AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Match list 1 and list 2 .
List - List
A) \( C O+H_{2} \)
1. Producer
gas
B) \( C O+N_{2} \)
2. Semi
water gas
C) \( \boldsymbol{C O}+\boldsymbol{H}_{2}+\boldsymbol{N}_{2} \)
3. Water gas
D) \( \boldsymbol{H}_{2}+\boldsymbol{C} \boldsymbol{H}_{4}+\boldsymbol{C O} \)
4. Coal gas
\( A \cdot 1342 \)
B. 2 4 13
\( c .3124 \)
D. 1432
Subject: Physics
In Young's double-slit experiment the
spacing between the slits is 'd and wavelength of light used is 6000 A. If the angular width of a fringe formed on a
distant screen is \( 1^{0}, \) then value \( ^{\prime} d^{\prime} \) is :
A . \( 1 m m \)
B. \( 0.05 \mathrm{mm} \)
c. \( 0.03 m m \)
D. \( 0.01 m m \)
Subject: Maths
A particle moves along a straight line and its velocity at a distance 'x' from the origin is \( k \sqrt{a^{2}-x^{2}} . \) Then acceleration of the particle is
\( A \cdot k \)
B. \( -k^{2} \)
c. \( k x \)
\( \mathbf{D} \cdot-k^{2} x \)
Subject: Physics
Assertion
Horse has to pull a cart harder during the first few steps of his motion.
Reason
The first few steps are always difficult.
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
The correct order of stability of the halous acids in aqueous solution is:
A. \( \mathrm{HClO}<\mathrm{HBrO}<\mathrm{HlO} \)
B. \( \mathrm{HClO}>\mathrm{HBrO}<\mathrm{HlO} \)
c. \( \mathrm{HClO}>\mathrm{HBrO}> \) HlO
D. HClO < HBrO > HlO
Subject: Maths
Choose the correct answer from the
alternatives given. If \( x-\frac{1}{x}=3 \) then find the value of \( x^{3}+\frac{1}{x^{3}} \)
A. \( 10 \sqrt{13} \)
(3) 5
B. \( 100 \sqrt{3} \)
c. \( 13 \sqrt{10} \)
D. \( 130 \sqrt{10} \)
Subject: Maths
The differential equation whose general
solution is \( \boldsymbol{y}=\boldsymbol{A} \cos (\boldsymbol{x}+\boldsymbol{3}), \) where \( \boldsymbol{A} \)
is arbitrary constant is
\( \mathbf{A} \cdot \cot (x+3) y_{1}+y=0 \)
B \cdot \( \tan (x+3) y_{1}+y=0 \)
\( \mathbf{c} \cdot \cot (x+3) y_{1}-y=0 \)
D \cdot \( \tan (x+3) y_{1}-y=0 \)
Subject: Physics
An electron having energy \( 10 e V \) is circulating in a path of radius \( 0.1 m \)
having a magnetic field of \( 10^{-4} \) T. The
speed of the electron will be :
A \( .2 .0 \times\left(10^{6}\right) m s^{-1} \)
B . \( 4.8 \times\left(10^{6}\right) m s^{-1} \)
c. \( 2.0 \times\left(10^{12}\right) m s^{-1} \)
D. \( 4.8 \times\left(10^{12}\right) m s^{-1} \)
Subject: Physics
An analyser is inclined to a polarizer at
an angle of \( 30^{\circ} . \) the intensity of light emerging from the analyser is \( \frac{1}{n} \) of that is incident on the polarizer. Then \( n \) is equal to
A .4
B. \( \frac{4}{3} \)
\( c \cdot \frac{8}{3} \)
D. \( \frac{1}{4} \)
Subject: Physics
For a CB amplifier current gain is \( 0.54 . \) I the emitter current is \( 6.8 m A \), the
collector current will be
A . \( 1.7 \mathrm{mA} \)
в. \( 2.7 \mathrm{mA} \)
\( c .3 .7 m A \)
D. \( 4.7 \mathrm{mA} \)
Subject: Chemistry
An electron in the hydrogen atom is excited from \( 1^{s t} \) orbit to \( 5^{t h} \) orbit. The
frequency of radiation is:
A \( \cdot 0.44 \times 10^{-9} \mathrm{Hz} \)
В. \( 3.15 \times 10^{15} \mathrm{Hz} \)
c. \( 6.2 \times 10^{8} \mathrm{Hz} \)
D. \( 1.13 \times 10^{-12} \mathrm{Hz} \)
Subject: Chemistry
Fill in the blanks:
\( N a C l \) an electrovalent compounds is formed as a result of tranfer of
[one,two, three] valence electrons from metallic sodium to non-metallic
chlorine atom. \( C a O \) is similarly formed
as a result of transfer of [one,
two, three] valence electrons from
metallic calcium to non-metallic
oxygen and magnesium chloride by transfer of \( _{----} \) [one, two, three] valence electrons from \( _{---} \) [one, two] magnesium atom/s to [one, two]
chlorine atom/s.
