AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
If the initial concentrations in a particular mixture of reactants and
products are \( \left[\boldsymbol{P C l}_{5}\right]=\mathbf{0 . 5} \boldsymbol{M},\left[\boldsymbol{P C l}_{3}\right]= \)
\( 0.15 M, \) and \( \left[C l_{2}\right]=0.6 M, \) the direction
in which the reaction proceed to reach equilibrium is:
A \( \cdot \) to the left \( \left[P C l_{5}\right]=0.325 M ;\left[P C l_{3}\right]=0.295 M ;\left[C l_{2}\right]= \)
\( 0.735 M \)
B. to the left, \( \left[P C l_{5}\right]=0.315 M ;\left[P C l_{3}\right]=0.245 M ;\left[C l_{2}\right]= \)
\( 0.735 M \)
c. to the right, \( \left[P C l_{5}\right]=0.365 M ;\left[P C l_{3}\right]= \) \( 0.285 M ;\left[C l_{2}\right]=0.735 M \)
D. None of these
Subject: Maths
If \( \boldsymbol{I}=\int_{0}^{\pi} x^{3} \log \sin x d x \) and \( I= \)
\( \int_{0}^{\pi} x^{2} \log (\sqrt{2} \sin x), \) then the value of
\( \frac{4}{3 \pi} I \) is equal to
Subject: Physics
A \( 2 \mathrm{kg} \) object moving with the speed of 2 \( \mathrm{m} / \mathrm{s} \) collides with \( 4 \mathrm{kg} \) objects, which is at rest. if the final velcocities of the
odjects are same, then what would be
the final velocity?
A \( \cdot \frac{2}{3} \mathrm{m} / \mathrm{s} \)
в. \( \frac{1}{3} \mathrm{m} / \mathrm{s} \)
c. \( \frac{2}{5} \) m/s
D. \( \frac{3}{5} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Which salt shows maximum osmotic
pressure in its \( 1 \mathrm{m} \) solution.
A \( . A g N O_{3} \)
в. \( N a_{2} S O_{4} \)
\( \mathrm{c} \cdot\left(N H_{4}\right)_{3} P O_{4} \)
D. \( M g C l_{2} \)
Subject: Maths
If \( 6^{t h} \) term of a G.P. is \( \frac{1}{32} \) and \( 9^{t h} \) term is \( \frac{1}{256}, \) then \( 11^{t h} \) term \( = \)
A . 1024
в. \( \frac{1}{1024} \)
c. \( \frac{1}{256} \)
D. \( \frac{1}{512} \)
Subject: Chemistry
\( K_{a} \) for \( C H_{3} C O O H \) is \( 1.8 \times 10^{-5} \) and
\( K_{b} \) for \( N H_{4} O H \) is \( 1.8 \times 10^{-5} . \) The pH of
ammonium acetate will be:
\( \mathbf{A} \cdot 7.005 \)
в. 4.75
\( c .7 .0 \)
D. between 6 and 7
Subject: Chemistry
The increasing order of \( p K_{b} \) for the
following compounds will be :
Refer above image.
\( (\mathbf{A}) \)
\( (\mathbf{B}) \)
(C) \( \mathbf{C H}_{3} \mathbf{N H C H}_{3} \)
A. \( (A)<(B)<(C) \)
B. \( (C)<(A)<(B) \)
c. \( (B)<(C)<(A) \)
D. \( (B)<(A)<(C) \)
Subject: Physics
A barometer reads \( 75 \mathrm{cm} \) of Hg. When
\( 2 \mathrm{cc} \) of air at atmpospheric pressure is introduced into the space above the mercury level, the volume of this space becomes 50 cc. The length by which the mercury column descends is
A. \( 3 \mathrm{cm} \)
B. 6 \( \mathrm{cm} \)
c. \( 1.5 \mathrm{cm} \)
D. 25 cm
Subject: Physics
In a potentiometer experiment the balancing with a cell is at length 240 \( \mathrm{cm} . \) On shunting the cell with a resistance of \( 2 \Omega \) the balancing length
becomes \( 120 \mathrm{cm} . \) The internal
resistance of the cell is?
