AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
\( \boldsymbol{n} \) small drops of small size are charged
to \( V \) volt each. If they collapse to form a
single large drop, then its potential will be
\( \mathbf{A} \cdot(V / n) \)
в. \( V n \)
\( \mathbf{c} \cdot V n^{2 / 3} \)
D. None of these
Subject: Maths
75 persons can sleep in a room \( 25 \mathrm{m} \) by
\( 9.6 . \) If each person requires \( 16 m^{3} \) of air; find the height of the room.
\( A \cdot 5 m \)
B. 3 m
\( c \cdot 6 m \)
D. \( 7 \mathrm{m} \)
Subject: Physics
Explorer \( 38, \) a radio-astronomy satellite of mass \( 200 k g \) circles the earth in an orbit of average radius \( \frac{3 R}{2}, \) where \( R \) is the radius of the earth. Assuming the gravitational pull on the mass of \( 1 k g \) at
the earth's surface to be \( 10 N \), calculate
the pull on the satellite.
\( \mathbf{A} \cdot 889 N \)
B. \( 8.89 N \)
\( c .8889 N \)
D. \( 88.9 N \)
Subject: Maths
If the straight lines \( A B \) and \( X Y \) intersect at the point 0 and \( \angle A O X=3 \angle X O B \)
then the four angles formed at 0 are:
A \( \cdot 30^{\circ}, 30^{\circ}, 90^{\circ}, 210^{\circ} \)
В. \( 30^{\circ}, 30^{\circ}, 150^{\circ}, 150^{\circ} \)
c. \( 45^{\circ}, 135^{\circ}, 90^{\circ}, 90^{\circ} \)
D . \( 45^{\circ}, 45^{\circ}, 135^{\circ}, 135^{\circ} \)
Subject: Physics
A large tank is filled with water (density
\( \left.=10^{3} k g / m^{3}\right) . \) A small hole is made at
depth \( 10 m \) below water surface. the
range of water issuing out of the hole is
R on ground. What extra pressure must
be applied on the water surface so that
the range becomes \( 2 R(\text { take } 1 a t m= \)
\( 10^{5} P a \) and \( g=10 m / s^{2} \)
A. \( 9 a t m \)
B. \( 4 a t m \)
\( c . \) 5atm
D. 3atm
Subject: Physics
Assertion
The maximum height reached by an object projected vertically up is directly proportional to the initial velocity u.
Reason

The maximum height reached by an object thrown up with an initial velocity
u is given by \( \boldsymbol{h}=\frac{\boldsymbol{u}^{\mathbf{2}}}{\mathbf{2} \boldsymbol{g}} \)
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: Maths
\( \lim _{x \rightarrow 1} \frac{1}{\sqrt{|x|-\{-x\}}}(\text { where }\{x\} \) denotes
the fractional part of \( x \) ) is equal to
A. does not exists
B. 1
\( c \cdot \alpha \)
D. \( \frac{1}{2} \)
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{a} \sin \boldsymbol{x}+\boldsymbol{b} \cos \boldsymbol{x}, \) then \( \boldsymbol{y}^{2}+ \)
\( \left(\frac{d y}{d x}\right)^{2} \)
A. function of \( x \)
B. function of \( y \)
c. function of \( x \) and \( y \)
D. constant
Subject: Chemistry
We have \( 1.6 g C H_{4}, 1.7 g N H_{3} \) and
\( 1.8 g H_{2} O . \) Select correct alternate(s)
This question has multiple correct options
A. There are equal number of moles of each reactant
B. Total number of atoms in \( C H_{4}>N H_{3}>H_{2} O \)
c. Total number of H-atoms are in the ratio of 4: 3: 2
D. Total number of \( C \) -atoms in \( C H_{4}< \) that of \( N- \)
atoms in \( N H_{3}< \)that of \( O \) -atoms in \( H_{2} O \)
Subject: Chemistry
A student conducted an experiment and obtained three values during three
repetitive trials: \( 1.65,1.68,1.71 . \) Later the student discovered that the true
value was \( 2.37 . \) In contrast to the rea
value, the experimental results should be characterized as:
A. not accurate and not precise
B. accurate but not precise
c. not accurate but precise
D. accurate and precise
E . accurate, precise, but unreliable
Subject: Physics
Show that the vector is parallel to a vector \( \vec{A}=\hat{i}-\hat{j}+2 \hat{k} \) is parallel to a vector \( \vec{B}=3 \hat{i}-3 \hat{j}+6 \hat{k} \)
A \( \cdot \frac{1}{3} \) times the magnitude of \( \vec{B} \)