Subject: Maths
The set of points where \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{\mathbf{1}+|\boldsymbol{x}|} \)
is differentiable, is
\( \mathbf{A} \cdot(-\infty, 0) \cup(0, \infty) \)
B \( \cdot(-\infty,-1) \cup(-1, \infty) \)
\( c \cdot(-\infty, \infty) \)
D・ \( (0, \infty) \)
Subject: Maths
Three groups \( A, B, C \) are contesting for positions on the Board of Directors of a company. The probabilities of their
winning are 0.5,0.3,0.2 respectively. If
the group \( A \) wins, the probability of
introducing a new product is 0.7 and the corresponding probabilities for groups \( B \) and \( C \) are 0.6 and 0.5
respectively. The probability that the new product will be introduced is given
by
A . 0.36
в. 0.35
c. 0.63
D. 0.53
Subject: Biology
Assertion
CuT, Cu7 and multiload 375 are the
hormone releasing IUDs.
Reason
Cu ions released by some UDS affect the ability of uterine wall to support embryo thus cause contraception.
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
Rate of formation of \( S O_{3} \) in the
following reaction \( 2 S O_{2}+O_{2} \longrightarrow \)
\( 2 S O_{3} \) is \( 100 g \quad \) min \( ^{-1} . \) Hence
disappearance of \( \boldsymbol{O}_{2} \) is:
\( \begin{array}{ll}\text { A. } 50 g & \min ^{-1}\end{array} \)
B. \( 40 g \) min\( ^{-1} \)
c. \( 200 g \) min\( ^{-1} \)
D. \( 20 g \) min\( ^{-1} \)
Subject: Chemistry
What are the products formed when ammonia reacts with excess chlorine?
A. \( \mathrm{N}_{2} \) and \( \mathrm{NCl}_{3} \)
B. NCls and HCl
c. \( \mathrm{N}_{2} \) and \( \mathrm{NH}_{4} \mathrm{Cl} \)
D. \( \mathrm{N}_{2} \) and \( \mathrm{HCl} \)
Subject: Chemistry
How many functional group are present in above compound?
\( \boldsymbol{C H}_{3}-\boldsymbol{O}-\underset{d}{_{\|}}-\underset{\boldsymbol{o}_{H}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}=\boldsymbol{C} \boldsymbol{H}- \)
\( C-\stackrel{N}{C}-O H \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Chemistry
Which of the following is a redox reaction?
A \( \cdot C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( H_{2}+C l_{2} \rightarrow 2 H C l \)
\( \mathrm{c} \cdot \mathrm{CaO}+2 \mathrm{HCl} \rightarrow \mathrm{CaCl}_{2}+\mathrm{H}_{2} \mathrm{O} \)
D. \( N a O H+H C l \rightarrow N a C l+H_{2} O \)
Subject: Physics
In the following circuit, the potential of
source is \( \boldsymbol{E}_{\mathbf{0}}=\mathbf{2 0 0} \) volts, \( \boldsymbol{R}=\mathbf{2 0 0 \Omega} \)
\( \boldsymbol{L}=\mathbf{0 . 1} \) henry, \( \boldsymbol{C}=\mathbf{1 0 . 6} \) farad and
frequency is variable, then the current
at \( f=0 \) and \( f=\infty \) is :
A. \( 0 A, 10 A \)
B. 10A, OA
C. \( 10 A, \) 10A
D. OA, OA
Subject: Physics
Ine velocıty or poınt \( \mathrm{K} \) or tne roa just
after impact with the bumper is (in
\( m / s) \)
A \( .1 .2 \sqrt{5} \)
B . 1.2
c. \( 1.2 \sqrt{5(2-\sqrt{3})} \)
D. \( 1.2 \sqrt{5(2+\sqrt{3})} \)
Subject: Maths
Represent set \( A, B, C \) such that \( A \subset \) \( \boldsymbol{B}, \boldsymbol{A} \cap \boldsymbol{C}=\boldsymbol{\phi} \) and \( \boldsymbol{B} \cap \boldsymbol{C} \neq \boldsymbol{\phi} \) by Venn
diagram. The number of separate
regions representing \( \boldsymbol{A} \cup(\boldsymbol{B} \cap \boldsymbol{C}) \)
is/are:
Subject: Physics
A transmitter transmits at a
wavelength of \( 300 m . \) A condenser of
capacitance \( 2.4 \mu F \) is being used. The
value of the inductance for the resonant
circuit is approximately
\( \mathbf{A} \cdot 10^{-4} H \)
в. \( 10^{-6} H \)
c. \( 10^{-8} H \)
D. \( 10^{-10} \mathrm{H} \)
Subject: Biology
Identify the correct pair of statements.
