AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
For the reaction of one mole of zinc dust
with one mole of sulphuric acid in a
bomb calorimeter, \( \triangle \boldsymbol{U} \) and \( \boldsymbol{w} \)
corresponds to:
A. \( \triangle U<0, w=0 \)
в. \( \triangle U<0, w<0 \)
c. \( \triangle U>0, w=0 \)
D. \( \triangle U>0, w>0 \)
Subject: Maths
If \( A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right], \) then \( \operatorname{det}\left(A+A^{2}+\right. \)
\( \left.\boldsymbol{A}^{3}+\boldsymbol{A}^{4}+\boldsymbol{A}^{5}\right) \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 32
c. 25
D. 30
Subject: Chemistry
3 moles of \( \boldsymbol{P} \) and 2 moles of \( \boldsymbol{Q} \) are
mixed, what will be their total vapour pressure in the solution if their partial
vapour pressures are 80 and 60 respectively.
A. 80 torr
B. 140 torr
\( c .720 \) torr
D. 70 torr
Subject: Physics
The ratio of the radii of two planets \( r_{1} \)
and \( r_{2} \) is \( k . \) The ratio of acceleration due
to gravity on them is \( r . \) Then the ratio of the escape velocities from them, will be:
A. \( \sqrt{\frac{r}{k}} \)
в. \( \sqrt{\frac{k}{r}} \)
\( c . k r \)
D. \( \sqrt{k s} \)
Subject: Chemistry
Select the correct statement about
elements of group \( 15^{t h} \)
A. the order of stability of oxidation state of +3 is \( B i^{3+}> \) \( S b^{3+}>A s^{3+} \) and for +5 is \( B i^{5+}<S b^{5+}<A s^{5+} \)
B. in case of nitrogen, all oxidation states from +1 to +4 tend to disproportionate in acid solution
C. there is a considerable increase in covalent radius
from \( \mathrm{N} \) to \( \mathrm{P} \) but from As to Bi only a small increase in covalent radius is observed
D. all of the above
Subject: Chemistry
The balanced chemical reaction with
\( \boldsymbol{C l}_{2} \) is
A \( \cdot C l_{2}+2 N a_{2} S_{2} O_{3} \rightarrow 2 N a C l+N a_{2} S_{4} O_{6} \)
в. \( C l_{2}+H_{2} O+N a_{2} S_{2} O_{3} \rightarrow N a_{2} S O_{4}+2 H C l+S \)
c. \( C l_{2}(g)+S_{2} O_{3}^{2-} \rightarrow S O_{4}^{2-}+S+C l \)
D. None of the above
Subject: Physics
A wire has a mass \( (0.3 \pm 0.003) g \) radius \( (0.5 \pm 0.005) \mathrm{mm} \) and length (6 土 \( 0.06) \mathrm{cm} . \) The maximum percentage error in the measurement of its density is -
\( A \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Maths
If the given planes \( a x+b y+c z+d= \)
0 and \( a x+b y+c z+d=0 \) be
mutually perpendicular, then
A \( \cdot \frac{a}{a}=\frac{b}{b}=\frac{c}{c} \)
В \( \cdot \frac{a}{a}+\frac{b}{b}+\frac{c}{c}=0 \)
c. \( a a+b b+c c+d d=0 \)
D. \( a a+b b+c c=0 \)
Subject: Chemistry
\( \mathbf{1 0 0 . 0} \mathrm{mL} \) of a saturated solution of
\( A g_{2} S O_{4} \) is added to \( 250.0 \mathrm{mL} \) of
saturate solution of \( P b C r O_{4} . \) Will any precipitate from and if so what?
Given \( \boldsymbol{K}_{s p} \) for
\( A g_{2} S O_{4}, A g_{2} C r O_{4}, P b C r O_{4}, \) and
\( P b S O_{4} \) are \( 1.4 \times 10^{-5}, 2.4 \times 10^{-12} \)
\( 2.8 \times 10^{-13} \) and \( 1.6 \times 10^{-8} \)
respectively.