A . \( 1 \Omega \)
в. \( 0.5 \Omega \)
\( c .4 \Omega \)
D. \( 2 \Omega \)
Subject: Maths
If \( \overrightarrow{D A}=\vec{a}, \overrightarrow{A B}=\vec{b}, \overrightarrow{C B}=\overrightarrow{k a} \) where
\( k>0 \mathrm{X}, \mathrm{Y} \) are the mid points of \( \mathrm{DB} \) and
AC respectively, such that \( |\vec{a}|=17 \) and \( |\vec{X} Y|=4, \) then k equal to \( ? \)
Subject: Maths
For the function \( f(x)=x \cos \frac{1}{x}, x \geq 1 \)
which of the following is/are true??
This question has multiple correct options
A. There is at least one \( x \) in the interval \( [1, \infty) \) for which \( f(x+2)-f(x)<2 \)
\( \mathbf{B} \cdot \lim _{x \rightarrow \infty} f^{\prime}(x)=1 \)
C \( . f(x+2)-f(x)>2 \) for all \( x \) in the interval \( [1, \infty) \)
D. \( f^{\prime}(x) \) is strictly decreasing in the interval \( [1, \infty) \)
Subject: Chemistry
Assertion
The preparation of lyophobic sol is more complex than the lyophilic sols.
Reason
Stabilizers are required to add extra stability to Iyophilic sols.
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
Consider the following reaction, Ethanol \( \stackrel{P B r_{3}}{\longrightarrow} X \stackrel{\text {alc. } K O H}{\longrightarrow} \)
\( \boldsymbol{Y} \frac{(i) \boldsymbol{H}_{2} \boldsymbol{S O}_{4} \text { room temperature }}{(i i) \boldsymbol{H}_{2} \boldsymbol{O}, \text { heat }} \boldsymbol{Z} \)
Product \( Z \) is:
\( \mathbf{A} \cdot C H_{2}=C H_{2} \)
в. \( C H_{3} C H_{2}-O-C H_{2}-C H_{3} \)
c. \( C H_{3} C H_{2}-O-S O_{3} H \)
D. \( C H_{3} C H_{2} \) О \( H \)
Subject: Physics
two blocks of masses \( m_{1}=2 k g \) and
\( \boldsymbol{m}_{2}=4 k g \) are moving in the same
direction with speeds \( \nu_{1}=6 m / s \) and
\( \nu_{2}=3 m / s, \) respectively on a
frictioneless surface as shown in the
figure. An ideal spring with spring
constant \( k=30000 N / m \) is attached
to the back side of \( m_{2} \). Then the
maximum compression of the spring
after collision will be:
\( \mathbf{A} \cdot 0.06 m \)
B. \( 0.04 m \)
c. \( 0.02 m \)
D. none of these
Subject: Physics
In the above figure, \( \boldsymbol{E}_{1} \) to \( \boldsymbol{E}_{6} \) represent
some of the energy levels of an electron in the hydrogen atom. Which one of the following transitions produces a photon of wavelength in the ultra-violet region of the electromagnetic spectrum?
\( e V \)
\( 85 \mathrm{eV} \)
A \( . E_{2}-E_{1} \)
в. \( E_{3}-E_{2} \)
\( \mathbf{c} \cdot E_{4}-E_{3} \)
D. \( E_{6}-E_{4} \)
Subject: Physics
A circular hole of radius \( \frac{x}{2} \) is cut from a
circular disc of radius \( R \). The disc lies
in the XY-plane and its centre coincides
with the origin. If the remaining mass of
the disc is \( M \) then,
(1)determine the initial mass of the
disc.
(2)determine its moment of inertia
about the z-axis.
Subject: Biology
Match the following
\( \begin{array}{ll}\text { A } & \text { B } \\ \text { a. Kingdom } & \text { (i) Amphibia } \\ \text { b. Phylum } & \text { (ii) Animalia } \\ \text { c. Class } & \text { (iii) Chordata } \\ & \text { (iv) Frog }\end{array} \)
ii
\( A \cdot a-i, b-i i, c- \)
B. a- ii, b- iii, c- -i
D. a- ii, b-i, c-iii
Subject: Physics
Assertion
A body is dropped form height \( h \) and
another body is thrown vertically upwards with a speed \( \sqrt{\boldsymbol{g} \boldsymbol{h}} \). They meet at height \( \frac{\boldsymbol{h}}{\mathbf{2}} \)
Reason
The time taken by both the blocks in reaching the height \( \frac{h}{2} \) is same.
