AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ccc}x & \text { if } & x \text { is rational } \\ 2-x & \text { if } & x \text { is irrational }\end{array} \) Then \right.
fof \( (x) \) is continuous
A. everywhere
B. no where
c. at all irrational \( x \)
D. at all rational \( x \)
Subject: Physics
An object is placed at \( 20 \mathrm{cm} \) in front of a concave mirror produces three times magnified real image. What is focal length of the concave mirror?
\( A \cdot 15 \mathrm{cm} \)
B. 6.6 \( \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. 7.5 cm
Subject: Chemistry
Study the given flowchart and identify
\( \boldsymbol{K}, \boldsymbol{L}, \boldsymbol{M} \) and \( \boldsymbol{N} \) respectively
*Produced from burning of coal and diesel
**Given off by petrol engines
A. Carbon dioxide, nitrogen oxides, methane, sulphur dioxide
B. Carbon monoxide, methane, sulphur dioxide, nitrogen oxides
C. Methane, carbon monoxide, carbon dioxide, sulphur dioxide
D. Sulphur dioxide, carbon monoxide, methane, nitrogen
Subject: Physics
The refractive index of glass is \( 1.5 . \) From a point \( P \) inside a glass block, draw rays \( P A, P B \) and \( P C \) incident on the
glass-air surface at an angle of incidence \( 30^{\circ}, 42^{\circ} \) and \( 60^{\circ} \)
respectively. What is the angle of
refraction for the ray \( \boldsymbol{P} \boldsymbol{B} \) ? (Take
\( \sin 42^{\circ}=\frac{2}{3} \)
A \( \cdot 0^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)
Subject: Physics
A wheel starts rotating from rest at time \( t=0 \) with a angular acceleration
of 50 radians/s\( ^{2} . \) The angular
acceleration \( (\alpha) \) decreases to zero
value after 5 seconds. During this
interval, \( \alpha \) varies according to the
question \( \boldsymbol{\alpha}=\boldsymbol{\alpha}_{0}\left(1-\frac{\boldsymbol{t}}{\mathbf{5}}\right) \)
The angular velocity at \( \boldsymbol{T}=\mathbf{5} \boldsymbol{s} \) will be
\( \mathbf{A} \cdot 10 \mathrm{rad} / \mathrm{s} \)
B. \( 250 \mathrm{rad} / \mathrm{s} \)
C \( .125 \mathrm{rad} / \mathrm{s} \)
D. \( 100 \mathrm{rad} / \mathrm{s} \)
Subject: Maths
\( \square A B C D \) is a trapezium in which
\( \boldsymbol{A B} \| \boldsymbol{D C} \) and \( \angle \boldsymbol{A}=\angle \boldsymbol{B}=\mathbf{4 5}^{\boldsymbol{o}} . \) Find \( \angle \boldsymbol{C} \)
and \( \angle D \) of the trapezium.
A \( \cdot 135^{\circ} \) each
B . \( 125^{\circ}, 145^{\circ} \)
c. \( 145^{\circ}, 125^{\circ} \)
D . \( 115^{\circ}, 155^{\circ} \)
Subject: Chemistry
Assertion
(A): Hydrogen shows resemblance with alkali metals as well
as halogens. Reason
(R): Hydrogen exists in atomic form only at high temperature.
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not a correct explanation of
c. \( A \) is true but \( R \) is false
D. A is false but R is true
Subject: Maths
Pugazh has been given four choices for his pocket money by his father. Which of the choices should he taken in order to
get the maximum money?
\( A \)
\( \frac{2}{3} \) of \( R s 150 \)
B. \( \frac{3}{5} \) of \( R s 150 \)
c. \( \frac{1}{6} \) of \( R s 150 \)
D. \( \frac{1}{5} \) of \( R s 15 \)
Subject: Chemistry
It has been observed that the ratio of the
molar heat of vaporization of liquid and its normal boiling point is approximately same for most of the liquids (called Trouton's rule). Which of the following does not follow this rule?
