AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of following can have vacant \( \boldsymbol{p} \) orbital?
\( \mathbf{A} \cdot \cdot \cdot C H_{3} \)
в. \( _{C H_{3}}^{\oplus} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. Both \( (B) \) and \( (C) \)
Subject: Maths
If \( f(x) \) be a quadratic polynomial such
that \( \boldsymbol{f}(\mathbf{0})=\mathbf{2}, \boldsymbol{f}^{\prime}(\mathbf{0})=-\mathbf{3} \) and
\( \boldsymbol{f}^{\prime \prime}(\mathbf{0})=\mathbf{4} \)
then \( \int_{-1}^{1} f(x) d x \) is equal to
A . -3
в. \( 16 / 3 \)
c. 0
D. none of these
Subject: Physics
\( N_{1} \) atoms of a radioactive element emit
\( N_{2} \beta \) -particles per second. The decay
constant of the elements is \( \left(\operatorname{in} s^{-1}\right) \)
A \( \cdot \frac{N_{1}}{N_{2}} \)
B. \( \frac{N_{2}}{N_{1}} \)
c. \( N_{1} \ln (2) \)
D. \( N_{2} \ln (2) \)
Subject: Maths
\( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) defined by \( f(x)=2 x+3 \) and if
\( A=\{-2,-1,0,1,2\} B=\{-1,1,3,5,7\} \) then which
type of function is \( f ? \)
A. One-one
B. onto
c. Bijection
D. constant
Subject: Biology
Match the columns.
\( \begin{array}{llll}\text { A. } & \begin{array}{l}\text { Obligate stem } \\ \text { parasite }\end{array} & \text { 1. } & \begin{array}{l}\text { Ochroma } \\ \text { lagopus }\end{array} \\ \text { B. } & \text { Erythrina } & \text { 2. } & \text { Coral tree } \\ \text { C. } & \text { Butea } & \text { 3. } & \text { Cuscuta } \\ \text { D. } & \text { Lightest wood } & \text { 4. } & \begin{array}{l}\text { Flame of } \\ \text { the forest }\end{array} \\ & \text { 5. } & \text { Guiacum }\end{array} \)
A. \( A-5, B-4, C-2, D-3 \)
B. \( A-3, B-4, C-3, D-2 \)
C. \( A-3, B-2, C-4, D-1 \)
D. \( A-3, B-2, C-4, D-5 \)
Subject: Maths
The A.M. of 'n' observations is M. If the
sum of \( (\boldsymbol{n}-\mathbf{4}) \) observation is 'a', what
is the mean of remaining 4 observations?
A \( . n M+a \)
в. \( \frac{n M-a}{2} \)
c. \( \frac{n M+a}{2} \)
D. \( \frac{n M-a}{4} \)
Subject: Maths
Let \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) be a differentiable curve
satisfying \( \int_{2}^{x} f(t) d t+2=\frac{x^{2}}{2}+\int_{x}^{2} t^{2} f(t) d t, \) then
\( \int_{-\pi / 4}^{\pi / 4} \frac{\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{x}^{9}-\boldsymbol{x}^{3}+\boldsymbol{x}+\mathbf{1}}{\cos ^{2} \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} \)
equals-
A . 0
B.