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 is incorrect but Reason is correct
Subject: Maths
If \( * \) is defined by \( a * b=a-b^{2} \) and \( \oplus \) is
defined by \( a \oplus b=a^{2}+b, \) where \( a \) and
\( b \) are integers, then \( (3 \oplus 4) * 5 \) is equal
to
A . 164
B. 38
c. -12
D. -28
E .144
Subject: Chemistry
A hydrocarbon \( \boldsymbol{A}\left(\boldsymbol{C}_{5} \boldsymbol{H}_{10}\right) \) on addition of
\( H B r \) in presence of a peroxide forms
\( \left(C_{5} H_{11} B r\right) B \) which is found to be
resolvable into enantiomers. \( \boldsymbol{A} \) on
addition of \( H B r \) in aqueous medium
produces \( C \) which is an isomer of \( B \) but
can't be resolved. \( \boldsymbol{A} \) on reductive
ozonolysis produced \( \left(C_{4} H_{8} O\right) D \) as one
product. \( D \) on catalytic reduction with
\( N a B H_{4} \) produced \( E\left(C_{4} H_{10} O\right) \) which is
resolvable. \( \boldsymbol{E} \) on dehydration with concentrated sulphuric acid produced
\( F\left(C_{4} H_{8}\right) \) which on ozonolysis followed
by work-up with \( Z n-H_{2} O \) produced
two molecules of ethanol. Identify \( \boldsymbol{A} \) to
\( \boldsymbol{F} \)
Subject: Chemistry
Assertion
\( \left[A l\left(H_{2} O\right)_{6}\right]^{3+} \) is a stronger acid than
\( \left[\boldsymbol{M} \boldsymbol{g}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{2+} \)
Reason
Size of \( \left[A l\left(H_{2} O\right)_{6}\right]^{3+} \) is smaller than
\( \left[M g\left(H_{2} O\right)_{6}\right]^{2+} \) and possesses more
effective nuclear charge.
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
Consider the following relation \( R \) on the
set of real square matrices of order 3
\( \boldsymbol{R}=\{(\boldsymbol{A}, \boldsymbol{B}), \mid \boldsymbol{A} \boldsymbol{B}=\boldsymbol{B} \boldsymbol{A}\} \)
STATEMENT-1: Relation R is
equivalence.
STATEMENT-2: Relation R is symmetric.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT -1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Maths
State true or false:
\( A B C D \) is a parallelogram. \( P \) and \( Q \) are the mid-points of sides \( A B \) and \( A D \) respectively. Hence, area of triangle \( A P Q=\frac{1}{8} \) of
the area of parallelogram \( A B C D \)
A. True
B. False
Subject: Physics
The quantities \( A \) and \( B \) are related by
the relation \( \boldsymbol{A} / \boldsymbol{B}=\boldsymbol{m}, \) where \( \boldsymbol{m} \) is the
linear mass density and \( A \) is the force, the dimensions of \( B \) will be :
A. Same as that of pressure
B. Same as that of work
c. Same as that of momentum
D. Same as that of latent heat
Subject: Chemistry
The IUPAC name of \( \boldsymbol{H}_{3} \boldsymbol{C}-\underset{\boldsymbol{O} \boldsymbol{C}_{3} \boldsymbol{H}_{7}}{\boldsymbol{H}}- \)
\( \boldsymbol{C}_{3} \boldsymbol{H}_{7} \) is:
Subject: Maths
Find \( x, \) if \( \triangle A B C \) is right-angled at \( A \)
where \( \boldsymbol{A} \equiv(\mathbf{4}, \mathbf{2}, \mathbf{3}), \boldsymbol{B} \equiv(\mathbf{3}, \mathbf{1}, \mathbf{8}), \boldsymbol{C} \equiv \)
\( (x,-1,2) \)
Subject: Physics
A nurse applies a force of \( 3.8 N \) to the
syringe's piston of radius \( 0.9 \mathrm{cm} \). Find the increase in pressure of the fluid in the syringe?
A . \( 14.927 k P a \)
в. 469.13 Ра
\( \mathbf{c} .46 .9 \mathrm{mPa} \)
D. 422 Pa
Subject: Physics
In an experiment of verification of
Ohm's law, following observations are obtained:
Potential difference
1.
\[
v \operatorname{cin}
\]
0.5
volt'
Current in
\( 0.4 \quad 0.6 \)
per
What will be the potential difference \( \mathbf{V} \) when the current I is 0.5 A ?
