AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Another ion that would behave similar
to \( A l^{+3}(a q) \) in forming an acidic solution is:
A \( \cdot B e_{(a q)}^{2+} \)
В. \( B a_{(a q)}^{2+} \)
c. \( N a^{+} \)
\( \mathbf{D} \cdot T l^{+} \)
Subject: Physics
A ray of light travels from ethanol into air. If the angle of incidence of the ray at the boundary is \( 30^{0} \) and the refractive
index of ethanol is \( 1.36, \) what is the
angle of refraction of the ray as it
emerges out of ethanol?
A \( \cdot 42.84^{0} \)
в. \( 21.5^{\circ} \)
\( c \cdot 46.8^{0} \)
D. None of the above
Subject: Physics
Consider a satellite moving in a circular orbit around Earth. If \( \mathrm{K} \) and \( \mathrm{V} \) denote its
kinetic energy and potential energy respectively, then(Choose the convention, where \( V=0 \text { as } r \rightarrow \infty) \)
A \( . K=V \)
в. \( K=2 V \)
\( \mathbf{c} \cdot V=2 K \)
D. \( K=-2 V \)
E . \( V=-2 K \)
Subject: Physics
The addition of soap changes the
surface tension of water to \( T_{1} \) and that
of salt solution changes to \( T_{2} \). Then:
A \( \cdot T_{1}=T_{2} \)
в. \( T_{1}>T_{2} \)
c. \( T_{1}<T_{2} \)
D. \( T_{1} \geq T_{2} \)
Subject: Chemistry
The bond enthalpies of \( \boldsymbol{H}-\boldsymbol{H}, \boldsymbol{C l}-\boldsymbol{C l} \)
and \( H-C l \) are 435,243 and \( 431 \mathrm{kJ} \)
\( m o l^{-1}, \) respectively. The enthalpy of formation of \( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \) will be:
B. -92 kJ mol \( ^{-1} \)
\( \mathbf{c} \cdot 247 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 770 kJ mol \( ^{-1} \)
Subject: Maths
A large solid sphere of diameter \( 18 \mathrm{cm} \) is melted and recast into several small
spheres of diameter \( 3 \mathrm{cm} \) The percentage increase in the surface area of the smaller spheres over that of
the larger sphere is
A . 500\%
B . 350\%
c. \( 450 \% \)
D. 545\%
Subject: Physics
The two femurs each of the cross-
sectional area \( 10 \mathrm{cm}^{2} \) support the upper
part of a human body of mass \( 40 \mathrm{kg} \) The average pressure sustained by the femurs is then (Takes \( g=10 \mathrm{m} \mathrm{s}^{-2} \) )
A \( \cdot 2 \times 10^{3} \mathrm{N} \mathrm{m}^{-2} \)
B. 2 \( \times 10^{4} \mathrm{N} \mathrm{m}^{-2} \)
c. \( 2 \times 10^{5} \mathrm{N} \mathrm{m}^{-2} \)
D. 2 \( \times 10^{6} \mathrm{N} \mathrm{m}^{-2} \)
Subject: Chemistry
How many electrons flow through a
metallic wire if a current of \( 0.5 A \) is
passed for 2 hours? (Given : \( 1 F= \)
\( \left.\mathbf{9 6}, \mathbf{5 0 0} \boldsymbol{C} \boldsymbol{m o l}^{-\mathbf{1}}\right) \)
Subject: Maths
Factorize:
\( a^{6}+27 b^{3} \)
\( \mathbf{A} \cdot\left(a^{2}-3 b\right)\left(a^{4}-3 a^{2} b+9 b^{2}\right) \)
B \( \cdot\left(a^{2}+3 b\right)\left(a^{4}-3 a^{2} b+9 b^{2}\right) \)
\( \mathbf{C} \cdot\left(a^{2}+3 b\right)\left(a^{4}-a^{2} b+9 b^{2}\right) \)
D. \( \left(a^{2}+3 b\right)\left(a^{4}-a^{2} b-9 b^{2}\right) \)
Subject: Chemistry
Balance the following equation, when it occurs in basic medium.