A \( \cdot P b C r O_{4} \)
в. \( A g_{2} C r O_{4} \)
\( \mathrm{c} \cdot \mathrm{PbSO}_{4} \)
D. \( A g_{2}, S O_{4} \)
Subject: Physics
A particle moves in the \( x \) -y plane with the velocity \( \overrightarrow{\boldsymbol{v}}=\boldsymbol{a} \hat{\boldsymbol{i}}+\boldsymbol{b} \boldsymbol{t} \hat{j} . \) AT the instant
\( \mathrm{t}=a \sqrt{3} / b \) the magnitude of tangential normal and total acceleration are
Subject: Maths
The differential equation obtained by eliminating arbitrary constants from \( \boldsymbol{y}=\boldsymbol{a} \cdot \boldsymbol{e}^{b \boldsymbol{x}}, \) is
A \( \cdot y \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}=0 \)
B. \( y \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0 \)
c. \( y \frac{d^{2} y}{d x^{2}}-\left(\frac{d y}{d x}\right)^{2}=0 \)
D. \( y \frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}=0 \)
Subject: Maths
Let \( A \) be a square matrix of order \( 3 \times 3 \)
then \( |k A| \) is equal to
\( \mathbf{A} \cdot k \mid A \)
в. \( k^{2}|A| \)
c. \( k^{3}|A| \)
D. \( 3 k|A| \)
Subject: Physics
A sphere of mass \( m \) is moving with a velocity \( (4 \hat{i}-\hat{j}) m / s \) hits a surface and rebounds with a velocity \( (\hat{i}+3 \hat{j}) m / s . \) The coefficient of restitution between the sphere and the
surface is \( k / 16 . \) find the value of \( k \)
\( A \cdot 9 \)
B. 8
\( c \cdot 7 \)
D. 6
Subject: Physics
Assertion
Mass of moving photon varies inversely as the wavelength.
Reason
Energy of the particle \( = \) Mass \( \times \) (speed
of light) \( ^{2} \)
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. If Assertion is incorrect but Reason is correct
Subject: Physics
The acceleration due to gravity at the
poles and the equator is \( g_{p} \) and \( g_{e} \) respectively. If the earth is a sphere of
radius \( R_{E} \) and rotating about its axis
with angular speed \( \omega, \) then \( g_{p}-g_{e} \) is
then given by
\( ^{\mathrm{A}} \cdot \frac{\omega^{2}}{R_{E}} \)
B. \( \frac{\omega^{2}}{R_{E}^{2}} \)
c. \( \omega^{2} R_{E}^{2} \)
D. \( \omega^{2} R_{E} \)
Subject: Maths
Choose the correct answer from the
alternatives given :
Directions for questions 71 to 75: Study the following graph carefully to answer these questions.

Production (in lakh tonnes) of six units
of a company in 2006 and 2007 What is the difference in the production (in lakh tonnes) of all companies in
\( \mathbf{2 0 0 6} \) and \( \mathbf{2 0 0 7} \) ?
ロ2006 므200
A . 45
В. 75
\( c \cdot 100 \)
0.125
Subject: Maths
Let the line \( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{y}-\mathbf{1}}{-\mathbf{5}}=\frac{\boldsymbol{z}+\mathbf{2}}{\mathbf{2}} \) lie
in the plane \( x+3 y-\alpha z+\beta=0 . \) Then
\( (\alpha, \beta) \) equals:
A \( \cdot(-6,7) \)
B \( \cdot(5,-15) \)
c. (-5,5)
D. (6,-17)
Subject: Chemistry
Statement I: Ground state electronic
configuration of chromium atom is \( (A r) 4 s^{1} 3 d^{5} \)
Statement II: Exchange energy is more wtih \( (\boldsymbol{A} \boldsymbol{r}) \boldsymbol{4} \boldsymbol{s}^{1} \boldsymbol{3} \boldsymbol{d}^{5} \) then \( (\boldsymbol{A} \boldsymbol{r}) \boldsymbol{4} \boldsymbol{s}^{2} \boldsymbol{3} \boldsymbol{d}^{4} \)
A. Statement I is true, Statement II is also true Statement is the correct explanation of Statement
B. Statementl is true, statement II is also true:
Statement II is not the correct explanation of Statement
c. statement l is true, Statement II is false
D. Statement I is false, Statement II is true
Subject: Maths
\( 2 \tan ^{-1}\left(\frac{3}{4}\right)= \)
A \( \cdot \sin ^{-1} \frac{24}{25} \)
B \( \cdot \sin ^{-1} \frac{12}{13} \)
c. \( \cos ^{-1}\left(\frac{24}{25}\right) \)
D. \( \cos ^{-1}\left(\frac{12}{13}\right) \)
Subject: Chemistry
\( (X)+K_{2} C O_{3}+A i r \stackrel{h e a t}{\longrightarrow}(Y) \)
\( (Y)+C l_{2} \longrightarrow(Z) \) Purple
Which of the following is correct?
