AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Assertion
Statement \( -1 f(x)=|x| \cos x \) is not
differentiable at \( \mathbf{x}=\mathbf{0} \)
Reason
Statement - 2 Every absolute value functions are not differentiable.
A. Statement-1 is True, Statement-2 is True
Statement- 2 is a correct explanation for
Statement-1.
B. Statement-1 is True, Statement-2 is True
Statement-2 is NOT a correct explanation
for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Maths
The probability that exactly one of the
independent events \( A \) and \( B \) occurs is
equal to
This question has multiple correct options
\( \mathbf{A} \cdot \mathbf{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-2 P(\mathrm{A} \cap B) \)
B \( . P(A)+P(B)-P(A \cap B) \)
\( \mathbf{c} \cdot P(\bar{A})+P(\bar{B})-2 P(\bar{A} \cap \bar{B}) \)
D \( . P(\bar{A})+P(\bar{B})-P(\bar{A} \cap \bar{B}) \)
Subject: Physics
A ring a radius \( r \) is rotating about a
vertical axis along its diameter with
constant angular velocity \( \omega . \) A read of
mass \( m \) remains at rest w.r.t. ring at the
position shown in figure. Then \( w^{2} \) is
A \( \cdot \frac{g}{\sqrt{3 r}} \)
B. \( \frac{2 g}{\sqrt{3}} \)
\( c \cdot \frac{\sqrt{3} g}{n} \)
\( D \)
Subject: Maths
Find the degree measures corresponding to the following radian measures \( \left(\boldsymbol{U s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right) \)
(i) \( \frac{11}{16} \)
(ii) -4
(iii) \( \frac{5 \pi}{3} \)
(iv) \( \frac{7 \pi}{6} \)
Subject: Chemistry
For Balmer series in the spectrum of
hydrogen, the wave number of each line is given by \( \overline{\boldsymbol{v}}=\boldsymbol{R}_{\boldsymbol{H}}\left[\frac{\mathbf{1}}{\boldsymbol{n}_{\mathbf{1}}^{2}}-\frac{\mathbf{1}}{\boldsymbol{n}_{2}^{2}}\right] \) where \( \boldsymbol{R}_{\boldsymbol{H}} \) is
constant and \( n_{1}, n_{2} \) are integers, which of the following statements is (are)
correct?
1. As wavelength decreases, the lines in the series converge.
2. The integer \( n_{1} \) is equal to 2
3. The ionization energy of hydrogen can be calculated from the wave number of
these lines.
4. The lines of longest wavelength
corresponds to \( n_{2}=3 \)
\( A \cdot 1,2 \) and 3
B. 2, 3 and 4
\( \mathbf{c} \cdot 1,2 \) and 4
D. 2 and 4
E. 2 only
Subject: Maths
Following polynomars write the degree
of each.
1). \( 6 x^{2}+x+1 \)
2). \( y^{9}-3 y^{7}+\frac{3}{2} y^{2}+4 \)
3). \( 2 x+1 \)
4). \( 5 t-\sqrt{11} \)
Subject: Chemistry
The correct name of the compound
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \) according to IUPAC
system is:
A. cuprammonium nitrate
B. terrammine copper(II) dinitrate
c. tetrammine copper(II) nitrate
D. tetrammine copper(III) dinitrate
Subject: Chemistry
An organic compound with molecular
formula \( C_{4} H_{10} O \) does not react with
sodium. With excess of HI it gives only one type of alkyl halide. The compound
is:
A. \( C_{2} H_{5} O C_{2} H_{5} \)
B \( . C H_{3} \) \( H_{3} C_{\} H C H_{3} \)
\( O C H_{3} \)
c. \( C H_{3} C H_{2} C H_{2} O C H_{3} \)
D. \( C H_{3} C H_{2} C H_{2} C H_{2} O H \)
Subject: Chemistry
Assertion
Positive catalysts increase the rate of
reaction.
Reason
Catalysts decrease the value of \( \Delta G^{o} \)
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
Given set of quantum numbers for a multi-electron atom is:
\( \boldsymbol{n} \)
\( l \) \( m \) \( s \)
2
\( \begin{array}{cc}0 & 0\end{array} \) \( +1 / 2 \)
2
\( -1 / 2 \)
What is the next higher allowed set of ' \( n \)
and 'l' quantum numbers for this atom
in the ground state?