\[
\boldsymbol{C l O}_{\boldsymbol{3}}^{-} \longrightarrow \boldsymbol{C l}^{-}
\]
A \( \cdot C l O_{3}^{-}+3 H_{2} O+6 e \rightarrow C l^{-}+6 O H^{-} \)
B . \( C l O_{3}^{-}+3 H_{2} O+5 e \rightarrow C l^{-}+6 O H^{-} \)
c. \( 3 C l O_{3}^{-}+3 H_{2} O+3 e \rightarrow C l^{-}+3 O H \)
D. None of these
Subject: Physics
An elastic spring is given a force of 1000
N over an area of \( 0.2 m^{2} \)
A. \( 3000 N m^{-2} \)
B. \( 5000 \mathrm{Nm}^{-2} \)
c. \( 500 N m^{-2} \)
D. \( 2500 N m^{-2} \)
Subject: Chemistry
\( 4 \mathrm{g} \mathrm{H}_{2} \) and \( 127 \mathrm{g} \mathrm{I}_{2} \) are mixed and
heated in 10 lit closed vessel until
equilibrium is reached. If the equilibrium concentration of HI is 0.05 M, the total number of moles presents
at equilibrium is
A . 3.25
в. 1.75
c. 2.25
D. 2.5
Subject: Physics
A sonar device fitted in a submarine
receives an echo \( 4 s \) later the signal is transmitted towards another
submarine \( 3060 m \) away. Find the speed of sound in water.
\( \mathbf{A} \cdot 1530 m s^{-1} \)
B . \( 1342 \mathrm{ms}^{-1} \)
c. \( 1600 m s^{-1} \)
D. \( 1250 m s^{-1} \)
Subject: Physics
A particle moves in such a way that its position vector at any time \( t \) is \( \vec{r}=t \hat{i}+ \) \( \frac{1}{2} t^{2} \hat{j}+t \hat{k} . \) Find as a function of time
(i) the velocity \( \left(\frac{d \vec{r}}{d t}\right) \)
(ii) the speed \( \left(\left|\frac{d \vec{r}}{d t}\right|\right) \)
(iii) the acceleration \( \left(\frac{\boldsymbol{d} \overrightarrow{\boldsymbol{v}}}{\boldsymbol{d} \boldsymbol{t}}\right) \)
(iv) the magnitude of the acceleration
(v) the magnitude of the component of acceleration along velocity (called tangential acceleration)
(vi) the magnitude of the component of acceleration perpendicular to velocity (called normal acceleration).
Subject: Maths
Two medians drawn from acute angles
of a right angled triangle intersect at an angle \( \frac{\pi}{6} . \) If the length of the hypotenuse
of the triangle is 3 units, then area of the triangle (in sq. units) is
A. \( \sqrt{3} \)
B. 3
\( c \cdot \sqrt{2} \)
D. 9
Subject: Physics
A rectangular coil placed in a region having a uniform magnetic field perpendicular to the plane of the coil. An
e.m.f. will not be induced in the coil if
the:
A. magnetic field increases uniformly
B. coil is rotated about an axis perpendicular to the plans of the coil and passing through its centre 0 , the coil remaining in the same plane
c. coil is routed about the axis \( 0 x \)
Subject: Physics
A car is traveling with linear velocity
on a circular road of radius \( r \). If it is
increasing its speed at the rate of 'a'
\( m s^{-2}, \) then the resultant acceleration
will be
A \( \cdot \sqrt{\frac{v^{4}}{r^{2}}+a^{2}} \)
B. \( \sqrt{\frac{v^{4}}{r^{2}}-a^{2}} \)
c. \( \sqrt{\frac{v^{2}}{r^{2}}+a^{2}} \)
D. \( \sqrt{\frac{v^{2}}{r^{2}}-a^{2}} \)
Subject: Physics
A fly wheel of moment of inertia lis rotating at n revolutions per sec. The work needed to double the frequency would be -
\( \mathbf{A} \cdot 2 \pi^{2} I n^{2} \)
В. \( 4 \pi^{2} I n^{2} \)
\( \mathbf{c} \cdot 6 \pi^{2} I N^{2} \)
D. \( 8 \pi^{2} I n^{2} \)
Subject: Physics
A conductor of length 2 m carrying
current \( 2 \mathrm{A} \) is held parallel to an infinitely long conductor carrying current of \( 12 \mathrm{A} \) at a distance of \( 100 \mathrm{mm} \)
the force j on a small conductor is:
A \( \cdot 8.6 \times 10^{-5} N \)
B. \( 6.6 \times 10^{-5} N \)
c. \( 7.6 \times 10^{-5} N \)
D. 9.6 \( \times 10^{-5} N \)
Subject: Chemistry
Assertion
Simple distillation can help in separating a mixture of propan-1-ol
(boiling point 97 ) and propanone (boiling point \( 56) \)
Reason
Liquids with a difference of more than
\( 20^{0} C \) in their boiling points can be separated by simple distillation.