\( c \cdot 2 \)
\( D \)
Subject: Chemistry
"Nitric oxide reacts with oxygen to form reddish brown nitrogen dioxide gas"" Choose the correct equation for the
above reaction
A \( \cdot 2 N O+O_{2} \rightarrow 2 N O_{2} \)
в. \( N_{2} O+O_{2} \rightarrow N O_{2}+N O \)
C. \( N a N O_{3} \stackrel{\text {heat}}{\longrightarrow} 2 \mathrm{NaNO}_{2}+\mathrm{O}_{2} \)
D. \( 2 N O_{3}+O_{2} \rightarrow 2 N O_{2}+2 O_{2} \)
Subject: Physics
A string of length \( ^{\prime} l^{\prime} \) is fixed at both
ends. It is vibrating in its \( 3^{r d} \) overtone
with maximum amplitude \( ^{\prime} a^{\prime} . \) The amplitude at a distance \( \frac{l}{3} \) from one end is:
\( A \)
B. 0
c. \( \frac{\sqrt{3} a}{2} \)
D. \( \frac{a}{2} \)
Subject: Maths
The figure shows a portions of the graph
\( y=2 x-4 x^{3} . \) The line \( y=c \) is such that
the areas of the regions marked I and II are equal. If a,b are the \( x \) -coordinates of A,B respectively, then a + b equals
\( A \cdot \frac{2}{\sqrt{7}} \)
B. \( \frac{3}{\sqrt{7}} \)
\( c \cdot \frac{4}{\sqrt{7}} \)
\( D \cdot \frac{5}{\sqrt{7}} \)
Subject: Maths
If for a continuous function \( \boldsymbol{f}, \boldsymbol{f}(\mathbf{0})= \)
\( \boldsymbol{f}(1)=\mathbf{0}, \boldsymbol{f}^{\prime}(1)=\mathbf{2} \) and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( f\left(e^{x}\right) e^{f(x)}, \) then \( g^{\prime}(0) \) is equal to
A . 1
B. 2
\( c \cdot 0 \)
D. None of these
Subject: Physics
A radioactive isotope decays as \( z A^{n} \rightarrow z-2 B^{m-4} \rightarrow z-1 C^{m-4} . \) The half
lives of \( A \) and \( B \) are 6 months and 10
months respectively. Assuming that
initially only \( A \) was present, will it be possible to achieve radioactive
equilibrium for \( B \). If \( s o, \) what would be
the ratio of nuclei of \( A \) and \( B \) at
equilibrium. What would happen if the half lives of \( A \) and \( B \) were 10 month and
6 month.
Subject: Maths
Find the area included between the
parabolas \( \boldsymbol{y}^{2}=\boldsymbol{x} \) and \( \boldsymbol{x}=\boldsymbol{3}-\boldsymbol{2} \boldsymbol{y}^{2} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.
Subject: Maths
Express the matrices as the sum of
systemmetric \( \& \) a skew- symmetric
\[
\text { matrices }\left[\begin{array}{ccc}
\mathbf{6} & -\mathbf{2} & \mathbf{2} \\
-\mathbf{2} & \mathbf{3} & -\mathbf{1} \\
\mathbf{2} & -\mathbf{1} & \mathbf{3}
\end{array}\right]
\]
Subject: Physics
A series LCR circuit containing a
resistance of \( 120 \Omega \) has angular resonance frequency \( 4 \times 10^{5} \) rad \( s^{-1} \)
At resonance the voltage across the
resistance and inductance are \( 60 \mathrm{V} \) and
\( 40 \mathrm{V} \) respectively. The angular frequency at which current in the circuit lags the
voltage by \( 45^{0} \) is
A \( \cdot 16 \times 10^{5} \) rad \( s^{-1} \)
B. \( 8 \times 10^{5} \) rad \( s^{-1} \)
C . \( 4 \times 10^{5} \) rad \( s^{-1} \)
D. \( 2 \times 10^{5} \) rad \( s^{-1} \)
Subject: Physics
Two bodies \( X \) and \( Y \) are in thermal
equilibrium. Body Y is also at the same temperature as a third body Z. The three
bodies are of different materials and
have different masses. Which
statement must be correct?
A. \( x \) and \( Y \) must have the same heat capacity
B. \( Y \) and \( Z \) have the same internal energy
C. There is no net transfer of energy if \( x \) is placed in thermal contact with z
D. It is not necessary that \( Y \) should be in thermal equilibrium with z
Subject: Chemistry
Which of following does not give white precipitate of \( A g C l \) on heating with silver nitrate.
