere of mass m moving with a constant velocity hits another stationary sphere of the same mass. If e is the coefficient of restitution, then a
ratio of the speed of the first sphere to the speed of the second sphere after head-on collision will be:
\( ^{A} \cdot\left(\frac{1-e}{1+e}\right) \)
в. \( \left(\frac{1+e}{1-e}\right) \)
c. \( \left(\frac{e+1}{e-1}\right) \)
D. \( \left(\frac{e-1}{e+1}\right) \)
Subject: Chemistry
For a dilute solution, Raoult's law states
that:
A. The relative lowering of vapour pressure is equal to the mole fraction of solute
B. The relative lowering of vapour pressure is equal to the mole fraction of solvent
C. The relative lowering of vapour pressure is proportional to the amount of solute in solution
D. The vapour pressure of the solution is equal to the mole fraction of solvent
Subject: Chemistry
The position of three elements \( A, B \) and
\( \mathrm{C} \) in the Periodic Table are shown below-
Group 16
\( B \)
\( \begin{array}{ll}6 & \text { Group17 } \\ & \\ & \mathrm{A} \\ & \\ & \\ & \mathrm{C}\end{array} \)
(a) State whether A is a metal or non-
metal.
(b) State whether \( C \) is more reactive or
less reactive than \( \mathbf{A} \)
(c) Will \( C \) be larger or smaller in size than B?
(d) Which type of ion, cation or anion, will be formed by element A?
Subject: Physics
What is the basis for the formation of
winds due to heating of different areas
on Earth?
A. The air in cold temperature regions gets cooled, expands and becomes more dense and rises up. It's place is taken by heavier air from adjacent regions.
B. The air in cold temperature regions gets cooled up, expands and becomes less dense and rises up. It's place is taken by heavier air from adjacent regions.
C. The air in high temperature regions gets heated up, expands and becomes less dense and rises up. It's place is taken by heavier air from adjacent regions.
D. The air in high temperature regions gets heated up, contracts and becomes more dense and rises up. It's place is taken by heavier air from adjacent regions.
Subject: Maths
\( F(n) \) be a polynomial function
satisfying \( \boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{f}\left(\frac{1}{x}\right)=\boldsymbol{f}(\boldsymbol{x})+ \)
\( f\left(\frac{1}{x}\right) \forall x \in R-\{0\} \) and \( f(3)=-26 \)
Determine \( \boldsymbol{f}(\mathbf{1}) \)
Subject: Chemistry
A reaction will never be spontaneous at
any temperature and pressure provided.
\( \mathbf{A} \cdot \Delta \) S positive and \( \Delta \) H positive
B. \( \Delta \) S positive and \( \Delta \) H negative
C. \( \Delta \) S negative and \( \Delta \) H positive
D. \( \Delta \) S negative and \( \Delta \) H negative
Subject: Chemistry
\( N H_{3} \) is formed in the following steps I. \( C a+2 C \rightarrow C a C_{2} \quad 50 \% \) yield
II. \( \boldsymbol{C a} \boldsymbol{C}_{2}+\boldsymbol{N}_{2} \rightarrow \boldsymbol{C a} \boldsymbol{C N}_{2}+\boldsymbol{C} \quad 100 \% \)
yield
III. \( \boldsymbol{C a} \boldsymbol{C N}_{2}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{H}_{3}+ \)
\( \begin{array}{ll}\boldsymbol{C a C O}_{3} & \text { 50\% yield }\end{array} \)
To obtain 2 moles \( N H_{3} \), calcium
required is:
A. 1 mol
B. 2 mol
c. 3 mol
D. 4 mol
Subject: Maths
An investigator interviewed 100
students to determine their preferences for the three drinks milk coffee and tea.
He reported the following, 10 students had all the three drinks, 20 had milk
and coffee, 30 had coffee and tea \( , 25 \)
had milk and tea, 12 had milk only. 5
had coffee only, 8 had tea only. The
number of students that did not take
any of the three drinks is.