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 coins are tossed 1000 times and
the outcomes are recorded as below:
\( \mathbf{2} \) No of heads \( \mathbf{0} \)
250 Frequency \( 200 \quad 550 \)
Based on this information, the probability for at most one head is \( \frac{a}{b} \)
Where \( (a, b)=1, \) then
A \( \cdot \frac{1}{5} \)
в.
\( c \cdot \frac{4}{5} \)
D.
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{1} \\ \mathbf{0} & \mathbf{0}\end{array}\right], \) show that \( (\boldsymbol{a} \boldsymbol{I}+\boldsymbol{b} \boldsymbol{A})^{n}= \)
\( a^{n} I+n a^{n-1} b A, \) where \( I \) is the identity
matrix of order 2 and \( n \in N \)
Subject: Chemistry
Example of physical equilibria is:
A. \( H_{2}+I_{2} \rightleftharpoons 2 H I \)
в. \( C a C O_{3} \rightleftharpoons C a O+C O_{2} \)
c. \( H_{2} O(s) \rightleftharpoons H_{2} O(l) \)
D. \( P C l_{5} \rightleftharpoons P C l_{3}+C l_{2} \)
Subject: Chemistry
Propylsulphinic acid is prepared by the reaction of the following, followed by hydrolysis:
A \( \cdot C_{3} H_{7} M g B r+S O_{2} \)
B. \( C_{2} H_{5} M g B r+S O_{2} \)
c. \( C_{3} H_{7} M g B r+S O_{3} \)
D. \( C_{2} H_{5} M g B r+S O \)
Subject: Maths
If \( y=\log (\log x) \) then \( \frac{d^{2} y}{d x^{2}} \) is equal to
A \( \cdot \frac{-(1+\log x)}{x^{2} \log x} \)
B. \( \frac{(1+\log x)}{x^{2} \log x} \)
c. \( \frac{-(1+\log x)}{(x \log x)^{2}} \)
D. \( \frac{(1+\log x)}{\left(x^{2} \log x\right)^{2}} \)
Subject: Physics
The moment of inertia of a uniform rod
of length \( 2 l \) and mass ' \( m \) ' about an axis through centre and inclined at an angle
\( \theta \) to rod is:
A \( \cdot \frac{m l^{2}}{3} \sin ^{2} \theta \)
B. \( \frac{m l^{2}}{6} \cos ^{2} \theta \)
c. \( \frac{m l^{2}}{2} \cos ^{2} \theta \)
D. \( \frac{m l^{2}}{12} \cos ^{2} \theta \)
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{2 1}\}, \boldsymbol{B}= \)
\( \{\mathbf{4}, \mathbf{8}, \mathbf{1 2}, \mathbf{1 6}, \mathbf{2 0}\}, \boldsymbol{C}= \)
\( \{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}, \mathbf{1 4}, \mathbf{1 6}\} \) and \( \boldsymbol{D}= \)
\( \{\mathbf{5}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{2 0}\} . \) Find \( \boldsymbol{B}-\boldsymbol{A} \)
Subject: Maths
The focal length of a mirror is given by \( \frac{1}{v}-\frac{1}{u}=\frac{2}{f} . \) If equal errors \( (\alpha) \) are
made in measuring \( u \) and \( v \), then the
relative error in \( \boldsymbol{f} \) is
A \( \cdot \frac{2}{\alpha} \)
B \( \cdot \alpha\left(\frac{1}{u}+\frac{1}{v}\right) \)
\( ^{c} \cdot \alpha\left(\frac{1}{u}-\frac{1}{v}\right) \)
D. none of these
Subject: Chemistry
The boiling point of liquid oxygen is:
\( \mathbf{A} \cdot-156^{\circ} \mathrm{C} \)
B . \( -196^{\circ} \mathrm{C} \)
c. \( -183^{\circ} \mathrm{C} \)
D. \( -173^{\circ} \mathrm{C} \)