A. \( n=2, l=0 \)
В. \( n=2, l=1 \)
c. \( n=3, l=0 \)
D. \( n=3, l=1 \)
Subject: Physics
The amplitude of the electric field in a parallel beam of light of intensity \( 2.0 \mathrm{Wm}^{-2} \) is:
A. \( 19.4 \mathrm{N} / \mathrm{C} \)
B. 38.8 N/C
c. \( 4.85 \mathrm{N} / \mathrm{c} \)
D. 77.9 N/C
Subject: Chemistry
If equal quantities of electricity are
passed through three voltmeter
containing \( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{F} \boldsymbol{e}_{2}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{3} \) and
\( F e\left(N O_{3}\right)_{2}, \) then which of the following
is not true?
A. Amount of iron deposited in \( F e S O_{4} \) and \( F e_{2}\left(S O_{4}\right)_{3} \) is equal
B. Amount of iron deposited in \( F e\left(N O_{3}\right)_{3} \) is \( \frac{2}{3} \) of the
amount of iron deposited in \( F e S O_{4} \)
C. Amount of iron deposited in \( F e_{2}\left(S O_{4}\right)_{3} \) and \( F e\left(N O_{3}\right)_{3} \) are equal
D. Same gas will evolve in all three cases at anode
Subject: Maths
Let a function be defined as \( \boldsymbol{f}(\boldsymbol{x})= \) \( \frac{\boldsymbol{x}-|\boldsymbol{x}|}{\boldsymbol{x}} . \) Then \( \boldsymbol{f}(\boldsymbol{x}) \) is
A. continuous nowhere
B. continuous everywhere
c. continuous for all \( x \) except \( x=1 \)
D. continuous for all \( x \) except \( x=0 \)
Subject: Chemistry
Select the incorrect statement(s).
This question has multiple correct options
A. Monosaccharides are insoluble in organic solvents like diethyl ether.
B. Anomers of cyclic monosaccharides differ in the position of the \( -O H \) group at the hemiacetal carbon.
C. In D-Ribose, the \( -O H \) group used to form the fivemembered furanose ring is located on \( C_{4} \) carbon.
D. Aldopentoses and ketohexoses form pyranose rings in solution
Subject: Physics
A moon of Saturn has a nearly circular orbit of radius \( R \) and an orbit period of \( T \). Which of the following expressions gives the mass of Saturn?
\( ^{A} \cdot \frac{2 \pi R}{T} \)
в. \( \frac{4 \pi^{2} R}{T} \)
\( ^{\mathbf{c}} \cdot \frac{2 \pi R^{3}}{\left(G T^{2}\right)} \)
D. \( \frac{4 \pi^{2} R^{2}}{\left(G T^{2}\right)} \)
E \( \cdot \frac{4 \pi^{2} R^{3}}{\left(G T^{2}\right)} \)
Subject: Biology
A stage in cell division is shown in the
figure. Identify the stage of cell division
with its characteristics.
A. Late anaphase - Chromosomes move away from equatorial plate, golgi complex not present
B. Cytokinesis - Cell plate formed mitochondria distributed between two daughter cells
C. Telophase - Endoplasmic reticulum and nucleolus not reformed yet
D. Telophase - Nuclear envelope reforms, golgi complex reforms
Subject: Physics
A circular disc of radius 0.2 meter is
placed in a uniform magnetic field of induction \( \frac{1}{\pi}\left(W b / m^{2}\right) \) in such way that
its axis makes an angle of \( 60^{\circ} \) with \( \vec{B} \). The magnetic flux linked with the disc is
A. \( 0.08 \mathrm{wb} \)
B. 0.01 Wb
c. \( 0.02 \mathrm{wb} \)
D. \( 0.06 \mathrm{wb} \)
Subject: Chemistry
Which is true about \( N_{2} O_{5} ? \)
This question has multiple correct options
A. It is anhydride of \( H N O_{3} \)
B. In solid state it exists as \( \left[N O_{2}^{+}\right]\left[N O_{3}^{-}\right] \)
C. It is structurally similar at \( P_{2} O_{5} \)