A. \( C H_{3} C H_{2} C l \)
B. \( \left(C H_{3}\right)_{2} C H_{2} C l \)
c. \( \left(C H_{3}\right)_{3} C C l \)
D. \( C C l_{4} \)
Subject: Physics
Fig shows an arrangment of masses hanging from a ceiling. In equilibrium, each rod is horizontal, has negligible
mass and extends three times as far to
the right of the wire supporting it as to
the left. If mass \( m_{4} \) is \( 48 \mathrm{kg} \) then mass
of \( m_{1} \) is equal to
A . \( 1 k g \)
в. \( 2 k g \)
\( c .3 k g \)
D. \( 4 k g \)
Subject: Biology
Assertion
Phytoplankton, algae \( \& \) higher plants are chief producers in pond ecosystem.
Reason
Many algae are responsible for
production of ethanol.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
A body with an initial temperature \( \theta_{1} \) is allowed to cool in a surrounding which
is at a constant temperature of \( \boldsymbol{\theta}_{0}\left(\boldsymbol{\theta}_{0}<\right. \)
\( \theta_{1} \) ). Assume that Newton's law of
cooling is obeyed. The temperature of the body after time \( t \) is best expressed
by, Let \( k= \) constant.
A \( \cdot\left(\theta_{1}-\theta_{0}\right) e^{-k t} \)
B \( \cdot\left(\theta_{1}-\theta_{0}\right) \ln (k t) \)
c. \( \theta_{0}+\left(\theta_{1}-\theta_{0}\right) e^{-k t} \)
D. \( \theta_{1} e^{-k t}=\theta_{0} \)
Subject: Maths
The degree of the differential equation \( \boldsymbol{y}_{3}^{2 / 3}+\mathbf{2}+\mathbf{3} \boldsymbol{y}_{2}+\boldsymbol{y}_{1}=\mathbf{0} \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. none of these
Subject: Physics
Optical axis of a thin equi-convex lens is the X-axis. The coordinate of a point object and its images are \( (-20 c m, 1 c m) \) and \( (25 c m,-2 c m) \)
respectively
A. the lens is located at \( x=5 \mathrm{cm} \)
B. the lens is located at \( x=-5 c m \)
c. the focal length of the lens is 10 cm
D. the focal length of the lens is \( 15 \mathrm{cm} \)
Subject: Physics
Two circularly shaped linear polarisers are placed coaxially. The transmission
axis of the first polarizer is at \( 30^{\circ} \) from
the vertical while the second one is at
\( 60^{\circ}, \) both in the clockwise sense. If an
unpolarised beam of light of intensity \( I=20 W / m^{2} \) is incident on this pair of
polarisers, then the intensities \( I_{1} \) and \( I_{2} \)
transmitted by the first and the second polarisers, respectively, will be close to.