A. \( 1.25 V \)
в. \( 0.5 V \)
c. \( 2 V \)
D. \( 1 V \)
Subject: Maths
\( A B C \) is an isosceles triangle in which
the altitudes \( B E \) and \( C F \) are drawn to
the equal sides \( A C \) and \( A B \)
respectively. Then
\( \mathbf{A} \cdot B E=C F \)
B. \( B E=A B \)
c. \( A B=B C \)
D. \( A C=B C \)
Subject: Physics
One end of massless rope, which passes over a massless and frictionless pulley
\( P \) is tied to a hook \( C \) while the other end
is free. Maximum tension that the rope
can bear is \( 360 N . \) With what value of
maximum safe acceleration \( \left(\text { in } m s^{-2}\right) \)
can a man of \( 60 \mathrm{kg} \) climb on the rope?
\( A \cdot 16 \)
B. 6
\( c \cdot 4 \)
D. None of these
Subject: Maths
Assertion
If \( \boldsymbol{f}, \boldsymbol{g} \) and \( \boldsymbol{h} \) be continuous function on
\( [0, a] \) such that \( f(x)=f(a-x) \)
\( g(x)=-g(a-x) \) and \( 3 h(x)-4 h(a- \)
\( \boldsymbol{x})=\mathbf{5}, \) then \( \int_{0}^{\boldsymbol{a}} \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{g}(\boldsymbol{x}) \boldsymbol{h}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}=\mathbf{0} \)
Reason \( \int_{0}^{a} f(x) g(x) d x=0 \)
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 water tank of height \( 10 m, \) completely filled with water is placed on a level
ground. It has two holes one at \( 3 m \) and
the other at \( 7 m \) from its base. The water
ejecting from:
A. both the holes will fall at the same spot
B. upper hole will fall farther than that from the lower hole
c. upper hole will fall closer than that from the lower hole
D. more information is required
Subject: Physics
A liquid of refractive index \( n \) is filled in a tank.A plane mirror is kept at the bottom of tank. A point like object P is kept at hieght h from the mirror.An observer observes \( \mathrm{P} \) and image
obtained of \( P \) from the top vertically upward direction.What will be the
distance observed by the observer.
\( A \cdot 2 n h \)
B. 2h/n
c. 2h/-n-
D \( \cdot\left(1+\frac{1}{n}\right) \)
Subject: Maths
If \( 4 \cos ^{-1} x+\sin ^{-1} x=\pi, \) then the
value of \( x \) is.
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{\sqrt{3}}{2} \)
D. \( \frac{2}{\sqrt{3}} \)
Subject: Chemistry
For a solution of chloroform and
acetone, if \( \boldsymbol{p}_{\boldsymbol{x}}(\boldsymbol{a} \boldsymbol{c t u a l}) \) is compared
with \( p_{s}(\text { Raoult }), \) then which of the following is/are true? This question has multiple correct options
A \( \cdot p_{s}(a c t u a l)<p_{s}(\text { Raoult }) \)
B. \( \quad \begin{array}{c}L t \\ X_{\text {chootsm}} \rightarrow 0\end{array}\left(p_{\text {actone}}^{o}-p_{s}(\text {actual})\right)=0 \)
C. \( \operatorname{Lt}_{X_{\text {attoce }} \rightarrow 0}\left(p_{\text {chloroform }}^{o}-p_{s}(\text { actual })\right)=0 \)
D. \( p_{\text {actone}}^{o}>p_{\text {chloroform}}^{o} \) near room temperature
Subject: Maths
The co-ordinates of the vertices \( P, Q, R \)
\( \& S \) of square \( P Q R S \) inscribed in the \( \triangle A B C \) with vertices \( A \equiv(0,0), B \equiv \)
(3,0)\( \& C \equiv(2,1) \) given that two of its vertices \( P, Q \) are on the side \( A B \) are
respectively
\( ^{\mathbf{A}} \cdot\left(\frac{1}{4}, 0\right),\left(\frac{3}{8}, 0\right),\left(\frac{3}{8}, \frac{1}{8}\right) \&\left(\frac{1}{4}, \frac{1}{8}\right) \)
в. \( \left(\frac{1}{2}, 0\right),\left(\frac{3}{4}, 0\right),\left(\frac{3}{4}, \frac{1}{4}\right) \&\left(\frac{1}{2}, \frac{1}{4}\right) \)
c. \( (1,0),\left(\frac{3}{2}, 0\right),\left(\frac{3}{2}, \frac{1}{2}\right) \&\left(1, \frac{1}{2}\right) \)
D. \( \left(\frac{3}{2}, 0\right),\left(\frac{9}{4}, 0\right),\left(\frac{9}{4}, \frac{3}{4}\right) \&\left(\frac{3}{2}, \frac{3}{4}\right) \)
Subject: Maths
There are 30 tickets numbered from 1 to
30 in a box. A ticket is drawn at random
from the box and if \( A \) is the event that
the number on the ticket is a multiple
of five, write the sample space \( \boldsymbol{S}, \boldsymbol{n}(\boldsymbol{S}) \) the event \( \boldsymbol{A} \) and \( \boldsymbol{n}(\boldsymbol{A}) \)
Subject: Chemistry
What is \( \Delta G^{o} \) for the following reaction?