B. \( \frac{1}{4} \) times the magnitude of \( \vec{B} \).
C \( \cdot \frac{1}{2} \) times the magnitude of \( \vec{B} \)
D. None of these
Subject: Biology
Statement A: For a particular character in an individual, each gamete gets only one allele.
Statement B: Chromatids of a
chromosome split (separate) and move towards opposite poles during anaphase of mitosis.
A. Both the statements are correct and \( B \) is the reason fo
\( A \)
B. Both the statements are correct and B is not the reason for \( A \)
c. statement A is correct and statement B is wrong.
D. statement B is correct and statement A is wrong
Subject: Physics
\( f(\operatorname{mis} 100 g) R \) is \( 4 \mathrm{cm}, h \) is \( 10 \mathrm{cm} \) and \( \omega \)
is 10 rad/s then find the value of \( \omega \)
\( A \cdot 10 \operatorname{rad} / \)
B. 62,5 rad/s
\( c \cdot 31,25 \mathrm{rad} / \mathrm{s} \)
D. None
Subject: Physics
\( \left\{\begin{array}{l}2 \pi \\ 0 \\ 1\end{array}\right. \)
\( a^{n / 2}\{\emptyset \)
\( \left[\begin{array}{l}y^{\prime \prime} \\ 0\end{array}\right\} \)
\( \left\{\begin{array}{l}y_{1} \\ \Delta\end{array}\right\} \)
Subject: Chemistry
The Bose-Einstein condensate is formed
by:
A. heating a gas of extremely low density, about onehundred-thousandth the density of normal air, to super low temperatures
B. cooling a gas of extremely high density, about onehundred-thousand times the density of normal air, to super low temperatures
C. heating a gas of extremely low density, about onehundred-thousandth the density of normal air, to super high temperatures
D. cooling a gas of extremely low density, about onehundred-thousandth the density of normal air, to super low temperatures
Subject: Chemistry
The IUPAC name of the compound
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)- \)
\( \boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C H O} \) is:
A. 5,6 -Dimethylhept- - -en-1-al
B. 2,3-Dimethyl-4-en-7-al
c. 5,6 -Dimethylhept- - -ene-1-al
D. 5,6-Isopropylpent-3-ene-1-al
Subject: Maths
Direction ratio of line given by \( \frac{x-1}{3}= \) \( \frac{6-2 y}{10}=\frac{1-z}{-7} \) are:
\( A \cdot<3,10,-7> \)
в. \( <3,-5,7> \)
c. \( <3,5,7> \)
D. \( <3,5,-7> \)
Subject: Maths
If \( X \) follows a binomial distribution
with parameters \( n=8 \) and \( P=\frac{1}{2}, \) than
\( \boldsymbol{P}(|\boldsymbol{x}-\mathbf{4}| \leq \mathbf{2})= \)
A \( \cdot \frac{119}{128} \)
в. \( \frac{9}{128} \)
c. \( \frac{101}{128} \)
D. \( \frac{11}{128} \)
Subject: Chemistry
The pH value of gastric juice in human stomach is about 1.8 and in the small
intestine it is about \( 7.8 . \) The \( p K_{a}, \) value
of aspirin is \( 3.5 . \) Aspirin will be :
A. Completely ionised in the small intestine and in the stomach
B. Unionised in the small intestine and in the stomach
c. lonised in the small intestine and almost unionised in the stomach
D. lonised in the stomach and almost unionised in the small intestine
Subject: Chemistry
Assertion
The electrical resistance of a column of
\( 0.05 \mathrm{M} \) NaOH solution of diameter \( 1 \mathrm{cm} \)
and length \( 50 \mathrm{cm} \) is \( 5.55 \times 10^{3} \) ohm.