Subject: Chemistry
Assertion
Amalgam of mercury with sodium is an
example of solid solutions
Reason
Mercury is solvent and sodium is solute
in the solution
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
Two aeroplanes \( I \) and \( I I \) bomb a target
in succession. The probability of \( \boldsymbol{I} \) and
\( I I \) scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
A . 0.06
B. 0.14
c. 0.32
D. 0.7
Subject: Maths
Find the slope of the inclination of the
line of the following:
\( \boldsymbol{\theta}=\mathbf{3 0}^{\circ} \)
A. \( \sqrt{3} \)
B. \( \frac{1}{\sqrt{3}} \)
c. \( \frac{2}{\sqrt{3}} \)
D. \( \frac{\sqrt{3}}{2} \)
Subject: Physics
A spring with spring constants K when compressed by \( 1 \mathrm{cm} \), the potential energy stored is U.If it is further
compressed by \( 3 \mathrm{cm}, \) then its final potential energy is
A . \( 16 U \)
в. \( 9 U \)
c. \( 8 U \)
D. \( 15 U \)
Subject: Maths
Let \( z=\cos \theta+i \sin \theta . \) Then the value of
\( \sum_{m=1}^{1} 5 \operatorname{Im}\left(z^{2 m-1}\right) \operatorname{at} \theta=2^{0} \) is
A \( \cdot \frac{1}{\sin 2^{0}} \)
в. \( \frac{1}{3 \sin 2^{\circ}} \)
c. \( \frac{1}{2 \sin 2^{\circ}} \)
D. \( \frac{1}{4 \sin 2^{\circ}} \)
Subject: Physics
The current gain of a transistor in a
Common base arrangement is \( 0.98 . \) The Change in collector current
corresponding to a change of \( 5 m A \) in emitter current is :
\( \mathbf{A} \cdot 0.1 m A \)
B. \( 0.2 m A \)
c. \( 4.9 m A \)
D. \( 9.2 m A \)
Subject: Maths
The formula to find SD is
This question has multiple correct options
\( \mathbf{A} \cdot \sqrt{\frac{\sum(x-\bar{x})^{2}}{n}} \)
B. \( \sqrt{\frac{\sum x^{2}}{n}-\left(\frac{\sum x}{n}\right)} \)
\( \mathbf{C} \cdot \sqrt{\frac{\sum x^{2}}{n}-\left(\frac{\sum x}{n}\right)^{2}} \)
\( ^{\mathrm{D}} \cdot \frac{\sum x}{n}-\left(\frac{\sum x}{2}\right)^{2} \)
Subject: Chemistry
What is the amount of heat given off by
\( 100 g \) of \( O_{2} \) when it is used to burn an
excess of sulfur according to the following reaction?
\( S(s)+O_{2} \rightarrow S O_{2}(g) \Delta H= \)
\( -296 k J / \) mole
A. \( 925,000 \mathrm{J} \)
B. 29,000 J
c. 1,850 J
D . 296 J
E. 100
Subject: Maths
Find the area of a regular hexagon each of whose sides measures \( 5 \mathrm{cm} .(\sqrt{3}= \)
1.732)
A \( \cdot 64.95 \mathrm{cm}^{2} \)
B . \( 69.95 \mathrm{cm}^{2} \)
c. \( 64.95 \mathrm{m}^{2} \)
D. None of these
Subject: Physics
A man can swim in still water with a
velocity \( 5 \mathrm{m} / \mathrm{s} \). He wants to reach at
directly opposite point on the other bank
of a river which is flowing at a rate of \( 4 m / s . \) River is \( 15 m \) wide and the man can
run with twice the velocity as compared
with velocity of swimming. If he swims perpendicular to river flow and then run
along the bank, then time taken by him to reach the opposite point is:
A. 3 sec
B. less than 3 sec
c. 5 sec
D. 4.2 sec
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{lll}2 & 3 & 1 \\ 4 & 1 & 5 \\ 3 & 9 & 7\end{array}\right] . \) Then the additive
inverse of \( \boldsymbol{A} \) is:
\( A \)
\[
\left[\begin{array}{ccc}
-2 & -3 & 1 \\
4 & -1 & -5 \\
-3 & 9 & -7
\end{array}\right]
\]
B.
\[
\left[\begin{array}{ccc}
-2 & -3 & -1 \\
-4 & -1 & -5 \\
-3 & -9 & -7
\end{array}\right]
\]
\( c \)
\[
\left[\begin{array}{ccc}
2 & -3 & -1 \\
-4 & 1 & -5 \\
-3 & -9 & 7
\end{array}\right]
\]
D.