\( \frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2}(g) \rightleftharpoons N H_{3}(g) ; K_{p}= \)
\( 4.42 \times 10^{4} \) at \( 25^{\circ} C \)
\( \begin{array}{lll}\text { A } .-26.5 k J & \text { mol }^{-1}\end{array} \)
B. \( -11.5 k J \) mol \( ^{-1} \)
\( \begin{array}{ll}\text { c. }-2.2 k J & \text { mol }^{-1}\end{array} \)
\( \begin{array}{lll}\text { D. }-0.97 k J & \text { mol }^{-1}\end{array} \)
Subject: Physics
The acceleration of aparticle is \( a= \) \( \mathbf{3} \boldsymbol{t}^{2} \hat{\boldsymbol{i}}+\mathbf{5} \boldsymbol{t} \hat{\boldsymbol{j}}-\left(\boldsymbol{8} \boldsymbol{t}^{3}+\mathbf{4 0 0}\right) \hat{\boldsymbol{k}} \boldsymbol{m} \boldsymbol{s}^{-2} . \) The
change in velocity form \( t=0 \) to \( 10 s \) is
\( \boldsymbol{n}_{1} \hat{\boldsymbol{i}}+\boldsymbol{n}_{2} \hat{\boldsymbol{j}}-\boldsymbol{n}_{3} \hat{\boldsymbol{k}} \)
A \( \cdot n_{1}=1000 \mathrm{ms}^{-1} \)
в. \( n_{2}=250 \mathrm{ms}^{-1} \)
c. \( n_{3}=2400 \mathrm{ms}^{-1} \)
D. All of these
Subject: Physics
A cyclist leans with the horizontal at an
angle of \( 30^{\circ}, \) while negotiating round a circular road of radius \( 20 \sqrt{3} \) meters.
Speed of the cycle should be:
A. \( 7 \sqrt{3} \mathrm{m} / \mathrm{s} \)
в. \( 14 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 7 \sqrt{6} m / s \)
D. \( 14 \sqrt{3} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Consider the reaction \( C_{2} H_{5} O^{\ominus}+ \)
Dimethyl sulphate
\( (M e-O-\underbrace{S}_{V}^{O}-O-M e) \rightarrow \)
The leaving group is:
A. \( M e O S O_{2} O^{\circ} \)
в. \( M e O^{\circ} \)
\( \mathrm{c} \cdot \mathrm{Me}^{\circ} \)
D. \( \operatorname{Me} \mathrm{O} \mathrm{SO}_{2}^{\text {o }} \)
Subject: Chemistry
The final step for the extraction of
copper pyrites in Bessemer converter involves the reaction
A \( \cdot C u_{2} S+2 F e O \rightarrow 2 C u+2 F e+S O_{2} \)
в. \( C u_{2} S+2 C u_{2} O \rightarrow 6 C u+S O_{2} \)
c. \( 4 C u_{2} O+F e S \rightarrow 8 C u+2 F e S O_{4} \)
D. \( 2 C u_{2} O+F e S \rightarrow 4 C u+F e+S O_{2} \)
Subject: Chemistry
What is true regarding the following
acid catalyzed esterification (Fischer)
reaction ?