A. \( C_{6} H_{6} \)
в. \( C_{6} H_{14} \)
c. \( C C l_{4} \)
D. \( N H_{3} \)
Subject: Physics
if \( \hat{i}, \hat{r}, \hat{n} \) are unit vectors along incident ray in air, refracted ray in a medium, normal respectively and \( \mu \) is refractive
index of medium, then the correct choice is:
A \( \cdot(\hat{i} \times \hat{n})=\mu(\hat{n} \times \hat{r}) \)
B . \( \mu(\hat{i} \times \hat{n})=\hat{n} \times \hat{r} \)
c. \( \hat{i} . \hat{n}=\mu(\hat{n} . \hat{r}) \)
D. \( \mu(\hat{i} . \hat{n})=\hat{n} . \hat{r} \)
Subject: Physics
Assertion
The relative among \( u, v \) and \( f \) for the
spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason
The laws of reflection are strictly valid
for plane surfaces but not for large
spherical surfaces.
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
Assertion
A rocket work on the principle of linear
momentum.
Reason
Whenever there is the change in
momentum of one body, the same change occur in the momentum of the
second body of the same system but in
the opposite direction.
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
Assertion
Third law of thermodynamics is
confined to pure crystalline solids.
Reason
Theoretical arguments and practical
evidence have shown that entropy of
solutions and super cooled liquids is
not zero at \( 0 \mathrm{K} \)
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 cofactors of elements in second row
of the determinant \( \left|\begin{array}{ccc}\mathbf{2} & \mathbf{- 1} & \mathbf{4} \\ \mathbf{4} & \mathbf{2} & \mathbf{- 3} \\ \mathbf{1} & \mathbf{1} & \mathbf{2}\end{array}\right| \) are
\( \mathbf{A} \cdot 5,6,4 \)
В. 6,0,-3
c. 5,1,8
\( \mathbf{D} \cdot 6,0,3 \)
Subject: Chemistry
The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for a
homogeneous gaseous reaction is \( 10^{-8} \) The standard Gibbs free energy change \( \Delta G^{\ominus} \) for the reaction (using \( \boldsymbol{R}= \)
\( \left.2 c a l K^{-1} m o l^{-1}\right) \) is:
A. \( 10.98 k c a l \)
B. - 1.8kcal
c. \( -4.1454 k c a l \)
D. \( +4.1454 k c a l \)
Subject: Physics
A long solenoid with 20 turns per \( c m \)
has a small loop of area \( 2.0 \mathrm{cm}^{2} \) placed inside the solenoid normal to its axis. If
the current carried by the solenoid changes steadily from \( 2.0 A \) to \( 4.0 A \) in
\( 0.1 \mathrm{sec}, \) calculate the induced emf in
the loop while the current is changing.
Subject: Maths
Fill in the blank: \( \left(-\frac{1}{3}\right)+ \) \( \left[\left(\frac{-4}{3}\right)+\frac{3}{7}\right]=\left[\left(\frac{-1}{3}\right)+\dots . .\right]+\frac{3}{7} \)
\( A \cdot \frac{-1}{3} \)
B. \( \frac{-4}{3} \)
\( c \cdot \frac{3}{7} \)
D. \( \frac{-3}{7} \)
Subject: Physics
A student says that he had applied a force \( F=-k \sqrt{x} \) on a particle and the
particle moves in simple harmonic
motion. He refuses to tell whether \( k \) is a
constant or not. Assume that he has
worked only with positive \( x \) and no other
force acted on the particle.
A . As \( x \) increases \( k \) increases
B. As \( x \) increases \( k \) decreases
C. As \( x \) increases \( k \) remains constant
D. The motion cannot be simple harmonic
Subject: Physics
A \( 20 k g \) load is suspended by a wire of
\( \operatorname{cross} \operatorname{section} 0.4 m m^{2} . \) The stress
produced in \( \mathrm{N} / \mathrm{m}^{2} \) is :
\( A \cdot 4.9 \times 10^{-6} \)
B. \( 4.9 \times 10^{8} \)
\( c \cdot 49 \times 10^{8} \)
D. 2.45 \times 10 \( ^{-6} \)
Subject: Chemistry
Density of heavy water is maximum at:
\( \mathbf{A} \cdot 3.82^{\circ} C \)
B . \( 101.42^{\circ} \mathrm{C} \)
c. \( 11.6^{\circ} \mathrm{C} \)
D. \( 4^{\circ} \mathrm{C} \)
Subject: Chemistry
Statement I : The reaction of BaCl
and \( N a_{2} S O_{4} \) doesnt go to completion.
