AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Arrange the following species according to their bond angle order:
(।) \( \boldsymbol{O}_{3} \)
(II) \( N O_{2}^{-} \)
(IIII) \( \boldsymbol{F} \boldsymbol{N} \boldsymbol{O} \)
A \( I>I I>I I I \)
\( I \)
В. \( I I>I>I I I \)
c. \( I I I>I I>I \)
D. \( I I>I I I>I \)
Subject: Physics
Given that \( \boldsymbol{E}=\left(\left(\mathbf{3} \boldsymbol{x}^{2}+\boldsymbol{y}\right) \hat{\boldsymbol{i}}+\right. \)
\( \boldsymbol{x} \hat{\boldsymbol{y}}) \boldsymbol{k} \boldsymbol{V} / \boldsymbol{m}, \) find the work done in
moving a \( -2 \mu C \) charge from (0,5,0) to (2,-1,0) by taking the path:
\( \boldsymbol{y}=\mathbf{5}-\mathbf{3} \boldsymbol{x} \)
A . \( 12 J \)
в. \( 12 m J \)
\( \mathbf{c} \cdot 12 k J \)
D. \( 12 \mu J \)
Subject: Chemistry
\( \mathbf{3} \boldsymbol{F} \boldsymbol{e}^{\mathbf{2}+}+\mathbf{4} \boldsymbol{H}^{+}+\boldsymbol{N} \boldsymbol{O}_{\mathbf{3}}^{-} \longrightarrow \mathbf{3} \boldsymbol{F} \boldsymbol{e}^{\mathbf{3}+}+ \)
\( 2 H_{2} O+N O \) is balanced reaction
If the balanced reaction is true enter 1
else enter 0
Subject: Chemistry
Assertion
Plastic grocery bags do not block drains during rains.
Reason
Plastics are lighter than water and
hence float over water
Read the above assertion and reason
and choose the correct option regarding
¡t.
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
At the top of a mountain a thermo meter read \( 7^{0} \mathrm{C} \) and barometer reads \( 70 \mathrm{cm} \) of
Hg. At the bottom of the mountain the barometer reads \( 76 \mathrm{cm} \) of Hg and thermometer reads \( 27^{0} \) C. The density of
air at the top of mountains is times the density at the bottom.
A . 0.99
B. 0.9
c. 0.89
D. 0.95
Subject: Physics
If the energy of an electron in Hydrogen atom is given by expression, \( -1312 / n^{2} k J m o l^{-1}, \) then the energy required to excite the electron from ground state to second orbit is
A \( \cdot 328 k J m o l^{-1} \)
B. \( 656 k J \) mol \( ^{-1} \)
\( \mathbf{c} \cdot 984 k J m o l^{-1} \)
D. \( 1312 k J m o l^{-1} \)
Subject: Maths
For real values of \( x, \) the range of \( \frac{x^{2}+2 x+1}{x^{2}+2 x-1} \) is
B \( \cdot\left[\frac{1}{2}, 2\right] \)
c. \( \left(-\infty, \frac{-2}{9}\right] \cup(1, \infty) \)
D \( \cdot(-\infty,-6] \cup(-2, \infty) \)
Subject: Maths
If the straight line, \( 2 x-3 y+17=0 \)
is perpendicular to the line passing through the points (7,17) and \( (15, \beta) \)
then \( \beta \) equals:-
A . -5
B. \( -\frac{35}{3} \)
c. \( \frac{35}{3} \)
D. 5
Subject: Maths
If latus rectum of ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \)
is double ordiante passing through
focus of parabola \( \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{a} \boldsymbol{x}, \) then find
the value of \( a \).
Subject: Maths
The following table gives the
distribution of IQ of 60 pupils of class X
in a school.
\( \begin{array}{ll}\text { IQ } & \text { No. of pupils } \\ \text { 60-70 } & \text { 2 } \\ \text { 70-80 } & \text { 3 } \\ \text { 80-90 } & \text { 5 } \\ \text { 90-100 } & \text { 16 } \\ \text { 100-110 } & \text { 14 } \\ \text { 110-120 } & \text { 13 } \\ \text { 120-130 } & \text { 7 }\end{array} \) Convert the above distribution to a more
than type cumulative frequency distribution and draw its ogive
Subject: Physics
Take \( C_{i c e}=0.53 c a l / g-^{\circ} C, C_{w a t e r}= \)
\( \mathbf{1 . 0 c a l} / \boldsymbol{g}-^{\circ} \boldsymbol{C},\left(\boldsymbol{L}_{f}\right)_{\text {water}}=\mathbf{8 0 c a l} / \boldsymbol{g} \)
and \( \left(\boldsymbol{L}_{v}\right)_{\text {water}}=\mathbf{5 2} \mathbf{9} \) cal \( / \mathbf{g} \). In a
container of negligible mass \( 140 g \) of ice
initially at \( -15^{\circ} \mathrm{C} \) is added to \( 200 \mathrm{g} \) of
water that has a temperature of \( 40^{\circ} \mathrm{C} \). If no heat is lost to the surroundings, what is the final temperature of system
in \( ^{\circ} \boldsymbol{C} \) ?