\( \mathbf{A} \cdot X= \)black\( , M n O_{2} ; Y=b l u e, K_{2} C r O_{4} ; Z=K M n O_{4} \)
B. \( X= \) green, \( C r_{2} O_{3} ; Y= \) yellow, \( K_{2} C r O_{4} ; Z= \)
\( K_{2} C r_{2} O_{7} \)
c. \( X= \) black, \( M n O_{2} ; Y= \) green, \( K_{2} M n O_{4} ; Z= \)
\( K M n O_{4} \)
D. \( X= \)black\( , \quad B i_{2} O_{3} ; Y= \)colourless\( , K B i O_{2} ; Z= \)
\( K B i O_{3} \)
Subject: Chemistry
In which of the following reactions \( \Delta S \)
is negative? This question has multiple correct options
\( \mathbf{A} \cdot H_{2} O_{(l)} \rightarrow H_{2} O_{(s)} \)
B. \( 3 O_{2(g)} \rightarrow 2 O_{3(g)} \)
c. \( H_{2} O_{(l)} \rightarrow H_{2} O_{(g)} \)
D. \( N_{2(g)}+3 H_{2(g)} \rightarrow 2 N H_{3(g)} \)
Subject: Chemistry
The freezing point of a 0.05 molal solution of a non-electrolyte in water is:
\( \mathbf{A} \cdot-0.093^{\circ} \mathrm{C} \)
B . \( 1.86^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 0.93^{\circ} \mathrm{C} \)
D. \( 0.093^{\circ} \mathrm{C} \)
Subject: Chemistry
Considering entropy(s) as a thermodynamic parameter, the criterion for the spontaneity of any
process is:
A \( \cdot \Delta S_{\text {system}}+\Delta S_{\text {surroundings}}>0 \)
B. \( \Delta S_{\text {system}}-\Delta S_{\text {surroundings}}>0 \)
C. \( \Delta S_{\text {system}}>0 \) only
D. \( \Delta S_{\text {surroundings}}>0 \) only
Subject: Chemistry
Which of the following reactions
represent correct method?

This question has multiple correct options
\( \mathbf{A} \cdot N a C l_{(\text {molten})} \longrightarrow N a^{+}+C l^{\ominus}: \) Down cell
B. \( N i(C O)_{4} \longrightarrow N i+4 C O: \) Mond process
\( ^{\mathrm{C}} \cdot \mathrm{Ag}_{2} \mathrm{CO}_{3} \longrightarrow 2 \mathrm{Ag}+\mathrm{CO}_{2}+\frac{1}{2} \mathrm{O}_{2}: \operatorname{Van} \) Arkel methoo
D. \( Z r I_{4} \longrightarrow Z r+2 I_{2}: \) Van Arkel method
Subject: Physics
An electron of charge \( e \) and mass \( m \) describes a circular path of radius \( r \) when it is projected with a velocity \( v \) perpendicular to a uniform magnetic field, then its frequency is :
\( ^{A} \cdot \frac{1}{2 \pi} \sqrt{\frac{B e}{m}} \)
в. \( \frac{1}{2 \pi} \frac{B e}{m} \)
c. \( \frac{1}{2 \pi} \frac{m}{B e} \)
D. \( \frac{1}{2 \pi} \frac{m e}{2} \)
Subject: Physics
Three waves of equal frequency having amplitudes \( 10 m m, 4 m m \) and \( 7 m m \) arrive at a given point with successive phase difference \( \frac{\pi}{2} . \) The amplitude of the resulting wave (in \( \mathrm{mm} \) ) is given by:
A . 7
B. 6
c. 5
D. 4
Subject: Maths
\( \int \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x} \cos \boldsymbol{\theta}+1} \cdot \)
A. \( \frac{1}{\cos \theta} \tan ^{-1} \frac{x-\cos \theta}{\sin \theta} \)
s. \( \frac{1}{\sin \theta} \tan ^{-1} \frac{1-\cos \theta}{\sin \theta} \)
D. \( \frac{1}{\sin \theta} \tan ^{-1} \frac{x-\cos \theta}{\sin \theta} \)
\( \frac{1}{\sin \theta} \tan ^{-1} \frac{x+\cos \theta}{\sin \theta} \)
Subject: Physics
Q Type your question.