Subject: Maths
Multiply \( (5-2 x) \) and \( (3+x) \)
A. \( 15-x+2 x^{2} \)
B . \( 15-x-x^{2} \)
c. \( 15-x-2 x^{2} \)
D. \( 15-x+x^{2} \)
Subject: Chemistry
The total energy of the electron in any orbit of one electron containing species is given by the expression:
A \( \cdot-e^{2} / r^{2} \)
B . \( -n^{2} h^{2} / 2 \pi^{2} Z^{2} e^{4} m \)
c. \( -2 \pi^{2} m Z^{2} e^{4} / n^{2} h^{2} \)
D. \( n h / 2 \pi \)
Subject: Maths
Assertion(A): If centroid and
circumcentre of a triangle are known its orthocentre can be found.

Reason (R) : Centriod, orthocentre and
circumcentre of a triangle are collinear
A. Both A and R are individually true and R is the correct explanation of
B. Both A and R individually true but R is not the correct explanation of \( A \)
c. \( A \) is true but \( R \) is false
D. A is false but R is true
Subject: Physics
A block of mass \( 5 k g \) is at rest on a smooth horizontal surface. Water
coming out of a pipe horizontally at the
rate of \( 2 k g s^{-1}, \) hits the block with a
velocity of \( 6 m s^{-1} \). The initial
acceleration of the block is:
A. Zero
B. \( 1.2 \mathrm{ms}^{2} \)
c. \( 2.4 m s^{2} \)
D. \( 0.6 \mathrm{ms}^{2} \)
Subject: Maths
The missing value in \( \frac{2}{3} \times \frac{5}{6}=\dots . . \times \frac{2}{3} \)
is
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{5}{6} \)
D.
Subject: Physics
Statement-1
Radiation involves transfer of heat by
electromagnetic waves. Statement-2
Electromagnetic waves do not required any material medium for propagation.
A. Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation for Statement-
B. Statement-1 is true, Statement-2 is true but Statement-2 is not the correct explanation for Staement-
c. statement-1 is true, statement-2 is false.
D. Statement- 1 is false, Statement-2 is true
Subject: Physics
A parallel plate capacitor is charged to \( 60 \mu C . \) Due to a radioactive source, the
plate loses charge at the rate of \( 1.8 \times \) \( 10^{-8} C / s . \) The magnitude of
displacement current is:
A . \( 1.8 \times 10^{-8} \mathrm{C} / \mathrm{s} \)
B. \( 3.6 \times 10^{-8} \mathrm{C} / \mathrm{s} \)
c. \( 4.1 \times 10^{-11} \mathrm{C} / \mathrm{s} \)
D. \( 5.7 \times 10^{-12} \mathrm{C} / \mathrm{s} \)
Subject: Chemistry
Lanthanoid contraction occurs because:
A. the \( 4 f \) electrons, which are gradually added, create a strong shielding effect
B. the \( 4 f \) orbitals are greater in size than the \( 3 d \) and \( 3 f \) orbitals
C. the \( 5 f \) orbitals strongly penetrate into the \( 4 f \) orbitals
D. the poor shielding effect of \( 4 f \) electrons is coupled with the increased attraction between the nucleus and
the added electrons
Subject: Physics
A satellite is in a circular orbit around a planet, Its period of revolution is \( \mathrm{T} \), radius of the orbit is \( R \), orbital velocity \( V \)