Reason

Its resistivity is equal to 76.234 ohm
\( \mathrm{cm} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
The limit of \( \left\{\frac{1}{x} \sqrt{1-x}-\sqrt{1+\frac{1}{x^{2}}}\right\} \) as
\( \boldsymbol{x} \rightarrow \mathbf{0} \)
A. Does not exist
B . Is equal to \( \frac{1}{2} \)
c. Is equal to 0
D. Is equal to
Subject: Chemistry
Assertion
\( P_{4} O_{10} \) is not used to dry \( N H_{3} \)
Reason
\( P_{4} O_{10} \) is acidic and \( N H_{3} \) is basic.
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: Chemistry
Which of the following statements
is/are not correct?
This question has multiple correct options
A. \( \pi \) - bond always exists with sigma -bond according to Valence Bond Theory
B. \( \pi \) - bond can exist independently according to Valence Bond Theory
C \( . \sigma \) - bond is weaker than pi-bond
D. \( \pi \) - bond is less reactive than sigma-bond
Subject: Physics
What is the final speed of the sphere's
centre of mass in ground frame when eventually pure rolling sets in
\( A \cdot \frac{5}{-11} \)
7
\( v \)
B. 2 \( 7^{v} \)
\( c \cdot 7 \)
\( v \)
\( v \)
\( D \cdot 7 \)
\( 2^{v} \)
Subject: Maths
Find the solution set of the inequality
\( |\boldsymbol{y}-\mathbf{5}| \leq \mathbf{1} \)
A. \( 4 \leq y \leq 6 \)
в. \( 4 \leq y \geq-6 \)
c. \( 4 \geq y \leq 6 \)
D. \( -4 \leq y \leq 6 \)
Subject: Maths
\( \int \sec ^{8 / 9} x \operatorname{cosec}^{10 / 9} x d x \) is equal to
A. \( -(\cot x)^{1 / 9}+c \)
B. \( 9(\tan x)^{1 / 9}+c \)
\( \mathbf{c} \cdot-9(\cot x)^{1 / 9}+c \)
D. \( -\frac{1}{9}(\cot x)^{1 / 9}+c \)
Subject: Physics
Spherical balls of radius R are falling in
a viscous fluid of velocity v. The
retarding viscous force acting on the spherical ball is
A. directly proportional to R but inversely proportional to
\( v \)
B. directly proportional to both radius R and velocity v.
c. inversely proportional to both radius R and velocity v
D. inversely proportional to R but directly proportional to velocity v
Subject: Chemistry
Find the number of ligands (s) which are monodentate, neutral as well as a non-classical ligand.
\( \left[\boldsymbol{C O}, \boldsymbol{C N}^{-}, \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}, \boldsymbol{P F}_{3}\right] \)
Subject: Chemistry
\( 20 \mathrm{ml} \) of \( 0.2 \mathrm{M} H C N \) mix with \( 10 \mathrm{ml} \) of
0.2 M \( N a O H, \) then calculate \( p H \) of resulting mixture, \( p K a \) value of \( H C N \)
is \( 5:- \)
A . 6
B. 7.5
\( c .5 \)
D. 11
Subject: Physics
The effficiency of carnot cycle is given by:
\( \mathbf{A} \cdot\left(1-T_{2} / T_{1}\right) \)
B. \( \left(1+T_{2} / T_{1}\right) \)
c. \( \left(1-T_{1} / T_{2}\right) \)
D. \( \left(1-T_{2} \times T_{1}\right) \)
Subject: Physics
The heat generated in a circuit is given
by \( Q=I^{2} R t, \) where I is current, \( \mathrm{R} \) is
resistance and t is time. If the
percentage errors in measuring I, R and \( t \) are \( 2 \%, 1 \% \) and1 \( \%, \) respectively, then the maximum error in measuring heat will be
A . \( 2 \% \)
B. \( 3 \% \)
c. \( 4 \% \)
D. \( 6 \% \)
Subject: Chemistry
Assertion
Lead, tin and bismuth are purified by liquation method.