D. It can be prepared by heating \( H N O_{3} \) over \( P_{2} O_{5} \)
Subject: Maths
The domain of \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{2}|-|\boldsymbol{x}-\mathbf{5}| \)
is
A. \( R-(2,5) \)
B . \( R-0 \)
\( c \cdot(0, \infty) \)
D. \( R \)
Subject: Physics
Weight of a body of mass m decreases
by \( 1 \% \) when it is raised to height \( h \) above the Earth's surface. If the body is taken to a depth h in a mine, then its weight will:
A. Decreases by \( 0.5 \% \)
B. Decreases by \( 2 \% \)
c. Increases by \( 0.5 \% \)
D. Increase by \( 1 \% \)
Subject: Biology
Floral formula of Cesalpinoideae is
\( A \)
\( \% \bigoplus_{\leftarrow} \mathrm{K}_{(5)} \mathrm{C}_{(5)} \mathrm{A}_{1+(9)} \mathrm{G} \)
в. \( \% G \mathbf{K}_{(5)} \mathbf{C}_{(5)} \mathbf{A}_{5} \underline{\mathbf{G}}_{\mathbf{1}} \)
c. \( \% \oint_{\mathrm{H}_{5}} \mathrm{C}_{(5)} \mathrm{A}_{\mathrm{l} 0} \mathrm{G}_{\mathrm{l}} \)
\( \% G \mathbf{K}_{5} \mathrm{C}_{5} \mathbf{A}_{7+3} \mathbf{G}_{\mathbf{1}} \)
Subject: Physics
A charge \( Q \) is divided into two parts of \( q \)
and \( Q-q . \) If the Coulomb repulsion
between them when they are separated, is to be maximum, the ratio of \( \frac{Q}{q} \) should be:
A .2
в. \( 1 / 2 \)
\( c \cdot 4 \)
D. \( 1 / 4 \)
Subject: Physics
(a) Show that the normal component of
electrostatic field has a discontinuity
from one side of a charged surface to another given by \( \$ \$\left(E_{-} 21,-\right. \)
\( \mathrm{~ I f r a c \{ s i g m a ~ \} \{ v a r e p s i l o n ~} \)
\( 03 \$ \$ \)
where \( \hat{n} \) is a unit vector normal to the
surface at a point and \( \sigma \) is the surface
charge density at that point. (The
direction of \( \hat{n} \text { is from side } 1 \text { to side } 2 .) \)
Hence show that just outside
a conductor, the electric field is \( \sigma \hat{n} / \epsilon_{0} \)
(b) Show that the tangential component of electrostatic field is continuous from
one side of a charged surface to another. [Hint: For (a), use Gauss's law. For, (b) use the fact that work done by
electrostatic field on a closed loop is zero.]
Subject: Chemistry
When copper is heated with
conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) it produces :
A \( \cdot C u\left(N O_{3}\right)_{2} \) and \( N O_{2} \)
B . \( C u\left(N O_{3}\right)_{2} \) and \( N O \)
c. \( C u\left(N O_{3}\right)_{2}, N O \) and \( N O_{2} \)
D. \( C u\left(N O_{3}\right)_{2} \) and \( N_{2} \)
Subject: Physics
A particle having mass \( m \) and charge \( q \) is released from the origin in a region in which electric field and magnetic fields are given by \( \vec{B}=-B_{0} \hat{j} \) and \( \vec{E}=E_{0} \hat{k} \)
Find the speed of the particle as a
function of its \( z- \) coordinate.
A \( \cdot \sqrt{\frac{q E z}{m}} \)
B. \( \sqrt{\frac{2(q v B+q E) z}{m}} \)
D. \( \sqrt{\frac{2 q E z}{m}} \)
Subject: Chemistry
\( \boldsymbol{P} \frac{\boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} / \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}}{\longrightarrow} \boldsymbol{Q} \frac{\text {Sodalime}}{\Delta} \boldsymbol{R} \frac{\boldsymbol{C H}_{3} \boldsymbol{C l}}{\boldsymbol{a n h y} \cdot \boldsymbol{A l} \boldsymbol{C l}_{3}} \boldsymbol{S} \)
If \( P \) and \( S \) are toluene, \( Q \) and \( R \)
and \( ----- \) respectively.