and acceleration 'a', then:
A \( \cdot V=a t \) and \( a=\frac{V^{2}}{R} \)
B. \( V=\frac{2 \pi R}{T} \) and \( V=a T \)
c. \( V=\frac{2 \pi R}{T} \) and \( a=\frac{V^{2}}{R} \)
D. \( V=\frac{1}{2} a T^{2} \)
Subject: Physics
The wire loop PQRSP formed by joining
two semi-circular wires of radii \( \boldsymbol{R}_{1} \) and
\( R_{2} \) carries a current I as shown. The
magnitude of the magnetic induction at
the centre \( C \) is
A \( \cdot \frac{\mu_{0} I}{4} \frac{R_{2}-R_{1}}{R_{2}} \)
В \( \cdot \frac{\mu_{0} I}{4} \frac{R_{2}-R_{1}}{R_{1}} \)
C \( \cdot \frac{\mu_{0} I}{4} \frac{R_{2}-R_{1}}{R_{2} R_{1}} \)
D. None of these
Subject: Chemistry
At \( p H=2, E_{\text {Quinhydrone will be: }} \)
Given: \( E_{\text {Quinhydrone }}^{o}=1.30 V \)
\( \mathbf{A} \cdot 1.36 V \)
B . \( 1.30 V \)
c. \( 1.42 V \)
D . \( 1.20 V \)
Subject: Maths
The number of revolutions made by a
wheel of diameter \( 56 \mathrm{cm} \) in covering a distance of \( 1.1 k m \) is \( \left(U s e \pi=\frac{22}{7}\right) \)
\( \mathbf{A} \cdot 31.25 \)
B. 56.25
c. 625
D. 62.5
Subject: Chemistry
Select pair of compounds in which both have different hybridization but have the same molecular geometry.
A. \( B F_{3}, B r F_{3} \)
B . \( I C l_{2}^{-}, B e C l_{2} \)
c. \( B C l_{3}, P C l_{3} \)
D. \( P C l_{3}, N C l_{3} \)
Subject: Maths
Two circles of radii \( 20 \mathrm{cm} \) and \( 37 \mathrm{cm} \)
intersect in \( A \) and \( B . \) If \( O_{1} \) and \( O_{2} \) are
their centres and \( A B=24 \mathrm{cm}, \) then the
distance \( O_{1} O_{2} \) is equal to
A . \( 44 \mathrm{cm} \)
B. \( 51 \mathrm{cm} \)
\( c .40 .5 \mathrm{cm} \)
D. \( 45 \mathrm{cm} \)
Subject: Physics
Two ships \( A \) and \( B \) are \( 10 k m \) apart on a line running south to north. Ship \( \boldsymbol{A} \) farther north is streaming west at \( 20 k m / h r \) and ship \( B \) is streaming north at \( 20 k m / h r . \) What is their
distance of closest approach and how long do they take to reach it?
A. \( 4 \sqrt{2} \mathrm{km}, 15 \mathrm{min} \)
В. \( 5 \sqrt{5} \) km, 15 min
c. \( 5 \sqrt{2} \mathrm{km}, 20 \mathrm{min} \)
D. \( 2 \sqrt{2} \mathrm{km}, 15 \mathrm{min} \)
Subject: Maths
Find the value of \( k \) is continuous at \( x= \)
where
2
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\frac{\boldsymbol{k} \cos \boldsymbol{x}}{\boldsymbol{\pi}-\mathbf{2} \boldsymbol{x}}, \text { if } \boldsymbol{x} \neq \frac{\boldsymbol{\pi}}{\mathbf{2}} \\ \boldsymbol{3}, \quad \text { if } \boldsymbol{x}=\frac{\boldsymbol{\pi}}{2}\end{array}\right. \)
Subject: Chemistry
Which one of the following is the ratio of the lowering of vapour pressure of \( 0.1 M \) aqueous solution of
\( B a C l_{2}, N a C l \) and \( A l_{2}\left(S O_{4}\right)_{3} \)
respectively?