Reason
Lead, tin and bismuth have low m.p. as
compared to impurities.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct.
Subject: Chemistry
Two mole of an ideal gas is heated at constant pressure of one atomosphere
from \( 27^{\circ} \mathrm{C} \) to \( 127^{\circ} \mathrm{C} . \) If \( C_{v, m}=20+ \)
\( 10^{-2} T J K^{-1} m o l^{-1}, \) then \( q \) and \( \Delta U \) for
the process are respectively.
A. 6362.8 J, 4700 .
B . 3037.2 J, 4700 J
c. 7062.8, 5400 J
D. 3181.4 J, 2350 J
Subject: Chemistry
Molecules with multiple bonds between dissimilar atoms e.g., \( \boldsymbol{O}=\boldsymbol{C}= \)
\( \boldsymbol{O}, \boldsymbol{O}=\boldsymbol{S}=\boldsymbol{O} . \) How many \( \mathbf{S} \mathbf{0} \boldsymbol{\pi} \) bonds
are present in \( S O_{3} \), etc.
Subject: Physics
A \( 10 \Omega \) resistance, \( 5 m H \) coil and \( 10 \mu F \)
capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance
is halved, the resonance frequency:
\( A \). is halved
B. is doubled
c. remains unchanged
D. is quadrupled
Subject: Maths
\( A, B, C \) try to hit a target simultaneously but inside- - target are \( \frac{3}{4}, \frac{1}{2}, \frac{5}{8}, \) the probability that target is bur by \( \boldsymbol{A} \) or \( \boldsymbol{B} \) but not by \( \boldsymbol{C} \) is
A \( \cdot \frac{21}{64} \)
B. \( \frac{7}{8} \)
c. \( \frac{7}{32} \)
D. \( \frac{9}{64} \)
Subject: Physics
If ball of steel (density \( \rho=7.8 \mathrm{cm}^{-3} \) )
attains a terminal velocity of \( 10 \mathrm{cms}^{-1} \)
when falling in a tank of water
(coefficient of viscosity \( \boldsymbol{\eta}_{\boldsymbol{w} \text {ater}}=\mathbf{8 . 5} \times \)
\( 10^{-4} \) Pa.s then its terminal velocity in
glycerin \( \left(\rho=1.2 g c m^{-3} \eta=13.2 P a . s\right) \)
would be nearly:
A \( .1 .5 \times 10^{-5} \mathrm{cms}^{-1} \)
в. \( 1.6 \times 10^{-5} \mathrm{cms}^{-1} \)
c. \( 6.25 \times 10^{-4} \mathrm{cms}^{-1} \)
D. \( 6.45 \times 10^{-4} \mathrm{cms}^{-1} \)
Subject: Maths
The maximum value of \( \sin \left(x+\frac{\pi}{5}\right)+\cos \left(x+\frac{\pi}{5}\right), \) where
\( \boldsymbol{x} \in\left(0, \frac{\pi}{2}\right) \) is attained at
\( ^{A} \cdot \frac{\pi}{20} \)
в. \( \frac{\pi}{15} \)
c. \( \frac{\pi}{10} \)
D.