Subject: Chemistry
Which is/are true statements?
A. Diamond is unaffected by conc acids but graphite reacts with hot conc. \( H N O_{3} \) forming mellitic acid, \( C_{6}(C O O H)_{6} \)
B. \( C O \) is toxic because it forms a complex with hemoglobin in the blood
\( \mathrm{C} \cdot \mathrm{C}_{3} \mathrm{O}_{2}, \) carbon sub-oxide, is a foul-smelling gas
D. All the above
Subject: Maths
Construct \( \triangle \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z} \) in which \( \angle \boldsymbol{Y}= \)
\( \mathbf{3 0}^{o}, \angle Z=\mathbf{6 0}^{\circ} \) and \( \boldsymbol{X} \boldsymbol{Y}+\boldsymbol{Y} \boldsymbol{Z}+\boldsymbol{Z} \boldsymbol{X}= \)
\( \mathbf{1 0} c \boldsymbol{m} \)
Subject: Chemistry
In which of the following reactions, the concentration of reactant is equal to the concentration of product at equilibrium? \( (K= \) equilibrium constant)
A. \( A \rightleftharpoons B ; K=0.01 \)
в. \( R \rightleftharpoons P ; K=1 \)
c. \( X \rightleftharpoons Y ; K=10 \)
D. \( L \rightleftharpoons J ; K=0.025 \)
Subject: Physics
A mercury thermometer reads \( 80^{\circ} \mathrm{C} \)
when the mercury is at \( 5.2 c m \) mark and
\( 60^{\circ} \mathrm{C} \) when the mercury is at \( 3.9 \mathrm{cm} \)
mark. The temperature (in \( ^{o} C \) ) when the
mercury level is at \( 2.6 \mathrm{cm} \) mark is \( 4 \times \)
\( \mathbf{1 0}^{x} \). Find the value of \( \boldsymbol{x} \)
Subject: Maths
Two straight lines passing through the point \( A(3,2) \) cut the line \( 2 y=x+3 \) and
x-axis perpendicularly at \( P \) and \( Q \) respectively. The equation of the line PQ
is
A. \( 7 x+y-21=0 \)
B. \( x+7 y+21=0 \)
\( \mathbf{c} \cdot 2 x+y-8=0 \)
D. \( x+2 y+8=0 \)
Subject: Physics
The velocity time graph of a particle
moving along a straight line has the form of a parabola \( \boldsymbol{v}=\boldsymbol{t}^{2}-\boldsymbol{6} \boldsymbol{t}+\boldsymbol{8} \mathrm{m} / \mathrm{s} . \) Find acceleration \( (\mathrm{in} \)
\( m / s^{2} \) ) when velocity is equal to zero:
This question has multiple correct options
A . 2
B. - -
c. 1
D. -
Subject: Physics
A parallel plate capacitor has area
\( 20 c m^{2} \) and separation between the plates is 0.1 m \( m . \) The dielectric break
down strength is \( 3 \times 10^{6} v / m \)

The maximum r.m.s voltage which can be safely applied is :
\( \mathbf{A} \cdot 210 V \)
в. \( 300 V \)
c. \( 100 V \)
D. 200
Subject: Maths
A die is thrown:
\( \boldsymbol{P} \) is the event of getting an odd number
\( Q \) is the event of getting an even number.
\( R \) is the event of getting a prime
number.
Which of the following pairs is mutually exclusive?
A. \( P, Q \)
в. \( Q, R \)
\( c . P, R \)
D. None of these
Subject: Chemistry
The electronegativity of fluorine
obtained from the following data is \( x \) \( \boldsymbol{E}_{\boldsymbol{H}-\boldsymbol{H}}=\mathbf{1 0 4} . \boldsymbol{2} \boldsymbol{k} \boldsymbol{c} \boldsymbol{n} \boldsymbol{m} \boldsymbol{l}^{-1} \)
\( \boldsymbol{E}_{\boldsymbol{F}-\boldsymbol{F}}=\mathbf{3 6 . 6} \) kcal \( \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{E}_{\boldsymbol{H}-\boldsymbol{F}}=\mathbf{1 3 4 . 6} \boldsymbol{k c a l} \boldsymbol{m o l}^{-1} \)
Electronegativity of hydrogen \( =2.1 \)
Find the value of \( x \) to the nearest
integer.
Subject: Chemistry
Which of the following is/are correct for
group 14 elements?