(1) Lutein is an oxygenated hydrocarbon.
(II) Inhibition of bacteroid respiration by oxygen is referred to as 'Warburg effect'.
(III) Triplet code 'UAA' is called 'Amber'.
(IV) Delay of senescence by cytokinins is known as 'Richmond-Lang effect'.
A \( .(\text { II }), \) (III)
B. (I), (IV)
c. \( (1),(\text { III }) \)
D. (II), (IV)
Subject: Chemistry
A solution contains \( 0.1 M C l^{-} \) and
\( \mathbf{0 . 0 0 1} \boldsymbol{M} \boldsymbol{C r} \boldsymbol{O}_{4}^{2-} . \) If solid \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} \) is
gradually added to this solution, which
will precipitate first, \( A g C l \) or \( A g_{2} C r O_{4} \)
? Assume that the addition causes no
change in volume. Given \( \boldsymbol{K}_{s p} \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}=\mathbf{1 . 7} \times \mathbf{1 0}^{-\mathbf{1 0}} \boldsymbol{M}^{\mathbf{2}} \)
\( \boldsymbol{K}_{s p} \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}=\mathbf{1 . 7 9} \times \mathbf{1 0}^{-\mathbf{1 2}} \boldsymbol{M}^{\mathbf{3}} \)
What percent of \( C l^{-} \) remains in the
solution when \( C r O_{4}^{2-} \) starts precipitating?
Subject: Chemistry
Given below are the half-cell reactions:
\( M n^{2+}+2 e^{-} \rightarrow M n ; E^{0}=-1.18 V \)
\( \mathbf{2}\left(\boldsymbol{M} \boldsymbol{n}^{3+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{M} \boldsymbol{n}^{2+}\right) ; \boldsymbol{E}^{0}= \)
\( +1.51 V \)
The \( \boldsymbol{E}^{0} \) for \( \boldsymbol{3} \boldsymbol{M} \boldsymbol{n}^{2+} \rightarrow \boldsymbol{M} \boldsymbol{n}+\boldsymbol{2} \boldsymbol{M} \boldsymbol{n}^{3+} \)
will be:
A. \( -0.33 V \); the reaction will not occur
B. \( -0.33 V ; \) the reaction will occur
c. \( -2.69 V \); the reaction will not occur
D. \( -2.69 V \); the reaction will occur
Subject: Maths
Referring the figure given below, for \( \Delta P Q R \) and \( \Delta X Y Z, P Q=Y Z, Q R= \)
\( \boldsymbol{X} \boldsymbol{Z} \) and \( \angle \boldsymbol{Q}=\angle \boldsymbol{Z} . \) The value of \( \angle \boldsymbol{P} \) is
A \( \cdot 42^{\circ} \)
B . \( 75^{\circ} \)
\( c \cdot 63^{\circ} \)
D. cannot be determine
Subject: Maths
Which one of the following relations on
\( R \) is equivalence redlation
A \( \cdot x R_{1} y \Leftrightarrow|x|=|y| \)
B . \( x R_{2} y \Leftrightarrow|x|>|y| \)
c. \( x R_{3} y \Leftrightarrow x \mid y \)
D. \( x R_{4} y \Leftrightarrow x<y \)
Subject: Maths
Find the range of \( \boldsymbol{f}(\boldsymbol{x})= \) \( \frac{\sin \left(\pi\left[x^{2}+1\right]\right)}{x^{4}+1} \) where [.] is greatest
integer function
A . [0,1]
в. [-1,1]
c. 0
D. None of these
Subject: Physics
Function \( \boldsymbol{x}=\boldsymbol{A} \sin ^{2} \boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{B} \cos ^{2} \boldsymbol{\omega} \boldsymbol{t}+ \)
\( C \sin \omega t \cos \omega t \) represents SHM
A. For any value of \( A, B \) and \( C \) (except \( C=0 \) )
B. \( A=-B, C=2 B, \) amplitude \( =\mid B \sqrt{2} \)
c. \( A=B ; C=0 \)
D. \( A=B ; C=2 B, \) amplitude \( =|B| \)
Subject: Chemistry
Assertion
Most probable velocity is the velocity possessed maximum fraction of
molecules at the same temperature.