Subject: Physics
A proton is moving in a uniform magnetic field \( B \) in a circular path of
radius \( a \) in a direction perpendicular to
\( Z \) axis along which field \( B \) exists. Calculate the angular momentum. If the
radius is \( a \) and charge on proton is \( e: \)
A \( \cdot \frac{B e}{a^{2}} \)
B \( \cdot e B^{2} a \)
\( \mathbf{c} \cdot a^{2} e B \)
D. \( a e B \)
Subject: Maths
\( \int \frac{1}{9 x^{2}-25} d x= \)
A \( \cdot \frac{1}{30} \log \mid \frac{3 x+5}{3 x-5} \)
B \cdot \( \log |x+\sqrt{3 x-5}| \)
c. \( \frac{1}{30} \log \left|\frac{3 x-5}{3 x+5}\right| \)
D \cdot \( \log \mid x-\sqrt{3 x-5} \)
Subject: Physics
Find a vector \( \vec{x} \) which is perpendicular to both \( \vec{A} \) and \( \vec{B} \) but has magnitude equal to that of \( \vec{B} \). Vector \( \vec{A}=3 \hat{i}- \) \( \mathbf{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\mathbf{4} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}-\mathbf{2} \hat{\boldsymbol{k}} \)
A \( \cdot \frac{1}{\sqrt{10}}(\hat{i}+10 \hat{j}+17 \hat{k}) \)
B \( \cdot \frac{1}{\sqrt{10}}(\hat{i}-10 \hat{j}+17 \hat{k}) \)
c. \( \sqrt{\frac{29}{390}}(\hat{i}-10 \hat{j}+17 \hat{k}) \)
D. \( \sqrt{\frac{29}{390}}(\hat{i}+10 \hat{j}+17 \hat{k}) \)
Subject: Physics
One end of a steel (density \( p \) ) rectangular girder is embedded into a wall (fig). Due to gravity it sags slightly. Find the radius of curvature of the
neutral layer in the vicinity of the point O if the length of the protruding section of the girder is equal to \( l=6.0 \mathrm{cm} \) and
the thickness of the girder equals \( h= \)
\( \mathbf{1 0} \mathrm{cm} \)
\( ^{\mathrm{A}} \cdot_{R}=\frac{h^{2} E}{p l^{2} g} \)
B. \( \quad R=\frac{h^{2} E}{6 p l^{2} g} \)
c. \( _{R}=\frac{h^{2} E}{3 p l^{2} g} \)
D. \( R=\frac{h^{2} E}{7 p l^{2} g} \)
Subject: Chemistry
A freshly obtained precipitate of \( S n O_{2} \)
is peptized by little of \( K O H \) to give a
sol. The sol particles may be represented as:
\( \mathbf{A} \cdot\left[S n O_{2}\right] K^{+} \)
B . \( \left[S n P_{2}\right] O H^{-} \)
\( \mathbf{c} \cdot\left[\operatorname{Sn} O_{2}\right] S n^{4+} \)
D. \( \left[S n O_{2}\right] S n O_{3}^{2} \)
Subject: Physics
A particle is projected at an angle \( \boldsymbol{\theta}= \)
\( 30^{\circ} \) with the horizontal, with a velocity
of \( 10 m s^{-1} . \) Then
This question has multiple correct options
A. After \( 2 s \), the velocity of particle makes an angle of \( 60^{\circ} \) with initial velocity vector.
B. After \( 1 s \), the velocity of particle makes an angle of \( 60^{\circ} \) with initial velocity vector
c. The magnitude of velocity of particle after 1 s is \( 10 \mathrm{ms}^{-1} \)
D. The magnitude of velocity of particle after 1 s is \( 5 m s^{-1} \)
Subject: Chemistry
What was the idea of Paul Ehrlich?
A. Chemicals which would adversely affect the invading bacteria but not the host, can be used for the
treatment of diseases caused by the bacteria
B. Chemicals which would adversely affect the invading bacteria but not the host, cannot be used for the treatment of diseases caused by the bacteria.
C. Chemicals which would adversely affect the invading bacteria but not the guest, can be used for the treatment of diseases caused by the bacteria.
D. Chemicals which would adversely affect the invading bacteria also the guest, can be used for the treatment of diseases caused by the bacteria.
Subject: Chemistry
A radioactive sample of \( U^{238} \) decay to \( P b \)
through a process for which half life is
\( 4.5 \times 10^{9} \) years. The ratio of number of
nuclei of \( P b \) to \( U^{238} \) after a time of \( 1.5 \times \)
\( 10^{9} \) years.