Because

Statement II : The compound barium sulfate is formed
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct
Subject: Chemistry
For a very dilute solution of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
Van't Hoff factor is:
\( \mathbf{A} \cdot i=7 \)
B. \( i=3 \)
\( c \cdot i=4 \)
\( \mathbf{D} \cdot i=5 \)
Subject: Maths
The area of the triangle formed by \( (0,0),\left(a^{x^{2}}, 0\right),\left(0, a^{6 x}\right) \) is \( \frac{1}{2 a^{5}} s q \) unit
then \( x \) is equal to
\( \mathbf{A} \cdot 1 \) or 5
B. -1 or 5
c. 1 or -5
D. -1 or -5
Subject: Maths
In the given figure, \( D E \| B C \) and
\( A D: D B=5: 4, \) find \( \frac{\operatorname{area}(\Delta D F E)}{\operatorname{area}(\Delta C F B)} \)
4. 5: 9
B . 25: 16
c. 25: 81
D. 81: 25
Subject: Chemistry
The precipitate of \( \boldsymbol{C a} \boldsymbol{F}_{2}\left(\boldsymbol{K}_{\boldsymbol{s} \boldsymbol{p}}=\mathbf{1 . 7} \times\right. \)
\( \left.10^{-10}\right) \) is obtained when equal volumes
of which of the following are mixed?
A \( \cdot 10^{-4} M C a^{+2}+10^{-4} M F^{-} \)
B . \( 10^{-2} M C a^{+2}+10^{-3} M F^{-} \)
c. \( 10^{-5} C a^{+2}+10^{-5} M F^{-} \)
D. \( 10^{-3} M C a^{+2}+10^{-5} M F^{-} \)
Subject: Maths
Arrange the given steps in CORRECT order, while constructing \( \triangle P Q R \) where \( P M \perp Q S \) and it is given that \( Q R=4.2 \)
\( \mathrm{cm}, \angle \mathrm{Q}=120^{\circ} \) and \( \mathrm{PQ}=3.5 \mathrm{cm} \)
Step 1: Now, extend RQ to S and with P
as centre and with a sufficient radius,
draw an arc, cuffing \( \mathrm{SQ} \) at \( \mathrm{A} \) and \( \mathrm{B} \). Step 2. Along QX, set off QP = 3.5 cm. Step 3. Draw a line segment \( Q R=4.2 \mathrm{cm} \)
and construct \( \angle \mathrm{RQX}=120^{\circ} \)
Step 4. Joint PR.
Step 5. Joint PC, meeting RQ product at
M. Then, PM \( \perp \) QS
Step 6. With A as centre and radius
more than half \( A B, \) draw an arc. Now
with \( \mathrm{B} \) as centre and with the same
radius draw another arc, cutting the previous arc at \( \mathbf{C} \)
A \( \cdot 1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 5 \rightarrow 6 \)
B . \( 4 \rightarrow 1 \rightarrow 2 \rightarrow 3 \rightarrow 5 \rightarrow 6 \)
\( c \cdot 2 \rightarrow 4 \rightarrow 3 \rightarrow 1 \rightarrow 5 \rightarrow 6 \)
D. \( 3 \rightarrow 2 \rightarrow 4 \rightarrow 1 \rightarrow 6 \rightarrow 5 \)
Subject: Chemistry
Which hydrogen-like species will have the same radius as that of Bohr's orbit
of the hydrogen atom?
A \( \cdot n=2, L i^{2+} \)
B . \( n=2, B e^{3+} \)
c. \( n=2, H e^{+} \)
D . \( n=3, L i^{3+} \)
Subject: Maths
The value of integral \( \int \tan ^{-1}\left(\frac{x^{3}}{1+x^{2}}\right)+ \)
\( \tan ^{-1}\left(\frac{1+x^{2}}{x^{3}}\right) d x \) is equal to
\( A \)
в. \( -\frac{\pi}{2}+c \)
c. \( \frac{\pi}{2}+c \)
D. \( \left(\frac{\pi}{2}\right) x+c \)
Subject: Physics
Calorie is defined as the amount of heat
required to raise temperature of \( 1 g \) of water by \( 1^{\circ} \mathrm{C} \) and it is defined under which of the following conditions?