Reason

On collision, more and more molecules
acquire has speed at the same temperature
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 transformations:
(I) \( \quad X e F_{6}+N a F \rightarrow N a^{+}\left[X e F_{7}\right]^{-} \)
(II) \( 2 P C l_{5}(s) \rightarrow\left[P C l_{4}\right]^{+}\left[P C l_{6}\right]^{-} \)
(III) \( \left[A l\left(H_{2} O\right)_{6}\right]^{3+}+H_{2} O \rightarrow \)
\( \left[A l\left(H_{2} O\right)_{5} O H\right]^{2+}+H_{3} O^{+} \)
Correct transformations are :
A . ।,
в. ।,॥
\( c \cdot \) ।,
D. ॥,॥
Subject: Chemistry
An organic compound contains \( 69 \% \) carbon and \( 4.8 \% \) hydrogen, the remainder being oxygen. Calculate the sum of masses (in \( g \) m) of carbon dioxide and water produced when 0.20 \( \mathrm{gm} \) of this compound is subjected to complete combustion. Report your
answer as \( 10 x, \) if \( x \) is the sum of masses
in the nearest integer.
Subject: Physics
The magnetic field due to a current carrying circular loop of radius \( 3 \mathrm{cm} \) at a point on the axis at a distance of \( 4 \mathrm{cm} \)
from the centre is \( 54 \mu \) T. What will be
its value at the centre of the loop?
A. 125 и \( T \)
в. \( 150 \mu T \)
c. \( 250 \mu T \)
D. \( 75 \mu T \)
Subject: Maths
The S.D. of the following frequency distribution is
\( \begin{array}{lllll}\text { Class } & 0- & 10 & 20- & 30- \\ & 10 & 20 & 30 & 40\end{array} \)
\( f_{i} \)
A . 7.8
B. 9
c. 8.1
D. 0.9
Subject: Chemistry
A current of 3 A has to be passed through a solution of silver nitrate for
\( t^{\prime} \) sec to coat a metal surface of \( 80 \mathrm{cm}^{2} \)
with a 0.005 -mm-thick layer, then \( t \) is:
(density of silver is 10.5 g \( c m^{-3} \) ) (write
your answer to nearest integer)
Subject: Chemistry
Assertion
On cooling, the brown colour of \( N O_{2} \) disappears.
Reason
On cooling \( N O_{2} \) forms dimer \( \left(N_{2} O_{4}\right) \) resulting in the pairing of the odd
electrons in \( N O_{2} \)
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. Assertion is incorrect but Reason is correct
Subject: Physics
A vessel containing \( 50 k g \) of water of height \( 15 m \) is placed above the ground. Assuming the gravitational potential energy at ground to be zero. What will be the gravitational potential energy of water in the vessel ? \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-\mathbf{2}}\right) \)
A . \( 0 . J \)
в. \( 750 J \)
c. \( 3750 J \)
D. \( 7500 J \)
Subject: Physics
Find the distance \( x_{0} \) to the point on the
axis at which the value of \( B \) differs by
\( \eta=1 \% \) from that in the middle section
of the solenoid.