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H}+\boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O H} \stackrel{\boldsymbol{H}^{+}}{\longrightarrow} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5} \)
This question has multiple correct options
A. The reaction involves production on \( s p^{3} \) -oxygen of acid in the first step
B. The reaction involves protonation on \( s p^{2} \) -oxygen of acid followed by formation of acylium ion \( \left(R O C^{+}\right) \) in the first step
C. The slowest step of reaction is the nucleophilic attack of alcohol on \( s p^{2} \) carbon of acid
D. Alcohol undergoes protonation in the first step
Subject: Maths
If \( A \) and \( B \) are two events such that
\( P(A)=\frac{3}{4} \) and \( P(B)=\frac{5}{8}, \) then
\( ^{\mathrm{A}} \cdot P(A \cup B) \geq \frac{3}{4} \)
в. \( P\left(A^{\prime} \cap B\right) \leq \frac{1}{4} \)
c. \( \frac{3}{8} \leq P(A \cap B) \leq \frac{5}{8} \)
D. All of the above
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{C} \boldsymbol{H}_{3}}{\boldsymbol{C} \boldsymbol{H}}-\stackrel{\boldsymbol{P} \boldsymbol{h}}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{N} \boldsymbol{H}_{2} \)
The IUPAC name of the compound is :
A. 1-Amino-1-phenyl-2-methyl propane
B. 2-Methyl-1-phenyl propan-1-amine
c. 2-Methyl-1-amino-1-phenyl propane
D. 1-lsopropyl-1-phenyl methyl amine
Subject: Physics
Which of the following statement is true regarding Bohr's Model of hydrogen atom?
I. Orbiting speed of an electron
decreases as it falls to discrete orbits
away from the nucleus
II. Radii of allowed orbits of electrons
are proportional to the principal quantum number III. Frequency with which electrons orbit around the nucleus in discrete
orbits is inversely proportional to the cube of principal quantum number
\( I V . \) Binding force with which the electron is bound to nucleus increases
as it shifts to outer orbits.
Select the correct answer using the
codes given below:
A. \( I \) and \( I I I \)
B. II and \( I V \)
c. \( I, I I \) and \( I I I \)
\( D \)
and \( I V \)
Subject: Maths
\( \sum_{p=1}^{32}(3 p+2)\left[\sum_{q=1}^{10}\left(\sin \frac{2 q \pi}{11}-i \cos \frac{2 q \pi}{11}\right)\right. \)
A \( \cdot 8(1-i) \)
B \( \cdot 16(1-i) \)
\( \mathbf{c} \cdot 48(1-i) \)
D. None of these
Subject: Physics
\( \ln \) YDSE, \( d=2 m m, D=2 m \) and \( \lambda= \)
\( 500 n m . \) If intensities of two slits are \( I_{0} \)
and \( 9 I_{0}, \) then find intensity at \( y= \)
\( \frac{1}{6} m m \)
A \( \cdot 7 I_{0} \)
в. \( 10 I_{0} \)
\( c \cdot 16 I_{0} \)
D. \( 4 I_{0} \)
Subject: Chemistry
Cis-dicholoroethylene can be converted to trans-dicholorethylene by irradiations. During the interconversion.
A. Both the \( \pi \) and \( \sigma \) bonds are broken and reformed
B. Only the \( \pi \) bond is broken and reformed
c. The \( C-C l \) and \( C-H \) bonds are broken, \( H \) and \( C l \)
atoms interchanges their positions and new bonds are formed
D. Both the \( \pi \) and \( \sigma \) bonds rotate along with the groups
Subject: Maths
The total surface area of a solid cylinder
is \( 462 \mathrm{cm}^{2} \). Its curved surface area is
one third of total surface area. Find the
volume of the cylinder.
A \( \cdot 229 ~ c m^{3} \)
В. \( 509 \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 439 \mathrm{cm}^{3} \)
D. \( 539 ~ c m^{3} \)
Subject: Physics
toppr loGın
Q Type your question
Here, \( \mu \) and \( \Delta \mu \) denote the \( R I \) of 0 th
layer and the difference in \( R I \) between
any two consecutive layers,
respectively. The integer \( m= \)
\( 0,1,2,3, \dots \) denotes the numbers of the
successive layers.