A. Benzaldehyde, Benzoic acid
B. Benzaldehyde, Sodium benzoate
C. Benzoic acid, Benzene
D. Benzene, Benzoic acid
Subject: Physics
A \( 0.50 k g \) object moves in a horizontal circular track with a radius of \( 2.5 m . \) An
external force of \( 3.0 N, \) always tangent
to the track, causes the object to speed
up as it goes around. The work done by the external force as the mass makes
one revolution is:
A \( .24 J \)
B. \( 47 J \)
c. \( 58 J \)
D. \( 67 J \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=(\mathbf{1}+\boldsymbol{x})^{15}=\boldsymbol{C}_{0}+\boldsymbol{C}_{1} \boldsymbol{x}+ \)
\( C_{2} x^{2}+\ldots+C_{15} x^{15}, \) then \( f(2)= \)
\( \mathbf{A} \cdot 1^{15} \)
B. \( 3^{15} \)
\( c \cdot 2^{15} \)
D. None of these
Subject: Maths
\( \operatorname{Let} g^{\prime}(x)>0 \) and \( f^{\prime}(x)<0 \forall x \epsilon R, \) then
This question has multiple correct options
A. \( f(f(x+1))>f(f(x-1)) \)
в. \( f(g(x-1))>f(g(x+1)) \)
\( \mathbf{c} . g(f(x+1))>g(f(x-1)) \)
D. \( g(g(x+1))>g(g(x-1)) \)
Subject: Physics
A satellite is revolving round the earth
with orbital speed \( v_{0} \). If it is imagined to stop suddenly, the speed with which it will strike the surface of the earth would
be \( \left(v_{e}- \) escape speed of a body from \right. earth's surface)
A \( \cdot \frac{v_{e}^{2}}{v_{0}} \)
в. \( v_{0} \)
c. \( \sqrt{v_{e}^{2}-v_{0}^{2}} \)
D. \( \sqrt{v_{e}^{2}-2 v_{0}^{2}} \)
Subject: Chemistry
Which of the reaction defines molar
\( \Delta \boldsymbol{H}_{\boldsymbol{f}}^{\circ} ? \)
This question has multiple correct options
\( \mathbf{A} \cdot H^{+}(a q)+O H^{-}(a q) \rightarrow H_{2} O(\iota) \)
B \( \cdot \quad B r_{2}(\iota)+H_{2}(g) \rightarrow H B r(g) \)
\( \mathbf{C} \cdot N_{2}(g)+2 H_{2}(g)+O_{2}(g) \rightarrow N H_{4} N O_{3} \)
\( \mathbf{D} \cdot H_{2}(g)+S_{\text {monoclinic}}+2 O_{2}(g) \rightarrow H_{2} S O_{4}(\iota) \)
Subject: Maths
\( (m x-n y)(m x-n y)= \)
A \( \cdot m^{2} x^{2}+2 m x n y-n^{2} y^{2} \)
B \( \cdot m^{2} x^{2}-2 m x n y-n^{2} y^{2} \)
C \( \cdot m^{2} x^{2}-2 m x n y+n^{2} y^{2} \)
D. \( m^{2} x^{2}+2 m x n y+n^{2} y^{2} \)
Subject: Physics
Dimensions of impulse are
\( \mathbf{A} \cdot\left[M L T^{-1}\right] \)
\( \mathbf{B} \cdot\left[M L T^{2}\right] \)
c. \( \left[M T^{-2}\right] \)
D・ \( \left[M L^{-1} T^{-3}\right] \)
Subject: Maths
The negative of the statement "lf a
number is divisible by 15 then it is divisible by 5 or \( 3 " \)
A. if a number is divisible by 15 then it is not divisible by and 3
B. a number is divisible by 15 and it is not divisible by 5 o
3
c. a number is divisible by 15 or it is not divisible by 5 and
3
D. a number is divisible by 15 and it is not divisible by 5 and 3
Subject: Physics
A metallic conductor at \( 10^{\circ} \mathrm{C} \) connected
in the left gap of Meter Bridge gives balancing length \( 40 \mathrm{cm} . \) When the
conductor is at \( 60^{\circ} \mathrm{C} \), the balance point
shifts by \( 5 \mathrm{cm} . \) The temperature coefficient of resistance of the material
of the wire
A . (1 / 210) / \( ^{\circ} \mathrm{C} \)
B. (1 / 220) / \( ^{\circ} \mathrm{C} \)
\( c \cdot(1 / 200) /^{\prime} c \)
D. (1 / 201) / \( ^{\circ} \mathrm{C} \)
Subject: Physics
The angular speed of the electron in the
\( \boldsymbol{n}^{t h} \) Bohr orbit of the hydrogen at om is
proportional to
\( A \cdot n \)
B \( \cdot n^{3} \)
c. \( \frac{1}{n} \)
D. \( \frac{1}{n^{3}} \)
Subject: Chemistry
In a 20 litre vessel initially \( 1-1 \) mole
\( C O, H_{2} O, C O_{2} \) is present, then for the
equilibrium of \( \boldsymbol{C O}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{2}+ \)
\( \boldsymbol{H}_{2} \) following is true?