A \( . x_{0} \approx R \)
в. \( x_{0} \approx 7 R \)
\( \mathbf{c} \cdot x_{0} \approx 5 R \)
D. \( x_{0} \approx 3 R \)
Subject: Physics
The kinetic energy of the body after the
collision is
A \( \cdot \frac{11 m v^{2}}{54} \)
B. \( \frac{m v^{2}}{108} \)
c. \( \frac{17 m v^{2}}{54} \)
D. \( \frac{17 m v^{2}}{108} \)
Subject: Chemistry
\( \beta \) Sulphur is stable between:
A \( \cdot 114^{\circ} \mathrm{C} \) to \( 160^{\circ} \mathrm{C} \)
B. 95.6 ^ \( C \) to \( 119^{\circ} C \)
c. \( 160^{\circ} \mathrm{C} \) to \( 230^{\circ} \mathrm{C} \)
D. 112.8 ' \( C \) to \( 140^{\circ} \mathrm{C} \)
Subject: Chemistry
At what temperature do zinc and carbon
have equal affinity for oxygen?
A \( \cdot 1000^{\circ} \mathrm{C} \)
в. \( 1500^{\circ} \mathrm{C} \)
\( c \cdot 500^{\circ} C \)
D. \( 1200^{\circ} \mathrm{C} \)
Subject: Physics
What is the De-Broglie wavelength associated with the hydrogen electron in its third orbit :
A \( .9 .96 \times 10^{-10} \mathrm{cm} \)
В. \( 9.96 \times 10^{-8} \mathrm{cm} \)
\( \mathrm{c} \cdot 9.96 \times 10^{4} \mathrm{cm} \)
D. \( 9.96 \times 10^{8} \mathrm{cm} \)
Subject: Physics
A small ball of mass \( m \) starts at a point
\( A \) with speed \( v_{0} \) and moves along a
frictionless track \( A B \) as shown. The
track \( B C \) has the coefficient of friction
\( \mu . \) The ball comes to stop at \( C \) after
travelling a distance \( L \) which is
\( ^{\mathrm{A}} \cdot \frac{h}{2 \mu}+\frac{v_{0}^{2}}{2 \mu g} \)
в. \( \frac{h}{\mu}+\frac{v_{0}^{2}}{2 \mu g} \)
c. \( \frac{2 h}{\prime \prime}+\frac{v_{0}^{2}}{2 \mu g} \)
Subject: Chemistry
The electronic configuration of
actinides is:
A \( \cdot[\operatorname{Rn}] 5 f^{0-14} 6 d^{0-2} 7 s^{1} \)
B . \( [R n] 5 f^{0-14} 6 d^{0} 7 s^{0} \)
C \( \cdot[R n] 5 f^{0-14} 6 d^{0-2} 7 s^{2} \)
D \cdot \( [R n] 5 f^{0-14} 6 d^{0-2} 7 s^{0} \)
Subject: Physics
A wire of length \( L \) has a linear mass
density \( \mu \) and area of cross-section \( \boldsymbol{A} \) and Young's modulus \( Y \) is suspended vertically from a rigid support. The extension produced in the wire due to its own weight is:
\( ^{\text {A } \cdot \frac{\mu g L^{2}}{Y A}} \)
в. \( \frac{\mu g L^{2}}{2 Y A} \)
c. \( \frac{2 \mu g L^{2}}{Y A} \)
D \( \cdot \frac{2 \mu g L^{2}}{3 Y A} \)
Subject: Chemistry
Ammonium hydrogen sulphide dissociates as follows
\( N H_{4} H S(s) \rightleftharpoons N H_{3}(g)+H_{2} S(g) \)
If solid \( N H_{4} H S \) is placed in an evacuated flask at certain temperature it will dissociate until the total pressure
is 600 torr.
a) Calculate the value of equillibrium constant for the dissociation reaction
b) Addional \( N H_{3} \) is introduced into the equillibrium mixture without changing the temperature until partial pressure
of \( N H_{3} \) is 750 torr, what is the partial
pressure of \( \boldsymbol{H}_{2} \boldsymbol{S} \) under these conditions? What is the total pressure in the flask?
Subject: Physics
Find the height of the building which is on moon without using any measuring device ?(you can use stopwatch)
A \( \cdot h=\frac{1}{12} g t^{2} \)
B. \( h=\frac{1}{24} g t^{2} \)
c. \( _{h}=\frac{1}{30} g t^{2} \)
D. \( h=\frac{1}{42} g t^{2} \)
Subject: Chemistry
A mixture of \( C u S O_{4} \) and \( C u S O_{4} .5 H_{2} O \)
has a mass of 1.245 g. After heating, it drives off all the water, the mass is only
0.832 g. What is the mass (in \( m g \) ) of
\( C u S O_{4} .5 H_{2} O \) in the mixture?