A .3: 2: 5
B. 5: 2: 3
\( \mathrm{c} .5: 3: 2 \)
D. 2: 3: 5
Subject: Chemistry
The correct order in which the 0 - 0 bond
length increases in the following is ?
A. \( H_{2} O_{2}<O_{2}<O_{3} \)
в. \( O_{3}<H_{2} O_{2}<O_{2} \)
c. \( O_{2}<O_{3}<H_{2} O_{2} \)
D. \( O_{2}<H_{2} O_{2}<O_{3} \)
Subject: Maths
If \( n \) is an integer,what is the remainder when \( 5 x^{2 n+1}-10 x^{2 n}+3 x^{2 n-1}+5 \) is
divided by \( x+1 ? \)
A .
B. 2
\( c \cdot 4 \)
\( D \cdot-8 \)
\( E \cdot-13 \)
Subject: Chemistry
Bond enegry of \( (N \equiv N)=948 k J M o l^{-1} \)
\( (\boldsymbol{P} \equiv \boldsymbol{P})=\mathbf{4 8 1} \boldsymbol{k} \boldsymbol{J} \boldsymbol{M} \boldsymbol{o l}^{-1} \)
\( (N-N)=160 k J M o l^{-1} \)
\( (\boldsymbol{P}-\boldsymbol{P})=\mathbf{2} \mathbf{1 5} \boldsymbol{k} \boldsymbol{J} \boldsymbol{M} \boldsymbol{o l}^{-1} \)
Which molecules do not exist?
This question has multiple correct options
A \( \cdot P_{4} \)
B. \( N_{4} \)
c. \( N_{2} \)
D. \( P_{2} \)
Subject: Maths
What is the smallest positive integer \( \boldsymbol{K} \) such that \( 2000 \times 2001 \times K \) is a perfect
cube?
A \( \cdot 2^{3} \times 3^{3} \times 23^{3} \times 29^{3} \)
B . \( 2 \times 3 \times 23 \times 29 \)
c. \( 2 \times 3^{2} \times 23^{3} \times 29^{4} \)
D . \( 2^{2} \times 3^{2} \times 23^{2} \times 29^{2} \)
Subject: Physics
The compressibility of water is \( 4 \times 10^{-5} \)
per unit atmosphere pressure. The
decrease in volume of \( 100 \mathrm{cm}^{3} \) water
under a pressure of 100atm will be
A \( \cdot 0.4 \mathrm{cm}^{3} \)
B. \( 4 \times 10^{-5} \mathrm{cm}^{3} \)
c. \( 0.025 \mathrm{cm}^{3} \)
D. \( 0.04 \mathrm{cm}^{3} \)
Subject: Physics
If object having total energy \( \boldsymbol{E}_{1} \) is
having the same \( P E \) curve as shown in
the figure, then
\( \mathbf{A} \cdot r_{0} \) is the maximum distance of the object from the
earth's centre
B. the object and the earth system is bounded one
C. the \( K E \) of the object is zero when \( r=r_{0} \)
D. all the above
Subject: Maths
If the area of the region bounded by the curves, \( \boldsymbol{y}=\boldsymbol{x}^{2}, \boldsymbol{y}=\frac{\mathbf{1}}{\boldsymbol{x}} \) and the lines
\( \boldsymbol{y}=\mathbf{0} \) and \( \boldsymbol{x}=\boldsymbol{t}(\boldsymbol{t}>\mathbf{1}) \) is \( \mathbf{1} \) sq. unit
then \( t \) is equal to?
A \( \cdot \frac{4}{3} \)
В. \( e^{2 / 3} \)
\( c \cdot \frac{3}{2} \)
\( \mathbf{D} \cdot e^{3 / 2} \)
Subject: Physics
A source emitting wavelengths \( 480 \mathrm{nm} \) and \( 600 \mathrm{nm} \) is used in YDSE. The
separation between the slits is 0.25 mm. The interference is observed \( 1.5 \mathrm{m} \) away from the slits. The linear separation between first maxima of the
two wavelengths is :
A. \( 0.72 \mathrm{mm} \)
в. 0.72 ст
c. \( 7.2 \mathrm{cm} \)
D. \( 7.2 \mathrm{mm} \)
Subject: Chemistry
An oxyacid of phosphorus has the
following properties:
Complex neutralization of the acid with
sodium hydroxide solution given an aqueous solution of sodium ions and
oxy-acid anions in the ratio 2:1. When a solution of the acid is warmed with a
silver nitrate solution, metallic silver is deposited.