A . From \( 14.5^{\circ} \mathrm{C} \) to \( 15.5^{\circ} \mathrm{C} \) at \( 760 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. From \( 98.5^{\circ} \mathrm{C} \) to \( 99.5^{\circ} \mathrm{C} \) at \( 760 \mathrm{mm} \) of \( \mathrm{Hg} \)
C. From \( 13.5^{\circ} \mathrm{C} \) to \( 14.5^{\circ} \mathrm{C} \) at \( 76 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. From \( 3.5^{\circ} \mathrm{C} \) to \( 4.5^{\circ} \mathrm{C} \) at \( 76 \mathrm{mm} \) of \( \mathrm{Hg} \)
Subject: Physics
The charge flowing through a resistance \( R \) varies with time \( t \) as \( Q=a t-b t^{2} \)
where a and b are positive constants.
The total heat produced in \( \boldsymbol{R} \) is:
A \( \cdot \frac{a^{3} R}{6 b b} \)
B. \( \frac{a^{3} R}{3 b} \)
c. \( \frac{a^{3} R}{2 b} \)
D. \( \frac{a^{3} R}{b} \)
Subject: Chemistry
Which of the following amine gives diazonium salt on reaction with
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2} ? \)
A \( \cdot\left(C H_{3}\right)_{2} N H \)
в. \( \left(C H_{3}\right)_{3} N \)
c. \( C_{6} H_{5} N H_{2} \)
D. \( C H_{3} N H_{2} \)
Subject: Maths
\( \int x \sin ^{2} x d x \)
A. \( \frac{x^{2}}{4}-\frac{\cos 2 x}{3}+\frac{1}{8} \sin 2 x+c \)
B. \( \frac{x^{2}}{4}-\frac{x \sin 2 x}{4}-\frac{1}{8} \cos 2 x+c \)
C \( \frac{x^{2}}{4}+\frac{x \sin 2 x}{4}+\frac{1}{8} \cos 2 x+c \)
D. \( \frac{-x^{2}}{4}-\frac{\cos 2 x}{3}+\frac{1}{8} \cos 2 x+c \)
Subject: Physics
A ball which is at rest is dropped from height \( h \) metre. As it bounces off the
floor, its speed is \( 80 \% \) of what it was just before touching the ground. The ball will then rise to nearly a height.
\( \mathbf{A} \cdot 0.94 h \)
B. \( 0.74 h \)
c. \( 0.64 h \)
D. \( 0.84 h \)
Subject: Physics
A hollow half cylinder surface of radius R and length I is placed in a uniform electric field \( \vec{E} \). Electric field is acting
perpendicular on the ABCD. If the flux through the curved surface of the hollow
cylindrical surface is \( \boldsymbol{E} \times \boldsymbol{X} \boldsymbol{R} \boldsymbol{l} \). Find \( \mathbf{X} \) ?
Subject: Physics
Formula of coloumbs inverse square
law is (using electric charges), assume \( k=\frac{1}{4 \pi \epsilon_{0}} \)
A. \( F=q_{1} q_{2} d^{2} \cdot K \)
B. \( F=\frac{q_{1} q_{2}}{K d^{2}} \)
\( ^{\mathrm{c}} \cdot_{F}=\frac{\sqrt{K} q_{1} q_{2}}{d^{2}} \)
D. None of these
Subject: Physics
Force acting on a particles moving in a
straight line varies with the velocity \( v \) of
the particles as \( \boldsymbol{F}=\boldsymbol{K} \) where \( \boldsymbol{K} \) is a
constant. The work done by this force in time \( t \) is
A \( \cdot \frac{K}{v^{2}} t \)
в. \( 2 K t \)
c. all the above
D. None of these
Subject: Chemistry
In which of the following compounds transition metal has zero oxidation
state?