Subject: Physics
The potential energy of a particle is given by formula \( U=100-5 x+ \)
\( 100 x^{2}, U \) and \( x \) are in SI units if mass of
the particle is \( 0.1 \mathrm{kg} \) then magnitude of it's acceleration.
A . At \( 0.05 \mathrm{m} \) from the origin is \( 50 \mathrm{m} / \mathrm{s}^{2} \)
B. At \( 0.05 \mathrm{m} \) from the mean position is \( 100 \mathrm{m} / \mathrm{s}^{2} \)
c. At \( 0.05 \mathrm{m} \) from the origin is \( 150 \mathrm{m} / \mathrm{s}^{2} \)
D. At 0.05 m from the mean position is 200 \( \mathrm{m} / \mathrm{s}^{2} \)
Subject: Chemistry
When plaster of paris comes in contact
with water it sets into a hard mass. The
composition of the hard mass is:
A \( \cdot \operatorname{CaSO}_{4} \cdot H_{2} O \)
в. \( \operatorname{CaSO}_{4} \cdot \operatorname{Ca}(O H)_{2} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \)
D. \( \operatorname{CaSO}_{4} .2 \mathrm{Ca}(\mathrm{OH})_{2} \)
Subject: Maths
\( \operatorname{et} z=\left|\begin{array}{ccc}1 & 1+2 i & -5 i \\ 1-2 i & -3 & 5+3 i \\ 5 i & 5-3 i & 7\end{array}\right| \) then
A. z is purely real
B. z is purely imaginary
C \( \cdot(z-\bar{z}) \) i is real and imaginary both
D \( \cdot(z+\bar{z})=0 \)
Subject: Maths
If a line \( L \) is perpendicular to the line
\( 5 x-y=1, \) and the area of the triangle
formed by the line \( L \) and the coordinate
axes is \( 5, \) then the distance of line \( L \)
from the line \( \boldsymbol{x}+\mathbf{5} \boldsymbol{y}=\mathbf{0} \) is
A \( \cdot \frac{7}{\sqrt{5}} \)
в. \( \frac{5}{\sqrt{13}} \)
c. \( \frac{7}{\sqrt{13}} \)
D. \( \frac{5}{\sqrt{7}} \)
Subject: Physics
Which of the following functions of time represent \( (A) \) simple harmonic, \( (B) \) periodic but not simple harmonic, and
\( (C) \) non-periodic motion? Give period for each case of periodic motion \( (\omega \) is any positive constant):
(a) \( \sin \omega t-\cos \omega t \)
\( (b) \sin ^{3} \omega t \)
(c) \( 3 \cos (\pi / 4-2 \omega t) \)
\( (d) \cos \omega t+\cos 3 \omega t+\cos 5 \omega t \)
\( (e) \exp \left(-\omega^{2} t^{2}\right) \)
(f) \( 1+\omega t+\omega^{2} t^{2} \)
Subject: Maths
The line joining the points \( A(3,0) \) and
\( B(5,2) \) is rotated about \( A \) in the
anticlockwise direction through an
angle \( 15^{\circ} \).If \( B \) goes to \( C \) in the new position now the line joining \( A \) and \( C \) is rotated about \( A \) in the anticlockwise
direction through an angle of \( 45^{\circ} \) of \( C \)
goes to \( D \) in the new position,then the
coordinates of \( D \) are
A. \( (4-\sqrt{3}, \sqrt{3}-1) \)
B. \( (4+\sqrt{3}, \sqrt{3}-1) \)
c. \( (4-\sqrt{3}, \sqrt{3}+1) \)
D. \( (4+\sqrt{3}, \sqrt{3}+1) \)
Subject: Physics
Both the strings shown in the figure are
made of same material and have the
same cross-section. The pulleys are
light. The wave speed of a transverse
wave in the string \( A B \) is \( v_{1} \) and in \( C D \) it
is \( \boldsymbol{v}_{2} \) The \( \boldsymbol{v}_{1} / \boldsymbol{v}_{2} \) is
\( A \)
B. 2
\( c \cdot \sqrt{2} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Maths
If \( \tan 22^{\circ}+\tan 38^{\circ}-\sqrt{3}= \)
\( k \tan 22^{\circ} \tan 38^{\circ} \) then find \( k \)
A \( \cdot \sqrt{3} \)
B. \( -\sqrt{3} \)
\( c \cdot \sqrt{7} \)
\( D \cdot 5^{-} \sqrt{5} \)
Subject: Physics
A particle moves from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) diametrically opposite in a circle of
radius \( 5 m \) with a velocity \( 10 m s^{-1} . \) Find
the average acceleration.