What is the structure of the oxy-acid?
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)
Subject: Chemistry
The rate constant for a given reaction is \( \boldsymbol{K}=\mathbf{3} \times \mathbf{1 0}^{-5} \boldsymbol{S}^{-1} \boldsymbol{a} \boldsymbol{t} \boldsymbol{m}^{-1} . \) Express it in
units of \( L m o l^{-1} s e c^{-1}(T=273.15 K) \)
Subject: Physics
A body rests on a rough horizontal
plane. A force is applied to the body
directly towards the plane at an angle \( \theta \) with the vertical. The body can be moved along the plane only if the value of angle
\( \boldsymbol{\theta} \) is:
A \( .45^{\circ} \)
\( \mathbf{B} \cdot>45^{\circ} \)
C. \( > \) limiting angle of friction
D. < limiting angle of friction
Subject: Maths
Define a binary operation \( * \) on the set
\{0,1,2,3,4,5\} as
\( \boldsymbol{a} * \boldsymbol{b}=\left\{\begin{array}{ll}\boldsymbol{a}+\boldsymbol{b}, & \boldsymbol{i f} \quad \boldsymbol{a}+\boldsymbol{b}<\mathbf{6} \\ \boldsymbol{a}+\boldsymbol{b}-\boldsymbol{6} \quad \boldsymbol{i} \boldsymbol{f} \quad \boldsymbol{a}+\boldsymbol{b} \geq \boldsymbol{6} & \boldsymbol{6}\end{array}\right. \)
Show that zero is the identity for this
operation and each element \( a \neq 0 \) of
the set is invertible with \( 6-a \) being the
inverse of \( a \)
Subject: Maths
set of rational numbers is \( \left\{-\mathbf{6},-\mathbf{5} \frac{\mathbf{3}}{\mathbf{4}},-\sqrt{\mathbf{4}},-\frac{\mathbf{3}}{\mathbf{5}},-\frac{\mathbf{3}}{\mathbf{8}}, \mathbf{0}, \frac{\mathbf{4}}{\mathbf{5}}, \mathbf{1}, \mathbf{1} \frac{\mathbf{2}}{\mathbf{3}}, \mathbf{3}\right. \)
A. True
B. False
Subject: Maths
If \( a, b, c \in+R \) such that \( \lambda a b c \) is the
minimum value of \( a\left(b^{2}+c^{2}\right)+b\left(c^{2}+\right. \)
\( \left.a^{2}\right)+c\left(a^{2}+b^{2}\right), \) then \( \lambda= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 4 \)
D. None of the above
Subject: Maths
Find the measure of the angle between two lines if their direction cosines
\( \ell, \boldsymbol{m}, \boldsymbol{n} \) satisfy \( \ell+\boldsymbol{m}-\boldsymbol{n}=\mathbf{0}, \ell^{2}+ \)
\( \boldsymbol{m}^{2}-\boldsymbol{n}^{2}=\mathbf{0} \)
Subject: Chemistry
How many mole of \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \) will be required to prepare one litre buffer solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{1 0 . 4} \) using \( \mathbf{0 . 0 1} \) mol
NaC N?