(Given \( 21 / 3=1.26) \)
A . 0.12
B. 0.26
\( c \cdot 1.2 \)
D. 0.37
Subject: Physics
The ionization energy of the hydrogen atom is \( 13.6 e V . \) The potential energy of
the eletron in \( n=2 \) state of hydrogen
atom is
A. \( +3.4 e V \)
в. -3.4eV
\( \mathrm{c} .+6.8 \mathrm{eV} \)
D. - \( 6.8 e V \)
Subject: Maths
Prove that \( \left|\begin{array}{lll}\boldsymbol{b} \boldsymbol{c} & \boldsymbol{b} \boldsymbol{c}^{\prime}+\boldsymbol{b}^{\prime} \boldsymbol{c} & \boldsymbol{b}^{\prime} \boldsymbol{c}^{\prime} \\ \boldsymbol{c} \boldsymbol{a} & \boldsymbol{c} \boldsymbol{a}^{\prime}+\boldsymbol{c}^{\prime} \boldsymbol{a} & \boldsymbol{c}^{\prime} \boldsymbol{a}^{\prime} \\ \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a} \boldsymbol{b}^{\prime}+\boldsymbol{a}^{\prime} \boldsymbol{b} & \boldsymbol{a}^{\prime} \boldsymbol{b}^{\prime}\end{array}\right|= \)
\( \left(\boldsymbol{a} \boldsymbol{b}^{\prime}-\boldsymbol{a}^{\prime} \boldsymbol{b}\right)\left(\boldsymbol{b} \boldsymbol{c}-\boldsymbol{b}^{\prime} \boldsymbol{c}\right)\left(\boldsymbol{c} \boldsymbol{a}^{\prime}-\boldsymbol{c}^{\prime} \boldsymbol{a}\right) \)
Subject: Chemistry
What is the best way to carry out the
following transformation? \( 1- \)pentyne\( \longrightarrow \) pentanal
A. \( H g S O_{4} / H_{2} S O_{4} \)
B. \( H_{2} / \)Lindlar's catalyst; \( O_{3} ; Z n . H_{2} O \)
c. \( H I O_{4} / H_{2} O \)
D. \( B H_{3} ; H_{2} O_{2} / N a O H \)
Subject: Maths
A ladder of length 17 meters rests with one end against a vertical wall and the other on the level ground. if the lower end slipes away at the rate of \( 1 \mathrm{m} / \mathrm{sec} \)
then, when it is \( 8 m \) away from the well, its upper end is coming down at the rate of
\( ^{\mathrm{A}} \cdot \frac{5}{8}^{m / s e c} \)
в. \( \frac{8}{15} m / \)sec.
c. \( \frac{5 \pi}{8} m / \) sec.
D. \( \frac{15}{8} m / \) sec.
Subject: Chemistry
The hydrolysis of \( N C l_{3} \) by water molecules produces:
A. \( N H_{2} O H+H O C l \)
B. \( N H_{2} N H_{2}+H O \)
c. \( N H_{4} O H+H O C l \)
D. \( N H_{2} C l+H O C l \)
Subject: Chemistry
The solubility of \( A g C l \) is \( 1 \times \)
\( 10^{-5} \) mol \( / L . \) Its solubility in 0.1 molar
sodium chloride solution is:
A \( \cdot 1 \times 10^{-10} \)
В. \( 1 \times 10^{-5} \)
c. \( 1 \times 10^{-9} \)
D. \( 1 \times 10^{-4} \)
Subject: Physics
In an induction coil, the coefficient of
mutual induction is 4 henry. If a current of 5 ampere in 1 the primary coil is cut
off in \( \frac{1}{1500} \) s, the e.m.f at the terminals of
the secondary coil will be:
A . \( 15 \mathrm{kv} \)
B. 60 kV
\( c \cdot 10 k v \)
D. 30 kV
Subject: Chemistry
Assertion
Atomic number of the element
ununtrium is 113
Reason
According to IUPAC systematic nomenclature, the numerical roots for
1,1 and 3 are un, un and tri respectively
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 mass of \( 0.5 \mathrm{kg} \) is suspended from wire, then length of wire increases by 3 mm then work done [RPMT 2000]
A \( \cdot 4.5 \times 10^{-3} \) Joule
B. \( 7.5 \times 10^{-3} \) Joule
c. \( 9.3 \times 10^{-3} \) Joule
D. \( 2.5 \times \) Joule
Subject: Physics
Assertion
To unscrew a rusted nut, we need a
wrench with a longer arm
Reason
Wrench with longer arm reduces the
torque applied by the arm
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: Maths
Examine if Mean value Theorem applies
to \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\mathbf{3} \boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x} \) in the interval
[1,2]. If it does, then find the intermediate point whose existence is asserted by theorem.