A \( \cdot I_{1}=10.0 W / m^{2} \) and \( I_{2}=7.5 W / m^{2} \)
B . \( I_{1}=20 W / m^{2} \) and \( I_{2}=15 W / m^{2} \)
C \( . I_{1}=10.0 W / m^{2} \) and \( I_{2}=8.6 W / m^{2} \)
D. \( I_{1}=15.0 W / m^{2} \) and \( I_{2}=0.0 W / m^{2} \)
Subject: Maths
Find the values of \( x, \) if
\( \left|\begin{array}{ll}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}-\mathbf{1} \\ \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{2}\end{array}\right|=\left|\begin{array}{ll}\boldsymbol{4} & -\mathbf{1} \\ \mathbf{1} & \mathbf{3}\end{array}\right| \)
Subject: Maths
If \( A \) and \( B \) are square matrices of the same order such that \( (\boldsymbol{A}+\boldsymbol{B})(\boldsymbol{A}- \)
\( B)=A^{2}-B^{2} \) then \( \left(A B A^{-1}\right)^{2} \) is equal
to
\( \mathbf{A} \cdot B^{2} \)
B. \( I \)
c. \( A^{2} B^{2} \)
D. \( A^{2} \)
Subject: Physics
A marble block of mass \( 2 \mathrm{kg} \) lying on ice
when given a velocity of \( 6 m s^{-1} \) is stopped by friction in 10 s. Then the coefficient of friction is ( Take \( \boldsymbol{g}= \)
\( \left.10 m s^{-2}\right) \)
A . 0.06
B. 0.03
\( c \cdot 0.04 \)
D. 0.01
Subject: Chemistry
The equilibrium constant for the
reaction is 9.40 at \( 900^{\circ} \mathrm{C} . S_{2}(g)+ \)
\( C(s) \rightleftharpoons C S_{2}(g) \)
The pressure of two gases at
equilibrium, when 1.42 atm of \( S_{2} \) and excess of \( C(s) \) come to equilibrium is :
A \( \cdot P_{C S_{2}}=1.284 a t m, P_{S_{2}}=0.1365 a t m \)
B . \( P_{C S_{2}}=0.1365 a t m, P_{S_{2}}=1.284 a t m \)
C . \( P_{C S_{2}}=1.345 a t m, P_{S_{2}}=0.1456 a t m \)
D. \( P_{C S_{2}}=1.444 a t m, P_{S_{2}}=0.1857 a t m \)
Subject: Chemistry
Light travels with a speed of \( 3 \times 10^{8} \) \( \{m s\} \wedge\{-1\} . \) The distance travelled by light in 1 femto second is:
A. \( 0.03 \mathrm{mm} \)
B. \( 0.003 m m \)
\( \mathbf{c} .3 m m \)
D. \( 0.0003 \mathrm{mm} \)
Subject: Maths
The value of \( ^{n-1} C_{r-2}+^{n-1} C_{r-1} \) is
A. \( ^{n-2} C_{r} \)
B. \( ^{n-1} C_{r} \)
c. \( ^{n+1} C_{r} \)
D. \( ^{n} C_{r-1} \)
Subject: Maths
An object stars from rest at \( t=0 \) and
accelerates at a rate given by \( a=6 t \)
What i) its velocity and ii) its
displacement at any time \( t ? \)
A \( \cdot t^{3}, 3 t^{2} \)
B. \( 3 t^{2}, t^{3} \)
\( \mathbf{c} \cdot t^{2}, t^{3} \)
D. \( 2 t^{2}, 3 t^{3} \)
Subject: Chemistry
Which is not a correct order of energy
for 1 st, 2 nd and 3 rd orbit?
\( \mathbf{A} \cdot E_{1}>E_{2}>E_{3} \)
\( \mathbf{B} \cdot(P E)_{1}<(P E)_{2}<(P E)_{3} \)
\( \mathbf{C} \cdot(K E)_{1}>(K E)_{2}>(K E)_{3} \)
D. A and C both
Subject: Physics
A potentiometer wire has length \( 4 \mathrm{m} \) and resistance \( 8 \Omega \).What should be the
resistance that must be connected in
series with the wire and an accumulator
of emf \( 2 \mathrm{V}, \) so as to get a potential gradient \( 1 \mathrm{m} \mathrm{V} \) per \( \mathrm{cm} \) on the wire?
A . \( 32 \Omega \)
B. \( 36 \Omega \)
c. \( 40 \Omega \)
D. \( 30 \Omega \)
Subject: Maths
Find the angle between the vectors \( \vec{r}_{1}=(4 \hat{i}-3 \hat{j}+5 \hat{k}) \) and \( \vec{r}_{2}=(3 \hat{i}+ \)
\( 4 \hat{j}+5 \hat{k}) \)
A \( \cdot \frac{\pi}{3} \)
B.