A. \( H_{2}, \) more than 1 mole
B. \( C O, H_{2} O, H_{2} \) less then 1 mole
c. \( C O_{2} \& H_{2} O \) both more than 1 mole
D. All of these
Subject: Maths
Three horses \( \boldsymbol{H}_{1}, \boldsymbol{H}_{2}, \boldsymbol{H}_{3} \) entered a field which has seven portions marked
\( P_{1}, P_{2}, P_{3}, P_{4}, P_{5}, P_{6} \) and \( P_{7} \). If no two
horses are allowed to enter the same
portion of the field, in how many ways can the horses graze the grass of the field?
Subject: Chemistry
The correct statement about the
compounds \( A, B \) and \( C \) is:
(A)
(B)
(C)
\( A \). A and \( B \) are identical
B. A and B are diastereomers
C. \( A \) and \( C \) are enantiomers
D. \( A \) and \( B \) are enantiomers
Subject: Maths
Factorise \( \left(3-4 y-7 y^{2}\right)^{2}-(4 y+1)^{2} \)
A \( \cdot\left(4-7 y^{2}\right)\left(2-8 y-7 y^{2}\right) \)
B \( \cdot\left(7 y^{2}-4\right)\left(2-8 y-7 y^{2}\right) \)
c. \( \left(4-7 y^{2}\right)\left(7 y^{2}+8 y-2\right) \)
D \( \cdot\left(7 y^{2}-4\right)\left(7 y^{2}-8 y-2\right) \)
Subject: Physics
Two whistles \( A \) and \( B \) produces notes of frequencies \( 600 \mathrm{Hz} \) and \( 596 \mathrm{Hz} \) respectively. There is a listener at the midpoint of the line joining them. Both
the whistles \( A, B \) and the listener start moving with speed \( 30 \mathrm{m} / \mathrm{s} \) in the same direction. If the speed of the sound is \( 330 \mathrm{m} / \mathrm{s} \), the number of beats that
will be heard by the listener are:
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D.
Subject: Physics
An electric motor driven pump fills an overhead tank placed at a height of 20
\( \mathrm{m} \) from the ground-level sump at a rate
of 20,000 litre water per hour.The motor has an operating resistance of \( 22 \Omega \) and is connected across a \( 220 \mathrm{V} \) source.The
efficiency of this motor is (Useg \( = \)
\( \left.9.8 m / s^{2}\right) \)
\( \mathbf{A} \cdot 12.5 \% \)
B. \( 73.5 \% \)
c. \( 49.5 \% \)
D. \( 22.5 \% \)
Subject: Maths
Evaluate
\( \lim _{x \rightarrow 0} \frac{\sqrt[k]{1+x}-1}{x}(\mathrm{K} \) is a positive
integer \( ) \)
\( A \cdot K \)
B. - -
c. \( \frac{1}{K} \)
D. \( -\frac{1}{K} \)
Subject: Maths
A particle moves along the curve \( y= \)
\( x^{3 / 2} \) in the first quadrant in such a way
that its distance from the origin increases at the rate of 11 units per
second. The value of when \( x=3 \) is
A . 4
B. \( \frac{9}{2} \)
c. \( \frac{3 \sqrt{3}}{2} \)
D. none of these
Subject: Biology
Correct sequence of stages in evolution
of Modern Man/Homo sapiens sapiens is
A. Australopithecus, Neanderthal Man, Cro-Magnon Man, Homo erectus, Modern Man
B. Australopithecus, Homo erectus, Neanderthal Man, Cro-Magnon Man, Modern Man
C. Neanderthal Man, Australopithecus, Cro-Magnon Man, Homo erectus, Modern Man
D. Homo erectus, Australopithecus, Neanderthal Man, Cro-Magnon Man, Modern Man
Subject: Physics
\( 0.003 m \) is dropped into a tube containing a viscous fluid filled up to
the \( 0 \mathrm{cm} \) mark as shown in the figure.