moving horizontally with a speed \( u \)
perpendicular to the direction of \( v \)
enters through a hole at an upper corner
\( A \) and strikes the diagonally opposite
corner \( B \). Assume \( g=10 m / s^{2} . \) Which
of the following values of \( u \) and \( v \) is(are)
correct?
This question has multiple correct options
A. \( v=20 \mathrm{m} / \mathrm{s} \)
в. \( u=3 \mathrm{m} / \mathrm{s} \)
c. \( v=15 \mathrm{m} / \mathrm{s} \)
D. \( u=2 m / s \)
Subject: Maths
If \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{9}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}\}, \boldsymbol{B}= \)
\( \{4,8,12,16,20\}, C= \)
\{2,4,6,8,10,12\} and \( D= \)
\( \{5,10,15,20,25\}, \) find
(i) \( \boldsymbol{A}-\boldsymbol{B} \)
(ii) \( B-C \)
(iii) \( C-D \)
(iv) \( D-A \)
\( (v) n(A-C) \)
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}\} \) and \( \boldsymbol{B}=\{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}\} \)
Then find \( A \Delta B \)
Subject: Physics
A wheel of radius \( r \) rolling on a straight
line, the velocity of its centre being \( \boldsymbol{v} \). At
a certain instant the point of contact of
the wheel with the grounds is \( M \) and \( N \)
is the highest point on the wheel
(diametrically opposite to \( M \) ). The
incorrect statement is:
A. The velocity of any point \( P \) of the wheel is proportional to MP.
B. Points of the wheel moving with velocity greater than v form a larger area of the wheel than points moving with velocity less than v.
C. The point of contact M is instantaneously at rest.
D. The velocities of any two parts of the wheel which are equidistant from centre are equal
Subject: Physics
gas in an enclosure as shown in Fig (a). When a pump removes some of the gas, the manometer reads as in Fig (b). The
liquid used in the manometers is
mercury and the atmospheric pressure
is \( 76 \mathrm{cm} \) of mercury.
(a) Give the absolute and gauge
pressure of the gas in the enclosure for
cases
(a) and (b), in units of \( c m \) of
mercury.
(b) How would the levels change in case
(b) if \( 13.6 \mathrm{cm} \) of water (immiscible with
mercury) are poured into the right limb of the manometer? (Ignore the small change in the volume of the gas).
\( (a) \)
Subject: Physics
Assertion
Heavy nuclides tend to have more
number of neutrons than protons.
Reason
In heavy nuclei, as there is coloumbic
repulsion between protons, so excess of
neutrons are preferable.
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
When the object is at distances \( u_{1} \) and
\( u_{2} \) the images formed by the same lens
are real and virtual respectively and of the same size. Then focal length of the
lens is:
A \( \cdot \frac{1}{2} \sqrt{\mu_{1} \mu_{2}} \)
в. \( \frac{\mu_{1}+\mu_{2}}{2} \)
c. \( \sqrt{\mu_{1} \mu_{2}} \)
D. \( \sqrt{\left(\mu_{1}+\mu_{2}\right)} \)
Subject: Physics
Assertion
Motion of a ball bouncing elastically in
vertical direction on a smooth
horizontal floor is a periodic motion, but
not an SHM.
Reason
Motion is SHM when restoring force is proportional to displacement from
mean position.
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
Acetone on addition to methyl magnesium bromide forms a complex, which on decomposition with acid gives
\( X \) and \( M g(O H) B r . \) Which one of the
following is \( \boldsymbol{X} \) ?