\[
\left[\begin{array}{ccc}
-2 & -3 & -1 \\
-4 & -1 & -5 \\
-3 & 9 & -7
\end{array}\right]
\]
Subject: Maths
The probability distribution of a random
variable \( X \) is given below:
\[
\begin{array}{lllll}
\mathrm{x}: & 0 & 1 & 2 & 3 \\
\mathrm{P}(\mathrm{x}): & \mathrm{k} & \frac{k}{2} & \frac{k}{4} & \frac{k}{8}
\end{array}
\]
Determine \( \boldsymbol{P}(\boldsymbol{X} \leq \mathbf{2}) \) and \( \boldsymbol{P}(\boldsymbol{X}>\mathbf{2}) \)
Subject: Chemistry
The number of \( P-O H \) bonds and the
oxidation state of phosphorus atom in
pyrophosphoric acid \( \left(\boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{7}\right) \)
respectively are:
A. Four and five
B. Four and four
c. Five and five
D. Five and four
Subject: Maths
The largest angle of a triangle is twice
the sum of the other two and the
smallest one is one fourth of the largest,
the angles are
A \( \cdot 120^{0}, 40^{0}, 20^{0} \)
В . \( 120^{0}, 30^{0}, 30^{0} \)
c. \( 90^{\circ}, 45^{\circ}, 45^{\circ} \)
D. \( 90^{0}, 60^{0}, 30^{0} \)
Subject: Maths
If \( a \hat{i}+b \hat{j}+c \hat{k} \) is the position vector of
the mid - point of the vector joining the points \( \boldsymbol{P}(\mathbf{2} \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{4} \hat{\boldsymbol{k}}) \) and \( \boldsymbol{Q}(\boldsymbol{4} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}- \)
\( 2 \hat{k}) \) then \( a+b+c \) is equal to
Subject: Chemistry
\( X Y_{2} \) dissociates as:
\( \boldsymbol{X} \boldsymbol{Y}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{X} \boldsymbol{Y}(\boldsymbol{g})+\boldsymbol{Y}(\boldsymbol{g}) \)
When the initial pressure of \( X Y_{2} \) is 600 \( \mathrm{mm} H g, \) the total equilibrium pressure is \( 800 \mathrm{mm} \) Hg. Calculate \( K \) for the reaction assuming that the volume of the system remains unchanged.
A. 50
в. 100
c. 166.6
D. 400.0
Subject: Chemistry
Whats the potential of the reaction below given the half-reaction potentials:
\( 2 F e_{2}++C l_{2} \rightarrow 2 F e^{3+}+2 C l^{-} \)
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+} ; \boldsymbol{E}=\mathbf{0 . 7 7} \boldsymbol{V} \)
\( \boldsymbol{C l}_{2}+\mathbf{2} \boldsymbol{e}^{-} \rightarrow \mathbf{2} \boldsymbol{C l}^{-} ; \boldsymbol{E}=\mathbf{1 . 3 6} \boldsymbol{V} \)
A . \( 0.18 V \)
B . \( 0.59 V \)
c. \( 1.05 V \)
D. \( 2.13 V \)
E \( .2 .90 V \)
Subject: Physics
A non conducting sphere of radius R is filled with uniform volume charge
density - \( \rho . \) The center of this sphere is displaced from the origin by \( \vec{d} \). The electric field \( \vec{E} \) at any point \( P \) having position vector inside the sphere is :
\( A \)
B \( \cdot \frac{\rho}{3 \varepsilon_{0}}(\vec{r}-\vec{d}) \)
c. \( \frac{\rho}{3 \varepsilon_{0}}(\vec{d}-\vec{r}) \)
D. \( \frac{\rho}{3 \varepsilon_{0}}(\vec{r}) \)
Subject: Chemistry
If the heats of formation of \( C_{2} H_{2} \) and
\( C_{6} H_{6} \) are \( 230 \mathrm{KJ} \mathrm{mol}^{-1} \) and \( 85 \mathrm{KJ} \mathrm{mol}^{-1} \)
respectively, the \( \Delta \mathrm{H} \) value for the trimerisation of \( C_{2} \mathrm{H}_{2} \) is:
A . - -605 KJ
B . -205 KJ
c. 205 KJ
D. 605 KJ