\( c \cdot \frac{\pi}{7} \)
D. \( \frac{\pi}{6} \)
Subject: Physics
A satellite is revolving around earth in a
circular orbit. The radius of orbit is half
of the radius of theorbit of moon.

Satellite will complete one revolution in.
A \( \cdot 1 / 2^{3 / 2} \) lunar month
B . \( 1 / 2^{2 / 3} \) |unar month
C. \( 2^{3 / 2} \) lunar month
D. \( 2^{2 / 3} \) lunar month
Subject: Maths
In a triangle \( P Q R, L \) and \( M \) are two points
on the base \( Q R, \) such that \( \angle L P Q= \)
\( \angle Q R P \) and \( \angle R P M=\angle R Q P . \) Prove
that
\( \boldsymbol{P Q}^{2}=\boldsymbol{Q} \boldsymbol{R} \times \boldsymbol{Q} \boldsymbol{L} \)
Subject: Maths
Find the value of:
(i) \( \left(3^{0}+4^{-1}\right) \times 2^{2} \)
(ii) \( \left(2^{-1} \times 4^{-1}\right) \div 2^{-2} \)
(iii) \( \left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2} \)
(iv) \( \left(3^{-1}+4^{-1}+5^{-1}\right)^{0} \)
\( (v)\left[\left(\frac{-2}{3}\right)^{-2}\right]^{2} \)
\( (v i) 7^{-20}-7^{-21} \)
Subject: Chemistry
When zinc reacts with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}(60 \%) \)
the oxidation state of nitrogen changes
from :
\( \mathbf{A} \cdot+5 t o+1 \)
B. +5 to -3
\( \mathbf{c} \cdot+5 t o+4 \)
\( \mathbf{D} \cdot+5 t o+3 \)
Subject: Physics
A current of \( 2 A \) is flowing through a
circular coil of radius \( 10 \mathrm{cm} \) containing 100 turns. The magnetic flux density at the centre of the coil is \( \left(\operatorname{in} W b / m^{2}\right) \)
В. \( 1.26 \times 10^{-2} \)
c. \( 1.26 \times 10^{-4} \)
D. \( 1.26 \times 10^{-5} \)
Subject: Chemistry
Assertion
Ammonium hydroxide solution is added to zinc nitrate solution slowly and then in excess we see white precipitates are soluble
Reason
Ammonium hydroxide solution is added to zinc nitrate solution slowly white precipitates of ammonium nitrate is formed and when ammonium hydroxide is added in excess then the white
precipitates are soluble in it
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
What is the IUPAC name of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}(\boldsymbol{O} \boldsymbol{N} \boldsymbol{O})\right] \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. pentaammine nitrito-0-cobalt
(III) sulphate
B. pentaammine nitro-N-cobalt (III) sulphate
c. pentaamine nitro-0-cobalt (III) sulphate
D. pentaammonia nitro-0-cobalt
(III) sulphate
Subject: Physics
Figure shows a plane mirror onto which
a light ray is incident. If the incident
light ray is turned ray is turned by \( 10^{\circ} \)
and the mirror by \( 20^{\circ} \) as shown, find the
angle turned by the reflected ray.
ted ray
\( \mathbf{A} \cdot 10^{\circ} \)
B. \( 20^{\circ} \)
\( c \cdot 30^{\circ} \)
D. 40
Subject: Maths
\( \int \cos \left\{2 \tan ^{-1} \sqrt{\frac{1-x}{1+x}}\right\} d x \) is equal to
A \( \cdot \frac{1}{8}\left(x^{2}-1\right)+k \)
B. \( \frac{1}{2} x^{2}+k \)
c. \( \frac{1}{2} x+k \)
D. none of these
Subject: Physics
The mutual inductance of the system of
two coils is \( 5 m H . \) The current in the
first coil varies according to the
equation \( \boldsymbol{I}=\boldsymbol{I}_{o} \sin \boldsymbol{w} \boldsymbol{t} \) where \( \boldsymbol{I}_{\boldsymbol{o}}=\mathbf{1 0} \boldsymbol{A} \)
and \( W=100 \pi r a d / s . \) The value of
maximum induced emf in the second
coil is
A \( .2 \pi V \)
в. \( \pi V \)
\( c .5 \pi V \)
D. \( 4 \pi V \)
Subject: Physics
Each of 27 identical spherical drops of a conducting liquid is charged upto a potential of Vo. They coal ease to form a bigger drop. What is the potential on the surface of this bigger drop.