\( \mathbf{A} \cdot C H_{3} O H \)
в. \( \left(C H_{3}\right)_{3} C O H \)
\( \mathrm{c} \cdot\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHOH} \)
D. \( C H_{3} C H_{2} \) OH
Subject: Physics
In an interference pattern produced by
two identical slits, the intensity at the
site of the central maximum is I. The
intensity at the same spot when either
of the two slits is closed is \( I_{0} \). We must
have:
\( \mathbf{A} \cdot I=I_{0} \)
в. \( I=2 I_{0} \)
c. \( I=4 I_{0} \)
D. \( I \) and \( I_{\circ} \) are not related
Subject: Maths
The function \( f \) is defined by \( f(x)= \)
\( (x+3)(x+1) \)
The graph of \( f \) in the \( x y- \) plane is a
parabola.Which of the following
intervals contains the \( x- \) coordinate
of the vertex of the graph of \( f ? ? \)
A. \( -4<x<-3 \)
B. \( -3<x<1 \)
c. \( 1<x<3 \)
D. \( 3<x<4 \)
Subject: Physics
A potential barrier of \( 0.50 \mathrm{V} \) exists across of PN Junction. If the depletion region is \( 5.0 \times 10^{-7} m \) wide, the
intensity of the electric field in this
region is
A \( \cdot 1.0 \times 10^{9} \mathrm{V} / \mathrm{m} \)
в. \( 2.0 \times 10^{5} \mathrm{V} / \mathrm{m} \)
c. \( 1.0 \times 10^{6} \mathrm{V} / \mathrm{m} \)
D. 2.0 \( \times 10^{6} \mathrm{V} / \mathrm{m} \)
Subject: Chemistry
Complete the following equation:
\( N a_{2} O_{2}+2 H_{2} O \rightarrow(\underline{W})+H_{2} O_{2} \)
\( 2 K O_{2}+2 H_{2} O \rightarrow(\underline{X})+(\underline{Y})+O_{2} \)
\( N a_{2} O+C O_{2} \rightarrow(Z) \)
A. \( W-4 N a, X-K_{2} O, Y-H_{2} O, Z-N a_{2} O_{2} \)
B. \( W-4 N a, X-K_{2} O, Y-H_{2} O_{2}, Z-N a_{2} C O_{3} \)
c. \( W-4 \) NaOH \( , X-2 \)КОН \( , Y-H_{2} \) О \( , Z- \) Na\( _{a} \) О \( _{3} \).
D. \( W-2 N a O H, X-2 K O H, Y-H_{2} O_{2}, Z-N a_{2} C O_{3} \)
Subject: Maths
The contents of three bags \( I, I I \) and \( I I I \)
are as follows:
Bag \( I: 1 \) white, 2 black 3 red balls
Bag \( I I: 2 \) white, 1 black 1 red balls
Bag III : 4 white, 5 black 3 red balls A bag is chosen at random and two
balls are drawn. What is the probability that the balls are white and red
Subject: Chemistry
The group number, number of valence electrons, and valency of an element with the atomic number 15
respectively, of \( \boldsymbol{P}, \) are:
\( \mathbf{A} \cdot 16,5 \) and 2
B. 16,6 and 3
c. 15,5 andb 3
D. 15,6 and 2
Subject: Maths
A sphere of radius \( 3 \mathrm{cms} \) is dropped into a cylindrical vessel of radius \( 4 \mathrm{cms} \). If the sphere is submerged completely, then the height (in \( \mathrm{cm} \) ) to which the water rises, is
A . 2.35
B. 2.30
c. 2.25
D. 2.15
Subject: Maths
Let \( \alpha, \beta, \gamma \) be the distinct real numbers. The vectors \( \boldsymbol{\alpha} \hat{\boldsymbol{i}}+\boldsymbol{\beta} \hat{\boldsymbol{j}}+\boldsymbol{r} \hat{\boldsymbol{k}} \)
\( \beta \hat{i}+r \hat{j}+\alpha \hat{k} ; \gamma \hat{i}+\alpha \hat{j}+\beta \hat{k} \) are
A. collinear
B. form an isosceles triangle
c. right angled triangle
D. equilatetral triangle
Subject: Physics
Initially, the spheres \( A \) and \( B \) are the
potential \( V_{A} \) and \( V_{B} \) respectively. Now
sphere \( \mathrm{B} \) is earthed by closing the switch. The potential of A will now
become \( _{--} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( V_{A} \)
\( \mathbf{c} \cdot V_{A}-V_{B} \)
D. \( V_{B} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & -\mathbf{2} \\ \mathbf{4} & -\mathbf{2}\end{array}\right], \) find \( \boldsymbol{K} \) such that \( \boldsymbol{A}^{\mathbf{2}}= \)
\( \boldsymbol{K} \boldsymbol{A}-\boldsymbol{2} \boldsymbol{I}, \) where \( \boldsymbol{I} \) is the identity
element.