A. \( \mathrm{CrO}_{5} \)
B. \( \mathrm{NH}_{2} \cdot \mathrm{NH}_{2} \)
c. \( \mathrm{NOClO}_{4} \)
D \( \cdot\left[F e(C O)_{5}\right] \)
Subject: Physics
A solid sphere is rolling on a rough surface, whose centre of mass is at \( C \) at
a certain instant. Find at that instant it
has angular velocity \( \omega \) Its radius is \( \mathrm{R} \). Find the angular acceleration at that instant mass of sphere is \( \mathrm{m} \)
A \( \frac{5}{2} \frac{g d}{R^{2}} \)
В \( \frac{5}{7} \frac{g d}{R^{2}} \)
c. \( \frac{5}{2} \frac{d\left(g+\omega^{2} R\right)}{R^{2}} \)
\( D \)
Subject: Chemistry
Select the incorrect statement(s):
This question has multiple correct options
\( \mathbf{A} \cdot N F_{3} \) has a highest dipole moment among \( C O, N H_{3} \) and \( N F_{3} \)
B. \( H F \) has a highest boiling point among \( C H_{4}, N H_{3} \) and
\( H F \)
\( \mathrm{C} \cdot \mathrm{Cl}_{2} \) has a lowest boiling point among \( \mathrm{Cl}_{2}, \mathrm{Br}_{2} \) and \( I_{2} \)
D. \( H C l O_{3} \) is weakest acid among \( H I O_{3}, H B r O_{3} \) and
\( H C l O_{3} \)
Subject: Physics
Figure shows three cases: in all cases
the circular part has radius \( r \) and
straight ones are infinitely long. For the
same current the ratio of field \( B \) at
center \( P \) in the three cases \( B_{1}: B_{2}: B_{3} \)
is :
\( ^{\mathrm{A}} \cdot\left(-\frac{\pi}{2}\right):\left(\frac{\pi}{2}\right):\left(\frac{3 \pi}{4}-\frac{1}{2}\right) \)
\( ^{\mathrm{B}} \cdot\left(-\frac{\pi}{2}+1\right):\left(\frac{\pi}{2}+1\right):\left(\frac{3 \pi}{4}+\frac{1}{2}\right) \)
\( ^{c} \cdot\left(-\frac{\pi}{2}\right):\left(\frac{\pi}{2}\right):\left(\frac{3 \pi}{4}\right) \)
\( \left(-\frac{\pi}{2}-1\right):\left(\frac{\pi}{2}-\frac{1}{4}\right):\left(\frac{3 \pi}{4}+\frac{1}{2}\right) \)
Subject: Maths
\( A, B, C \) are three points on a circle such
that \( A B \) is the chord and \( C P \) is the
perpendicular to \( O P, \) where \( O \) is the
centre and \( P \) is any point on \( A B . \) The
radius \( r \) of the circle is given by
A \( \cdot r^{2}=O P^{2}+A P \times C P \)
B . \( r^{2}=O P^{2}+A P \times P B \)
c. \( r^{2}=O P^{2}+P B \times P C \)
D . \( r^{2}=O P^{2}+P B^{2} \)
Subject: Maths
Two adjacent sides of parallelogram are \( 24 \mathrm{cm} \) and \( 18 \mathrm{cm} . \) If the distance
between the longer sides is \( 12 \mathrm{cm} \); find the distance between the shorter sides.
A. \( 9 \mathrm{cm} \)
B. \( 16 \mathrm{cm} \)
c. \( 24 \mathrm{cm} \)
D. Data insufficient
Subject: Maths
Let \( A=\left(\begin{array}{l}3^{2} \\ 5\end{array}\right) \) and \( B=\left(\begin{array}{c}8-1 \\ 3\end{array}\right) . \) Find the
matrix \( \mathrm{C} \) if \( \boldsymbol{C}=\mathbf{2} \boldsymbol{A}+\boldsymbol{B} \)
Subject: Physics
The equation of the stationary wave is \( y=2 A \sin \left(\frac{2 \pi c t}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right) \)
Which of the following statements is wrong?
A. The unit of ct is same as that of \( \lambda \)
B. The unit of \( x \). is same as that of \( \lambda \)
c. The unit of ct is same as that of \( x \)
D. The unit of ct, \lambda and \( x \) are same
Subject: Chemistry
Given below are some organic
compounds containing certain functional group.