\( \mathbf{A} \cdot 9 V^{\circ} \)
B. \( 3 V^{\circ} \)
\( \mathrm{c} \cdot 27 \mathrm{V}^{\circ} \)
D. \( V^{\text {d }} \)
Subject: Chemistry
Protonation of 1,2 -butadiene gives
carbocation \( (\mathrm{A}) \) and protonation of \( 3^{-} \)
methyl-1, 2-butadiene gives carbocation \( (\mathrm{B}) . \) In both case the most
stable carbocation possible is produced
but no carbocation rearrangements
take place. Which of the two carbocation is more stable and why?
A. A is more stable because it is a terminal carbocation, according to Markownikoff's rule
B. A is more stable because it is stabilized by resonance and hyperconjugation
C. A is more stable because cationic carbon is \( s p \) hybridized
D. B is more stable because it has two methyl groups that can provide extra stabilization by hyperconjugation and inductive effect
Subject: Biology
Match the two sets
\( \mathbf{A} \)
I- D, II- A, III- B, IV- C
B. I- A, II- B, III-C, IV-D
\( \mathbf{C} \cdot \mid-\mathrm{B},\|-\mathrm{A},\| \mathrm{I}-\mathrm{D}, \mathrm{IV}-\mathrm{C} \)
D. \( |-A,| I-D,|I|-C, \mid V-B \)
Subject: Physics
Two identical calorimeters 'X' and 'Y', of water equivalent 10 g each, contain equal quantities of the same liquid. The mass, initial temperature and specific heat capacity of the liquid present in
both calorimeters are 50 g, \( 25^{\circ} \mathrm{C} \) and \( \frac{1}{2} c a l g^{-1 \circ} C^{-1} \) respectively.A 10 g metal
piece (say A) of specific heat capacity \( 0.4 c a l g^{-1 \circ} C^{-1} \) is dropped in calorimeter "X". and 25 g of metal piece (say B) of specific heat capacity " \( S_{B} \) "is dropped into calorimeter "Y". Due to this, the equilibrium temperature in 'X'
and 'Y' rises to \( 30^{\circ} \mathrm{C} \) and \( 40^{\circ} \mathrm{C} \)
respectively. If the initial temperature of B' is twice that of 'A', then find the value
of "S \( _{B} " \)
Subject: Maths
The D. E of the family of all circles in the first quadrant touching the coordinate
axes
\( \mathbf{A} \cdot\left[1+y_{1}^{2}\right]^{3}=r^{2} y_{2}^{2} \)
B \( \cdot\left[1+y_{2}\right]^{3}=r^{2} y_{1}^{2} \)
C \( \cdot\left[1+y_{1}^{2}\right]^{2}=r^{2} y_{2}^{3} \)
D. \( \left[1+y_{1}\right]^{3}=r^{2} y_{2}^{2} \)
Subject: Chemistry
12 g of impure cyanogen undergoes hydrolysis by two different paths.
\( (\boldsymbol{C N})_{2}+\mathbf{4} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow\left(\boldsymbol{N} \boldsymbol{H}_{4}\right)_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4} \)
ii. \( (\boldsymbol{C N})_{2}+\mathbf{2 H}_{\mathbf{2}} \boldsymbol{O} \rightarrow \boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{N} \boldsymbol{H}_{2} \)
When 11.52 g of pure ammonium
carbonate \( \left[\left(N H_{4}\right)_{2} C O_{3}\right] \) was heated
the exact amount of urea was obtained.