Subject: Physics
A bomb at rest explodes into three fragments. Two fragments fly off at right angles to each other.These two
A \( .14 \mathrm{m} / \mathrm{s} \)
B. \( 15 \mathrm{m} / \mathrm{s} \)
\( c \cdot 18 m / s \)
D. \( 16 \mathrm{m} / \mathrm{s} \)
Subject: Maths
Let \( A, B, C, D \) be (not necessarily square) real matrices such that \( \boldsymbol{A}^{\boldsymbol{T}}= \)
\( \boldsymbol{B} \boldsymbol{C} \boldsymbol{D} ; \boldsymbol{B}^{T}=\boldsymbol{C} \boldsymbol{D} \boldsymbol{A} ; \boldsymbol{C}^{T}=\boldsymbol{D} \boldsymbol{A} \boldsymbol{B} \) and
\( D^{T}=A B C \)
for the matrix \( S=A B C D \), consider the
two statements.
\( \boldsymbol{S}^{3}=\boldsymbol{S} \)
\( \| S^{2}=S^{4} \)
A. II is true but not
B. I is true but not I
c. Both I and II are true
D. Both I and II are false.
Subject: Maths
A trader purchases \( 70 \mathrm{kg} \) of tea at Rs.15.00 per kg and 30kg of tea at
Rs.18.00 per kg and mixes the two. If
the packing charges are 5 percent and he would like to make a profit of 20 percent, he should sell the tea at (approximately):
A . \( R s .17 .50 \) per kg
B. Rs.18.20 per kg
c. \( R s .20 \) per kg
D. Rs.19.50 per kg
Subject: Physics
Two satellites of identical masses orbit
the earth at different heights. The ratio of their distances from the centre of
earth is \( d: 1 \) and the ratio of the
acceleration due to gravity at those height is \( g: 1 . \) Then find the ratio of their orbital velocities.
A \( \cdot \sqrt{\frac{g}{d}} \)
B. \( \sqrt{g d} \)
\( \mathrm{c} \cdot \sqrt{g} \)
D. \( \sqrt{g} d \)
Subject: Maths
Assertion
If \( f(x)=0 \) has two distinct positive
real roots then number of non-
differentiable points of \( \boldsymbol{y}=|\boldsymbol{f}(-|\boldsymbol{x}|)| \) is
\( \mathbf{1} \)
Reason
Graph of \( \boldsymbol{y}=\boldsymbol{f}(|\boldsymbol{x}|) \) is symmetrical
about y-axis
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
The intensity of radiation emitted by the
sun has its maximum value at a
wavelength of \( 510 n m \) and that emitted
by the North Star has the maximum value at 350 nm. If these stars behave
like black bodies, the ratio of the
surface temperature of the sun and the North Star is
A . 1.46
B. 0.69
c. 1.21
D. 0.83
Subject: Chemistry
The increasing order of volatility of
hydrides of the group 16 elements is :
A. \( H_{2} S<H_{2} O<H_{2} S e<H_{2} T e \)
в. \( H_{2} O<H_{2} T e<H_{2} S e<H_{2} S \)
c. \( H_{2} O<H_{2} S<H_{2} S e<H_{2} T e \)
D. none of these
Subject: Physics
Two capacitors of unknown
capacitances \( C_{1} \) and \( C_{2} \) are connected
first in series and then in parallel across a battery of \( 100 \mathrm{V} \). If the energy stored in two combinations is 0.045
and 0.25 J respectively, determine the
value of \( C_{1} \) and \( C_{2} . \) Also calculate the
charge on each capacitor in parallel combination.