¡. \( \boldsymbol{C H}_{3}- \) COOH
ii. \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
iii. \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2} \cdot \boldsymbol{N} \boldsymbol{H}_{2} \)
iv. \( \boldsymbol{C H}_{3}-\boldsymbol{C H O} \)
(a) Write the names of functional group of any of the two compounds given
above.
(b) Write the IUPAC name of \( \boldsymbol{C H}_{3}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
(c) Give the structural formula and
IUPAC name of functional group isomer
of \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
Subject: Maths
If \( X, Y \) are two matrices given by the equations \( \boldsymbol{X}+\boldsymbol{Y}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \boldsymbol{X}-\boldsymbol{Y}= \)
\( \left[\begin{array}{cc}\mathbf{3} & \mathbf{2} \\ -\mathbf{1} & \mathbf{0}\end{array}\right] \)
\( \operatorname{then} \boldsymbol{X} \boldsymbol{Y}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right], \) find \( \boldsymbol{a}-\boldsymbol{b}+\boldsymbol{c}+\boldsymbol{d} \)
Subject: Physics
A small conducting sphere of radius \( a \)
carrying a charge \( +Q, \) is placed inside
an equal and oppositely charged conducting shell of radius \( b \)
such that their centers coincide.
Determine the potential at a point
which is at a distance \( c \) from center
such that \( a<c<b \)
A. \( k(Q / c+Q / b) \)
в. \( k(Q / a+Q / b) \)
c. \( k(Q / a-Q / b) \)
D. \( k(Q / c-Q / b) \)
Subject: Physics
Pick the incorrect statement from the
following:
A. Iris is the part of the eye which gives it, its distinctive colour
B. The most comfortable distance at which one can read
with a normal eye is about \( 50 \mathrm{cm} \)
C. If still images of a moving object are flashed on the eye at a rate faster than \( 16 / s \), then, the eye perceives this object as moving
D. Eye lens becoming cloudy is called cataract
Subject: Chemistry
The rate constant for the forward and
backward reactions of hydrolysis of
ester are \( 1.1 \times 10^{-2} \) and \( 1.5 \times 10^{-3} \)
respectively. The equilibrium constant of the following reaction is:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5}+\boldsymbol{H}^{+} \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H} \)
A . 6.33
в. 7.75
\( c .7 .33 \)
D. 8.33
Subject: Chemistry
Marshall's acid is:
\( \mathbf{A} \cdot H_{2} S O_{5} \)
\( \mathbf{B} \cdot H_{2} S_{2} O_{7} \)
\( \mathbf{c} \cdot H_{2} S_{2} O_{3} \)
D. \( H_{2} S_{2} O_{8} \)
Subject: Physics
A sonar echo takes \( 4.4 s \) to return from a
submarine. If the speed of sound in
water is \( 1500 m s^{-1}, \) then the distance of submarine from the sonar is:
A \( .1500 m \)
в. \( 3000 m \)
c. \( 3300 m \)
D. 3600m
Subject: Physics
A photon of wavelength \( 300 \mathrm{nm} \) interacts with a stationary hydrogen atom in ground state. During the interaction,whole energy of the photon is transferred to the electron of the
atom. State which possibility is correct (Consider,Plancks constant \( =\mathbf{4} \times \mathbf{1 0}^{-1 \mathbf{1}} \)
\( \mathrm{eVs}, \) velocity of light \( =3 \times 108 \mathrm{m} / \mathrm{s} \)
ionization energy of hydrogen \( =13.6 \mathrm{e} \)
A. Electron will be knocked out of the atom
B. Electron will go to any excited state of the atom
c. Electron will go only to first excited state of the atom
D. Electron will keep orbiting in the ground state of ato
Subject: Chemistry
How much \( O_{2} \) gas will be collected at
the anode at \( 300 K \) temperature and 1
bas pressure if 2.5 ampere electric
current is passed for one hour in electrolysis of aqueous solution of \( N a_{2} S O_{4} .(F=96500 \text { Coulomb) }[1\text { mole } \)
gas volume is 22.4 litre at STP].