A ray of light from the Oth layer enters
the 1 st layer at an angle of incidence of
\( 30^{0} . \) After undergoing the \( m \) th
refraction, the ray emerges parallel to
the interface. If \( \mu=1.5 \) and \( \Delta \mu= \)
\( 0.015, \) the value of \( m \) is:
\( A \cdot 20 \)
B. 30
\( c \cdot 40 \)
D. 50
Subject: Chemistry
\( 1.22 \mathrm{g} \) of a monobasic acid is dissolved in 100 g of benzene. The boiling point of the solution increases by \( 0.13^{\circ} \mathrm{C} \) with respect to pure benzene. Find the
molecular mass of aid in benzene
solvent (in \( u \) ). Report your answer after dividing it by 100 and Round it off to the
nearest integer. \( \left(K_{b} \text { of benzene }=2.6 \mathrm{K}\right. \)
\( \mathrm{kg} \mathrm{mol}^{-1} \) ).
Subject: Physics
A liquid with coefficient of volume
expansion \( \gamma \) is filled in a container of a
material having coefficient of linear
expansion \( \alpha \). If the liquid overflows on
heating, then:
A \( \cdot \gamma=3 \alpha \)
в. \( \gamma>3 \alpha \)
c. \( \gamma<3 \alpha \)
D . \( \gamma=a^{3} \)
Subject: Maths
A invested Rs 5000 in a business. After
4 months B joined him by investing Rs \( 4800 . \) After a further of 2 months, \( C \)
joined them with Rs \( 5200 . \) If after the end of year, they earned a total profit if Rs \( 14,400, \) then what is the difference
between the shares of \( A \) and \( B ? \)
Subject: Physics
A sphere of density \( d \), specific heat
capacity \( c \) and radius \( r \) is hung by a
thermally insulating thread in an enclosure which is kept at lower
temperature than the sphere. The temperature of the sphere starts to drop at a rate which is proportional to:
A \( \cdot c / r^{3} d \)
B . \( 1 / r^{3} d c \)
\( \mathbf{c} \cdot 3 r^{3} d c \)
D. \( 1 / r d c \)
Subject: Physics
Three concentric conducting spherical
shells of radii \( \boldsymbol{R}, 2 \boldsymbol{R} \) and \( \boldsymbol{3} \boldsymbol{R} \) carry
charges \( Q,-2 Q \) and \( 3 Q, \) respectively
Compute the potential at \( r=R \), and
the charges on the spheres of radii \( \boldsymbol{R} \)
and \( 3 R \)
A \( \cdot \frac{Q+2 Q_{1}}{12 \pi \varepsilon_{0} R}, Q_{1}=\frac{Q}{4}, Q_{2}=\frac{7 Q}{2} \)
в. \( \frac{Q+2 Q_{1}}{12 \pi \varepsilon_{0} R}, Q_{1}=\frac{Q}{2}, Q_{2}=\frac{7 Q}{2} \)
c. \( \frac{Q+2 Q_{1}}{12 \pi \varepsilon_{0} R}, Q_{1}=\frac{Q}{2}, Q_{2}=\frac{7 Q}{4} \)
D. \( \frac{Q+2 Q_{1}}{12 \pi \varepsilon_{0} R}, Q_{1}=\frac{Q}{4}, Q_{2}=\frac{7 Q}{4} \)
Subject: Maths
A line passes through the points (6,-7,-1) and \( (2,-3,1) . \) The direction cosines of the line so directed that the
angle made by it with the positive direction of x-axis is acute, is?
A \( \cdot \frac{2}{3},-\frac{2}{3},-\frac{1}{3} \)
B. \( -\frac{2}{3}, \frac{2}{3}, \frac{1}{3} \)
c. \( \frac{2}{3},-\frac{2}{3}, \frac{1}{3} \)
D. \( \frac{2}{3}, \frac{2}{3}, \frac{1}{3} \)
Subject: Maths
Let the equation of the plane which contains the line \( \boldsymbol{x}=\frac{\boldsymbol{y}-\boldsymbol{3}}{\boldsymbol{2}}=\frac{\boldsymbol{z}-\boldsymbol{5}}{\boldsymbol{3}} \)
and which is perpendicular to the plane \( 2 x+7 y-3 z=1 . \) be \( k x-m y-z+ \)
\( \boldsymbol{p}=\mathbf{0} . \) Find \( \boldsymbol{p}-\boldsymbol{k}-\boldsymbol{m} ? \)