Subject: Physics
If \( i \) is the angle of incidence, the angle
between the incident wave front and the
normal to the reflecting surface is
\( \mathbf{A} \cdot i \)
B. \( 90^{\circ}-i \)
\( \mathbf{c} \cdot 90^{\circ}+i \)
D . \( i-90^{\circ} \)
Subject: Chemistry
Select the correct statements.
a. There is asymmetry between converting work to heat and converting heat to work.
b. No process is possible in which the sole result is the absorption of heat
from a reservoir and its complete
conversion into work.
c. For every chemical reaction at
equilibrium, standard change in Gibbs
free energy is zero.
At constant temperature and pressure, chemical reactions are
spontaneous in the direction of
decreasing Gibbs energy. This question has multiple correct options
A. Statement a
B. Statement b
c. statement c
D. Statement d
Subject: Physics
Which of the following statement is/ are correct?
I. A person suffering from myopia can see distant obhects clearly.
II.. The bluish color of water in deep sea is only due to reflection of sky in water.
III. In vacuum, all the colored of the light
move with the same speed.
IV. At noon, the sun appears white as light is least scattered
A. I only
B. Il only
c. I and II only
D. III and IV only
Subject: Maths
\( \lim _{x \rightarrow 1}\left(\frac{1}{x-1}-\frac{2}{x^{2}-1}\right)= \)
A . 1 3
B. \( \frac{-1}{2} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{-1}{3} \)
Subject: Physics
A plane wave of monochromatic light falls normally on a uniformly thin film of oil which covers a glass plate. The wavelength of source constructive interference is observed for \( \lambda_{1}=5000 \stackrel{\circ}{A} \) and \( \lambda_{2}=10000 A \) and for no other
wavelength in between. If \( \mu \) of oil is 1.25
and that of glass is \( 1.5, \) the thickness of film will be
A . 0.2
B. 0.1
\( c .0 .8 \)
D. 0.4
Subject: Maths
The number of integral solutions \( (x, y) \) of the equations \( \boldsymbol{x} \sqrt{\boldsymbol{y}}+\boldsymbol{y} \sqrt{\boldsymbol{x}}=\mathbf{2 0} \)
and \( \boldsymbol{x} \sqrt{\boldsymbol{x}}+\boldsymbol{y} \sqrt{\boldsymbol{y}}=\boldsymbol{6 5} \) is:
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of these
Subject: Physics
Assertion
The plot of atomic number \( (y \text { -axis) } v s \)
number of neutrons \( (x- \) axis ) for stable
nuclei shows a curvature towards \( x- \)
axis from the line of \( 45^{\circ} \) slope as the
atomic number is increased.
Reason
Proton-proton electrostatic repulsion begins to overcome attractive forces involving proton and neutrons in heavier nucleides.
A. \( S \) is correct but \( E \) is wrong
B. \( S \) is wrong but \( E \) is correct
c. Both \( S \) and \( E \) are correct and \( E \) is correct explanation of \( S \)
D. Both \( S \) and \( E \) are correct but \( E \) is not correct explanation of \( S \)
Subject: Chemistry
Which of the following structures
represents terylene?
B.
\[
\left[-\mathrm{ocH}_{2}-\mathrm{cH}_{2}-\mathrm{o}-\mathrm{c}-\mathrm{c}_{\mathrm{b}} \mathrm{H}_{4}-\mathrm{C}-\right]_{\mathrm{n}}
\]
\( c \)
\[
\left[-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}=\mathrm{CH}_{2}-\mathrm{C}_{\mathrm{n}}-\mathrm{CH}_{2}-\right]_{\mathrm{n}}
\]
\( D \)
\( \left(-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{2}-\right)_{\mathrm{n}} \)
Subject: Maths
At a school, \( 20 \% \) of the students are
seniors. If all of the seniors attended the
school play, and \( 60 \% \) of all the students
attended the play, then what percent of the non-seniors attended the play?
A . \( 20 \% \)
B. \( 40 \% \)
\( c .50 \% \)
D. \( 100 \% \)
Subject: Maths
\( \int_{0}^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1+\sin x \cdot \cos x} d x \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{2} \)
D.