Subject: Maths
If \( f^{\prime \prime}(x)=-f(x) \) and \( g(x)=f^{\prime}(x) \) and
\( \boldsymbol{F}(\boldsymbol{x})=\left(\boldsymbol{f}\left(\frac{x}{2}\right)\right)^{2}+\left(\boldsymbol{g}\left(\frac{x}{2}\right)\right)^{2} \) and given
that \( F(5)=5, \) then \( F(10) \) is equal to
A . 5
B. 10
c. 0
D. 15
Subject: Physics
Consider the following decay series:
\( \boldsymbol{A} \longrightarrow \boldsymbol{B} \longrightarrow \boldsymbol{C} \longrightarrow \boldsymbol{D} \)
Where, \( A, B \) and \( C \) are radioactive
elements with half lives of 4.5 sec, 15
days and 1 sec respectively and \( D \) is
non-radioactive element. Starting with
1 mole of \( A \), the number of moles of \( A \)
\( B, C \) and \( D \) left after 30 days are:
A. One mole of \( D \) and none of \( A, B \) or \( C \)
B. \( 3 / 4 \) mol of \( B, 1 / 4 \) mol of \( D \) and none of \( A \) or \( C \)
C. \( 1 / 4 \) mol of \( B, 3 / 4 \) mol of \( D \) and none of \( A \) or \( C \)
D. \( 1 / 2 \) mol of \( B, 1 / 4 \) mol of \( C, 1 / 4 \) mol of \( D \) and none of \( A \)
E . \( 1 / 4 \) mol of each \( A, B, C \) and \( D \)
Subject: Maths
The value of \( \int e^{2 x}\left(\frac{1}{x}-\frac{1}{2 x^{2}}\right) d x \) is
\( ^{A} \cdot \frac{e^{2 x}}{2}+c \)
B. \( \frac{e^{2 x}}{2 x}+c \)
c. \( \frac{e^{2 x}}{3 x}+c \)
D. \( \frac{e^{2 x}}{x}+c \)
Subject: Chemistry
\( A B, A_{2} \) and \( B_{2} \) are diatomic molecules. If
the bond enthalpies of \( A_{2}, A B \) and \( B_{2} \) are
in the ratio1:1:0.5 enthalpy of formation of \( A B \) from \( A_{2} \) and \( B_{2} \) is \( -100 K J \mathrm{mol}^{-1} . \) What
is the bond energy of \( A_{2} ? \)
B. 100 KJmol-
c. 300 KJmol \( ^{-1} \)
D. 400 KJmol-
Subject: Physics
\( \mathbf{7}^{\mathbf{N}^{\mathbf{1 4}}}+_{\mathbf{2}} \mathbf{H} e^{\mathbf{4}} \rightarrow \mathbf{X}+_{\mathbf{1}} \boldsymbol{H}^{\mathbf{1}} ; \mathbf{X} \) is
\( \mathbf{A} \cdot_{9} F^{18} \)
В. \( _{10} N e^{18} \)
\( \mathbf{c} \cdot_{8} O^{17} \)
\( \mathrm{D} \cdot_{6} C^{15} \)
Subject: Chemistry
Which of the following azeotropes is not
correctly matched?
\( \mathbf{A} \cdot H N O_{3}(68 \%)+H_{2} O(32 \backslash \%): \) Maximum boiling
azerotrope, boiling point \( =393.5 K \)
B \( \cdot H_{2} O(43 \%)+H I(57 \%): \) Minimum boiling azeotrope, boiling point \( =290 K \)
C \( \cdot C_{2} H_{5}(95.5 \%)+H_{2} O(4.5 \%): \) Minimum boiling azerotrope, boiling point \( =351.15 K \)
D. Chloroform (93.2\%) \( +C_{2} H_{5} O H \) (6.8\%): Minimum boiling azeotrope, boiling point \( =332.3 K \) )
Subject: Chemistry
What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of
the following atoms or ions:
¡) \( \boldsymbol{F}^{-} \)
ii) \( \boldsymbol{A} \boldsymbol{r} \)
iii) \( M g^{2+} \)
iv) \( \boldsymbol{R} \boldsymbol{b}^{+} \)