\( 20 \mathrm{mL} \) of \( 1.6 \mathrm{M} \) acidic \( K M n O_{4} \) is
required to completely oxidise. The percentage progress of the reaction in path (ii) is:
A . \( 40 \% \)
B. \( 60 \% \)
c. \( 30 \% \)
D. \( 70 \% \)
Subject: Physics
Two coherent monochromatic light beams of intensities \( I \) and \( 4 I \) are
superposed. The maximum and minimum possible resulting intensities
are :
A \( .5 I \) and 0
B. \( 5 I \) and \( 3 I \)
c. \( 9 I \) and \( I \)
D. \( 9 I \) and \( 3 I \)
Subject: Chemistry
The value of equilibrium constant \( \left(\boldsymbol{K}_{\boldsymbol{f}}\right) \)
for the reaction: \( Z n^{2+}(a q)+ \)
\[
4 O H^{-}(a q) \rightleftharpoons Z n(O H)_{4}^{2-}(a q) \text { is }
\]
represented in scientific notation as
\( \boldsymbol{p} \times \mathbf{1 0}^{\boldsymbol{q}}, \) then q is:
Given \( : Z n^{2+}(a q)+2 e^{-} \rightarrow \)
\[
\begin{array}{c}
\operatorname{Zn}(s) ; \boldsymbol{E}^{0}=-\mathbf{0 . 7 6} \boldsymbol{V} \\
\boldsymbol{Z n}(\boldsymbol{O H})_{4}^{2-}(\boldsymbol{a q})+\boldsymbol{2 e}^{-} \rightarrow \\
\boldsymbol{Z n}(\boldsymbol{s})+\boldsymbol{4 O H}^{-}(\boldsymbol{a q}) ; \boldsymbol{E}^{0}=-\mathbf{1 . 3 6} \boldsymbol{V} \\
\boldsymbol{2 . 3 0 3} \frac{\boldsymbol{R T}}{\boldsymbol{F}}=\mathbf{0 . 0 6}
\end{array}
\]
A . 20
B. 10
c. 15
D. 21
Subject: Maths
The eccentricity of the ellipse \( 9 x^{2}+ \)
\( 25 y^{2}-18 x-100 y-116=0, \) is
A \( .25 / 16 \)
в. \( 4 / 5 \)
c. \( 16 / 25 \)
D. \( 5 / 4 \)
Subject: Physics
A body is projected with a velocity \( u \). It
passes through a certain point above
the gound after \( t_{1} \) sec. The time after which the body passes through the same point during the return journey is:
A \( \cdot\left(\frac{u}{g}-t_{1}\right) \)
в. \( 2\left(\frac{u}{g}-t_{1}\right) \)
c. \( _{3}\left(\frac{u}{g}-t_{1}\right) \)
D. \( _{3}\left(\frac{u^{2}}{g^{2}}-t_{1}\right) \)
Subject: Physics
Two thin uniform circular rings each of
radius \( 10 m \) and mass \( 0.1 k g \) are arranged such that they have Common centre and their planes are perpendicular to each other. The M.I. of the system about an axis passing through their common centre and perpendicular to the plane of either of the ring in \( k g m^{-2} \) is:
A. 1.5
в. 4.5
c. 15
D. 18
Subject: Chemistry
For the reaction \( 2 A+B \leftrightharpoons C \)
1 moles of \( A, 2 \) moles of \( B \) and 4 moles
of \( C \) were taken initially in \( 1 L \) vessel. At
equilibrium moles of \( C \) was 0.5 what is
the equilibrium constant?