A. Mean Value theorem is applicable and intermediate points are \( c=-3.55,1.55 \)
B. Mean Value theorem is not applicable
c. Mean Value theorem is applicable and intermediate points are \( c=3.55,-1.55 \)
D. none of these
Subject: Maths
The radius of a right circular cylinder increases at a constant rate. Its altitude
is a linear function of the radius and
increases three times as fast as radius.
When the radius is \( 1 \mathrm{cm} \) the altitude is
\( 6 \mathrm{cm} . \) When the radius is \( 6 \mathrm{cm} \), then
volume is increasing at the rate of \( 1 \mathrm{Cu} \) \( c m / \)sec. When the radius is \( 36 \mathrm{cm}, \) the
volume is increasing at a rate of \( n \) cu.
\( \mathrm{cm} / \) sec. The value of ' \( n^{\prime} \) is equal to:
A .12
в. 22
\( c .30 \)
D. 33
Subject: Chemistry
Shows which type of isomerism:
\[
\mathrm{CH}_{3} \mathrm{CH}_{2}-\mathrm{O}-\mathrm{CH}_{2} \mathrm{CH}_{3} \quad \mathrm{CH}_{3}^{\mathrm{O}} \mathrm{C}-\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}
\]
Diethyl ether Methyl propyl ether
A. Functional group isomerism
B. Geometrical isomerism
C . Metamerism
D. Position isomerism
Subject: Maths
Two dice are thrown. The probability that the sum of the numbers coming up
on them is 9 , if it is known that the
number 5 always occurs on the first die, is
A \( \cdot \frac{1}{6} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{5}{6} \)
Subject: Maths
If \( f(x) \) is an even function, and \( n \in N \) then \( \int_{-\pi}^{\pi} \boldsymbol{f}(\boldsymbol{x}) \sin \boldsymbol{n} \boldsymbol{x} \boldsymbol{d} \boldsymbol{x}= \)
A .
B \( \cdot 2 \int_{0}^{\pi} f(x) \sin n x d x \)
c. \( 4 \int_{0}^{\frac{\pi}{2}} f(x) \sin n x d x \)
D. \( \int_{0}^{\pi} f(x) \sin x d x \)
Subject: Physics
Two resistance at \( 0^{\circ} \mathrm{C} \) with
temperature coefficient of resistance
\( \alpha_{1} \) and \( \alpha_{2} \) joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be
A \( \cdot \alpha_{1}+\alpha_{2} \)
В. \( \frac{\alpha_{1} \alpha_{2}}{\alpha_{1}+\alpha_{2}} \)
c. \( \frac{\alpha_{1}-\alpha_{2}}{2} \)
D. \( \frac{\alpha_{1}+\alpha_{2}}{2} \)
Subject: Maths
Statement
(I): If
\( \sin \alpha=\frac{12}{13},\left(0<\alpha<\frac{\pi}{2}\right) \) and
\( \cos \beta=-\frac{3}{5},\left(\pi<\beta<\frac{3 \pi}{2}\right) \) then
\( \sin (\alpha+\beta)=\frac{56}{65} \)
Statement (II): If
\( \theta \) and \( \phi \) are angles in the first quardrant such that \( \tan \theta=\frac{1}{7} \) and \( \sin \phi=\frac{1}{\sqrt{10}} \operatorname{then} \theta+2 \phi=45^{\circ} \)
Which of the above statements is
correct?
A. only
B. only ॥
c. Both I\&॥
D. Neither I nor I
Subject: Physics
A particle has an initial velocity of \( 9 m / s \) due east and a constant acceleration of \( 2 m / s^{2} \) due west. The distance covered by the particle in the fifth second of its motion is:
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 0.5 \mathrm{m} \)
\( c .2 m \)
D. \( 0.25 m \)
Subject: Physics
The velocity acquired by a body moving with uniform acceleration is \( 30 m / s \) in
2 seconds and \( 60 m / s \) in 4 seconds. The initial velocity is:
A. Zero
B. \( 2 m / s \)
c. \( 4 m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)