Viscosity of the fluid \( =1.2160 N . m^{-2} \)
and its density \( \rho_{L}=\rho / 2= \)
\( 1260 k g . m^{-3} . \) Assume the ball reaches
terminal speed by the \( 10 c m \) mark. Find the time taken (in sec) by the ball to
traverse the distance between the \( 10 \mathrm{cm} \)
and \( 20 c m \) mark. ( \( g \) =acceleration due to
gravity \( =10 m s^{-2} \)
Subject: Maths
\( \boldsymbol{C} \cdot \boldsymbol{P}=\boldsymbol{R} \boldsymbol{s} .16000, \boldsymbol{S} \cdot \boldsymbol{P}=\boldsymbol{R} \boldsymbol{s} .18500, \boldsymbol{x} \% \)
\( =\frac{x}{100}, \) Profit \( \% \)
A . \( 25 \% \) \%
в. \( _{15} \frac{1}{4} \% \)
c. \( 25 \frac{1}{8} \% \)
D. \( _{15} \frac{5}{8} \% \)
Subject: Chemistry
Assertion
In an atom, the velocity of electron in
the higher orbits keeps on decreasing.
Reason
Velocity of electrons is inversely proportional to the radius of the orbit.
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
Water stands at a height H in a tall cylinder (see figure). Two holes \( A \) and \( B \)
are made on the sides of the cylinder. If
hole \( A \) is at a height \( h \) above the ground,
what is the height of hole \( B \) above the
ground so that the two streams of water emerging from holes \( A \) and \( B \) strikes the ground at the same point?
Subject: Chemistry
Correct balanced equation from the
following reactions is:
\( \mathbf{A} \cdot S+3 H N O_{3} \rightarrow H_{2} S O_{4}+N O_{2}+3 H_{2} O \)
B \( \cdot S+H N O_{3} \rightarrow H_{2} S O_{4}+2 N O_{2}+H_{2} O \)
\( \mathbf{c} \cdot S+3 H N O_{3} \rightarrow H_{2} S O_{4}+6 N O_{2}+2 H_{2} O \)
\( \mathbf{D} \cdot S+6 H N O_{3} \rightarrow H_{2} S O_{4}+6 N O_{2}+2 H_{2} O \)
Subject: Physics
A helium nucleus makes a full rotation
in a circle of radius \( 0.8 m \) in two
seconds. The value of the magnetic field
B at the centre of the circle will be
\( \mathbf{A} \cdot 10^{-19} / \mu_{0} \)
B . \( 10^{-19} \) p \( _{0} \)
c. \( 2 \times 10^{-19} \mu_{0} \)
D. \( 2 \times 10^{-19} / \mu_{0} \)
Subject: Physics
A metallic rod of length \( l \) and cross
sectional area \( A \) is made of a material
of Young modules \( Y \). If the rod is
elongated by an amount \( y, \) then the work done is proportional to
A \( . y \)
B. \( \frac{1}{y} \)
c. \( y^{2} \)
D. \( \frac{1}{y^{2}} \)
Subject: Maths
State true or false:
In quadrilateral \( A B C D, \) its diagonals \( A C \) and \( B D \) intersect at point \( O, \) such
that \( \frac{\boldsymbol{O C}}{\boldsymbol{O A}}=\frac{\boldsymbol{O D}}{\boldsymbol{O B}}=\frac{1}{3}, \) then
\( \triangle \boldsymbol{O} \boldsymbol{A} \boldsymbol{B} \sim \triangle \boldsymbol{O C D} \)
A. True
B. False
Subject: Maths
If \( m \) be the slope of a tangent to the
curve \( e^{2 y}=1+4 x^{2}, \) then
\( \mathbf{A} \cdot m<1 \)
B . \( |m| \leq 1 \)
\( \mathrm{c} \cdot|m|>1 \)
D. None of these
Subject: Physics
An incident ray strikes a plane mirror at
an angle of incidence of \( 40^{\circ} . \) What is the
percentage decrease in the angle of reflection if the incident ray moves to an
angle of incidence of \( 30^{\circ} ? \)
A . \( 10 \% \)
B . 20\%
c. \( 25 \% \)
D. 30\%
Subject: Maths
An isosceles triangle contains three
angles that measure \( 40^{\circ}, x^{\circ}, \) and \( y^{\circ} \)
Which of the following CANNOT be true?