(Given: \( \left.\boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{C N})=\boldsymbol{4} \times \mathbf{1 0}^{-10}\right) \)
\( \mathbf{A} \cdot 2 \times 10^{-2} \mathbf{M} \)
В. \( 9 \times 10^{-4} \) М
\( \mathbf{c} \cdot 4 \times 10^{-4} \mathrm{M} \)
D. \( 9 \times 10^{-3} \mathrm{M} \)
Subject: Chemistry
One natural source of atmospheric \( C O_{2} \)
is precipitation reaction such as the precipitation of silicates in the oceans:
\( M g^{2+}(a q)+S i O_{2}(\text {dispersed})+ \)
\( 2 H C O_{3}(a q) \rightarrow M g S i O_{3}(s)+ \)
\( \mathbf{2} C O_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
How many grams of magnesium silicate would be precipitated during
the formation of 100 L of \( C O_{2} \) at \( 30^{\circ} C \)
and 775 torr?
\( (M g=24, S i=28, C=12, O=16) \)
A \( .102 g \)
в. \( 410 g \)
c. \( 205 g \)
D. \( 51 g \)
Subject: Chemistry
\( 2 H_{2} O_{2}(l) \rightarrow 2 H_{2} O(l)+O_{2}(g) \)
\( 100 \mathrm{mL} \) of \( X \) molar \( H_{2} O_{2} \) gives \( 3 \mathrm{L} \) of \( O_{2} \) gas under the condition when 1 mol
occupies 24 L. The value of \( X \) is :
A . 2.5
B. 1.0
\( c \cdot 0.5 \)
D. 0.25
Subject: Physics
A disc of mass \( M \) and radius \( R \) rolls on
a horizontal surface and then rolls up
an inclined plane as shown in figure. If the velocity of the disc is \( v, \) height to
which the disc will rise will be
\( \mathbf{A} \cdot \frac{3 v^{2}}{2 g} \)
B. \( \frac{3 v^{2}}{4 g} \)
c. \( \frac{v^{2}}{4 g} \)
\( \frac{v^{2}}{2 g} \)
Subject: Maths
The equation of a straight line passing through the point of intersection of \( x- \)
\( \boldsymbol{y}+\mathbf{1}=\mathbf{0} \) and \( \mathbf{3} \boldsymbol{x}+\boldsymbol{y}-\mathbf{5}=\mathbf{0} \) and
perpendicular to one of them, is?
A. \( x+y+3=0 \)
в. \( x-y-3=0 \)
c. \( x-3 y-5=0 \)
D. \( x-3 y+5=0 \)
Subject: Chemistry
\[
\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \stackrel{\text {Complete } \boldsymbol{H} \boldsymbol{y} \text {drolysis}}{\boldsymbol{P}}+
\]
other product
\[
\begin{array}{l}
\downarrow \boldsymbol{O H}^{-} / \boldsymbol{H}_{2} \boldsymbol{O} \\
\boldsymbol{Q} \\
\downarrow
\end{array}
\]
slow disproportionation in \( O H^{-} / H_{2} O \)
Products
Under ambient conditions, the total
number of gases released as products in the final step of the reaction scheme
shown below is:
A . 0
B. 1
\( c \cdot 2 \)
D. 3
Subject: Maths
\( \int \cos x \sqrt{4-\sin ^{2} x} d x \)
A. \( \frac{t}{2} \sqrt{4-t^{2}}-\frac{1}{2} \cdot 4 \sin ^{-1} \frac{t}{2} \)
B \( \cdot \sqrt{4-t^{2}}+4 \sin ^{-1} \frac{t}{2} \)
C \( \cdot \frac{t}{2} \sqrt{4-t^{2}}+\frac{1}{2} \cdot 4 \sin ^{-1} \frac{t}{2} \)
D \( \cdot \frac{t}{2} \sqrt{4+t^{2}}+\frac{1}{2} \cdot 4 \sin ^{-1} \frac{t}{2} \)
Subject: Physics
The objective lens of an optical instrument is an achromat
combination with a focal length of
\( 90 \mathrm{cm} . \) The two lenses possess
dispersive powers 0.024 and 0.036 respectively and are in contact with each other. Then their focal lengths are:
A. \( -30 \mathrm{cm}, 45 \mathrm{cm} \)
в. \( 45 \mathrm{cm}, 30 \mathrm{cm} \)
c. \( 30 \mathrm{cm},-45 \mathrm{cm} \)
D. 30 \( c m,-30 \mathrm{cm} \)