A \( \cdot 1.4 \times 10^{-3} \)
B . \( 1.1 \times 10^{-2} \)
c. \( 3.5 \times 10^{-4} \)
D. \( 2.8 \times 10^{-2} \)
Subject: Maths
The vectors \( \overline{A B}=\overline{3 i}-\overline{2 j}+\overline{2 k} \) and
\( B C=-\bar{i}-\overline{2 k} \) are the adjacent sides
of a parallelogram. The angle between its diagonals is
A \( \cdot \frac{\pi}{2} \)
В \( \cdot \frac{\pi}{3} \) or \( \frac{2 \pi}{3} \)
c. \( \frac{3 \pi}{4} \) or \( \frac{\pi}{4} \)
D. \( \frac{5 \pi}{6} \) or \( \frac{\pi}{6} \)
Subject: Physics
The given diagram shows a series of images of moving ball captured by a
camera.
The ball was moving at a constant speed and the image were taken
constant rate of 10 per second.What is
the speed of ball?
A. \( 30 m s^{-1} \)
B. \( 20 m s^{-1} \)
c. \( 45 m s^{-1} \)
D. \( 15 \mathrm{ms}^{-1} \)
Subject: Maths
In the following figures, \( A B C D \) is a
rhombus. Find the values of \( x \) and \( y \)
\( \mathbf{A} \cdot 50^{\circ}, 50^{\circ} \)
B \( \cdot 30^{\circ}, 50^{\circ} \)
c. \( 20^{\circ}, 50 \)
D. None of these
Subject: Physics
The velocity of a particle moving in the positive direction of the \( x \) axis varies as
\( V=\alpha \sqrt{x} \) where \( \alpha \) is a
positive constant. Assuming that at the moment \( t=0 \) the particle was
located at the point \( x=0, \) find
acceleration at \( t=51 s \)
\( A \cdot \alpha^{2} \)
B . \( \alpha^{2} / 2 \)
\( c \cdot a \)
D. \( \alpha^{3} \)
Subject: Chemistry
If uncertainity in position and momentum are equal, then uncertainity in velocity is:
A \( \cdot \sqrt{\frac{h}{\pi}} \)
в. \( \frac{1}{2} \sqrt{\frac{h}{\pi}} \)
\( ^{\mathrm{c}} \cdot \frac{1}{2 m} \sqrt{\frac{h}{\pi}} \)
D. \( 2 m \frac{1}{2} \sqrt{\frac{h}{\pi}} \)
Subject: Chemistry
At \( 100^{\circ} \mathrm{C} \) and 1 atm, if the density of the
liquid water is \( 1.0 g c m^{-3} \) and that of
water vapour is \( 0.0006 g \mathrm{cm}^{-3}, \) then the volume occupied by water molecules in
1 L of steam at this temperature is:
\( \mathbf{A} \cdot 6 \mathrm{cm}^{3} \)
B. \( 60 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 0.6 \mathrm{cm}^{3} \)
D. \( 0.06 \mathrm{cm}^{3} \)
Subject: Maths
If \( f(x)=\left\{\begin{array}{cc}x \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}, \) then at \right.
\( \boldsymbol{x}=\mathbf{0} \) the function \( \boldsymbol{f}(\boldsymbol{x}) \) is
A. Continuous
B. Differentiabl
c. continuous but not differentiable
D. None of the above
Subject: Chemistry
If two liquids \( A \) and \( B \) form minimum
boiling azeotrope at some specific
composition then:
A. \( A \) -B interactions are stronger than those between \( A-A \) or B-B
B. vapour pressure of solution increases because more number of molecules of liquids \( A \) and \( B \) can escape from the solution
C. vapour pressure of solution decreases because less number of molecules of liquids \( A \) and \( B \) can escape from the solution
D. show a large positive deviation from Raoult's law
Subject: Physics
The refractive indices of glass and
quartz w.r.t. air are \( 3 / 2 \) and \( 12 / 5 \) respectively. The refractive index of quartz w.r.t. glass is:
A. \( 8 / 5 \)
B. 5/8
\( c \cdot 5 / 18 \)
D. 18/5