A \( . x=y \)
B. \( x=50 \)
c. \( x-y=60 \)
D. \( x=70 \)
E . \( x=100 \)
Subject: Maths
Assertion
If both functions \( f(t) \) and \( g(t) \) are
continuous on the closed interval \( [\boldsymbol{a}, \boldsymbol{b}] \)
differentiable on the open interval \( (a, b) \)
and \( g^{\prime}(t) \) is not zero on that open
interval, then there exists some \( c \) in
\( (a, b) \) such that \( \frac{f^{\prime}(c)}{g^{\prime}(c)}=\frac{f(b)-f(a)}{g(b)-g(a)} \)
Reason
If \( f(t) \) and \( g(t) \) are continuous and
differntiable in \( [a, b], \) then there exists
some \( c \) in \( (a, b) \) such that \( f^{\prime}(c)= \) \( \frac{\boldsymbol{f}(\boldsymbol{b})-\boldsymbol{f}(\boldsymbol{a})}{\boldsymbol{b}-\boldsymbol{a}} \) and \( \boldsymbol{g}^{\prime}(\boldsymbol{c})=\frac{\boldsymbol{g}(\boldsymbol{b})-\boldsymbol{g}(\boldsymbol{a})}{\boldsymbol{b}-\boldsymbol{a}} \)
from Lagrange's mean value theorm.
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
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\underset{\boldsymbol{C H}_{3}}{\boldsymbol{C}}^{\boldsymbol{C H}_{3}}- \)
\( C H_{2}-C H_{2}-O H \frac{H^{+}}{\Delta}(A) \)
Product (A) is:
A. \( C H_{3}-C H_{2}-C H_{2}-C H_{2}-C_{C H_{3}}=C H-C H_{3} \)
в. \( C H_{3}-\left(C H_{2}\right)_{3}-C\left(C H_{3}\right)=C\left(C H_{3}\right)_{2} \)
c. \( C H_{3}-C H_{2}-C H_{2}-C H_{2}-C_{I H_{3}}=C H_{2} \)
Subject: Physics
A motor car is moving with the speed of
\( 20 m s^{-1} \) on a circular track of radius
\( 100 \mathrm{m} . \) If its speed is increasing at the
rate of \( 3 m s^{-} 2, \) the resultant
acceleration is
\( A \cdot 3 m s^{-2} \)
B. \( 5 m s^{-2} \)
c. \( 2.5 m s^{-2} \)
D. \( 3.5 m s^{-2} \)
Subject: Maths
Three sides \( A B, B C \) and \( C A \) of a
triangle \( A B C \) are \( 5 x-3 y+2=0, x- \)
\( 3 y-2=0 \) and \( x+y-6=0 \)
respectively. Find the equation of the
altitude through the vertex \( \boldsymbol{A} \)
Subject: Chemistry
Which of the following lanthanoid ions is diamagnetic ? (At. No. \( C e= \)
\( \mathbf{5 8}, \boldsymbol{S m}=\mathbf{6 2}, \boldsymbol{E u}=\mathbf{6 3}, \boldsymbol{Y b}=\mathbf{7 0}) \)
A \( \cdot C e^{2} \)
B . \( S m^{2+} \)
c. \( E u^{2+} \)
D. \( Y b^{2} \)
Subject: Chemistry
Identify the true statements(s).
This question has multiple correct options
A. The electron density in the xy plane in \( 3 d_{y z} \) orbital is
zero
B. The electron densities in the xy and xz planes in \( 3 d_{y z} \)
orbital are zero
C. Paulis principle states that the total wave function of two identical fermions is anti-symmetric with respect to exchange of particles
D. Paulis principle is not obeyed by bosons
Subject: Physics
A stone is released from a hydrogen balloon, going upwards with velocity 12 \( \mathrm{m} / \mathrm{s} . \) When it is at height of \( 65 \mathrm{m} \) from
the ground, time the stone will take to reach the ground is?
A . 5 sec
B. 6 sec
\( c \cdot 7 \sec \)
D. 8 sec
Subject: Physics
The resistance of a wire at \( 20 C \) is 20
ohms and at \( 500 C \) is 60 ohms. At which
temperature its resistance will be 25 ohm?
A \( \cdot 80^{\circ} \mathrm{C} \)
B . \( 70^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 60^{\circ} C \)
D. \( 50^{\circ} \mathrm{C} \)