A . zero
в. \( \frac{40}{\pi} m s^{-2} \)
c. \( \frac{20}{\pi} m s^{-2} \)
D. none
Subject: Chemistry
The \( p H \) of the solution cantaining
\( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \& \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{H} \boldsymbol{C O O H} \mathbf{~ i s : ~} \)
\( \left[\boldsymbol{K}_{s} \text { of } \boldsymbol{H} \boldsymbol{C O O H} \text { is } \mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{1 4}}\right] \)
A . \( 0 . \)
B.
\( c \cdot 2 \)
D. 0.2
Subject: Maths
Discuss the countinuity of the following
function at \( \boldsymbol{x}=\mathbf{0} \)
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\frac{1-\cos x}{x^{2}}, & x \neq 0 \\ \frac{1}{2}, & x=0\end{array}\right. \)
Subject: Chemistry
If \( \mathrm{SR}=100 \) torr and \( \mathrm{PR}=350 \) torr, then
which of the following cannot be a mole
fraction of \( A \) in vapour phase and a mole
fraction of \( A \) in liquid phase
respectively?
This question has multiple correct options
A \( \cdot \frac{3}{10} \) and \( \frac{2}{9} \)
B. \( \frac{7}{9} \) and \( \frac{3}{10} \)
c. \( \frac{2}{9} \) and \( \frac{7}{10} \)
D. \( \frac{2}{9} \) and \( \frac{3}{10} \)
Subject: Physics
Let us list some of the factors, which could possibly influence the speed of wave propagation:
(i) nature of the source.
(ii) direction of propagation.
(iii) motion of the source and/or
observer.
(iv) wavelength.
(v) intensity of the wave. On which of these factors, if any, does
(a) The speed of light in vacuum
(b) The speed of light in a medium (say, glass or water), depend?
Subject: Physics
A small block of mass of \( 0.1 k g \) lies on a
fixed inclined plane PQ which makes an
angle \( \theta \) with the horizontal. A horizontal
force of \( 1 ~ N \) acts on the block through
its center of mass as shown in the
figure. The block remains stationary if
\( \left(\operatorname{take} g=10 m / s^{2}\right) \)
This question has multiple correct options
\( \mathbf{A} \cdot \theta=45^{\circ} \)
B. \( \theta>45^{\circ} \) and a frictional force acts on the block towards
\( P \)
C \( \cdot \theta>45^{\circ} \) and a frictional force acts on the block towards
Q.
D. \( 45^{\circ} \) and a frictional force acts on the block towards \( Q \).
Subject: Maths
Let \( P(2,-4) \) and \( Q(3,1) \) be two given points. Let \( R(x, y) \) be a point such that \( (x-2)(x-3)+(y-1)(y+4)=0 \)
area of \( \Delta P Q R \) is \( \frac{13}{2}, \) then the number
of possible positions of \( \boldsymbol{R} \) are
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)
Subject: Physics
Which of the following statement best
describe Nuclear fusion reaction?
A. two smaller nuclei are combined into a more massive
nuclei
B. the electrons are exchanged from one or more substances to produce a different substance, and the elements are the same in the products and reactants.
C. the nucleus of a large atom is split into two or more fragments.
D. the particles in the nucleus are changed, and one element is transformed into another element when
particles in the nucleus are gained or lost.
E. radiation is made
Subject: Maths
If \( \boldsymbol{A}+\boldsymbol{B}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) then value of \( (\boldsymbol{1}+ \)
\( \tan A)(1+\tan B)= \)
\( A \cdot 4 \)
B.
\( c \cdot 2 \)
D. none of these
Subject: Chemistry
Which of the following species does not
exert a resonance effect?
A \( \cdot C_{6} H_{5} N H_{2} \)
B. \( C_{6} H_{5} N^{+} H_{3} \)
\( \mathbf{c} \cdot C_{6} H_{5} O H \)
D. \( C_{6} H_{5} C l \)