This question has multiple correct options
A. The stability of dihalide is in the order of \( P b X_{2}> \)
\( \operatorname{Sn} X_{2}>\operatorname{Ge} X_{2}>\operatorname{Si} X_{2}>C X_{2} \)
B. the ability to form \( p \Pi-p \Pi \) multiple bonds among
themselves increases down the group
C. the tendency for catenation decreases down the group
D. they all from oxides with the formula MO
Subject: Physics
A transparent solid cylindrical rod has a refractive index of \( \frac{2}{\sqrt{3}} . \) It is surrounded by air. A light ray is incident at the mid-
point of one end of the rod as shown in
the figure. The incident angle \( \theta \) for
which the light ray grazes along the wall
of the rod is -
\( \mathbf{A} \cdot \sin ^{-1}\left(\frac{1}{2}\right) \)
B. \( \sin ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
\( c \cdot \sin ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)
D \( \cdot \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
Subject: Maths
If \( a, b, c \) and \( d \) are in \( G . P . \) show that \( \left(a^{2}+b^{2}+c^{2}\right)\left(b^{2}+c^{2}+d^{2}\right)= \)
\( (a b+b c+c d)^{2} \)
Subject: Maths
The middle term in the expansion of
\( (1+x)^{2 n} \) is
A. \( \frac{1.3 .5 \ldots(2 n-1)}{n} x^{n} \)
B. \( \frac{1.3 .5 \ldots(2 n-1)}{n !} 2^{n-1} x^{n} \)
c. \( \frac{1.3 .5 \ldots(2 n-1)}{n !} x^{n} \)
D. \( \frac{1.3 .5 \ldots(2 n-1)}{n !} 2^{n} x^{n} \)
Subject: Chemistry
1 gram graphite on combustion in oxygen liberates \( 7.82 \mathrm{kcal} \) of heat. The amount of
heat evolved when 1 mole of oxygen is used in this oxidation process is:
\( \mathbf{A} \cdot 7.82 k c a l \)
B. 78.2 kcal
c. 9.384 kcal
D. \( 93.84 \mathrm{kcal} \)
Subject: Maths
\( \int x \cdot e^{x^{2}} d x= \)
A \( \cdot e^{x^{2}}+c \)
B. \( \frac{1}{2} e^{x^{2}}+c \)
\( \mathbf{C} \cdot-e^{x^{2}}+c \)
D. \( \frac{1}{7} e^{x^{2}}+c \)
Subject: Physics
The liquids shown in fig. in the two arms
are mercury (specific gravity \( =\mathbf{1 3 . 6} \) )
and water. If the difference of heights of
the mercury columns is \( 2 \mathrm{cm} \), find the
height h of the water column
\( A \cdot 27 c m \)
В. \( 30 \mathrm{cm} \)
\( c .35 c m \)
D. \( 440 \mathrm{cm} \)
Subject: Maths
The differential equation of the family of circles passing through the fixed points \( (a, 0) \) and \( (-a, 0) \) is:
A \( \cdot y_{1}\left(y^{2}-x^{2}\right)+2 x y+a^{2}=0 \)
B . \( y_{1} y^{2}+x y+a^{2} x^{2}=0 \)
C. \( y_{1}\left(y^{2}-x^{2}+a^{2}\right)+2 x y=0 \)
D. none of these
Subject: Maths
If \( \vec{a} \) and \( \vec{b} \) are two unit vectors such that \( \vec{a}+2 \vec{b} \) and \( 5 \vec{a}-4 \vec{b} \) are perpendicular
to each other then the angle between \( \vec{a} \) and \( \vec{b} \) is
A . 45
B. \( 60^{\circ} \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left(\frac{1}{3}\right) \)
D. \( \cos ^{-1}\left(\frac{2}{7}\right) \)
Subject: Physics
The end of a wire of length \( 0.5 \mathrm{m} \) and
radius \( 10^{-3} m \) is twisted through 0.80
radian. The shearing strain at the surface of wire will be :
A \( .1 .6 \times 10^{-3} \)
B . \( 1.6 \times 10^{3} \)
C \( .16 \times 10^{3} \)
D. \( 16 \times 10^{6} \)
Subject: Physics
A transmitter transmits at a wavelength
of \( 300 \mathrm{m} . \) A condenser of capacitance \( 2.4 \mu F \) is being used. The value of the
inductance for the resonant circuit is
approximately
B. \( 10^{-6} \) Н \( z \)
\( c \cdot 10^{-8} \mathrm{Hz} \)
D. \( 10^{-10} \) Н \( z \)
Subject: Chemistry
The correct statement among the following is:

This question has multiple correct options
A. the first ionization potential of \( A \) l is less than the first ionization potential of Mg
B. the second ionization potential of Mg is greater than the second ionization potential of \( \mathrm{Na} \)
C. the first ionization potential of Na is less than the first ionization potential of Mg
D. the third ionization potential of Mg is greater than the third ionization potential of Al
Subject: Physics
In the Wheatstone's network given, \( \boldsymbol{P}= \)
\( \mathbf{1 0 \Omega}, \boldsymbol{Q}=\mathbf{2 0 \Omega}, \boldsymbol{R}=\mathbf{1 5 \Omega}, \boldsymbol{S}=\mathbf{3 0 \Omega}, \) the
current passing through the battery (of
negligible internal resistance) is
A \( .0 .36 A \)
B. Zero
\( c .0 .18 A \)
D. \( 0.72 A \)
Subject: Chemistry
The wavelength of the first number of Balmer series of hydrogen spectrum is:
\( \left[\mathrm{R} \text { for hydrogen }=1.09678 \times 10^{7} \mathrm{m}^{-1}\right] \)
A \( .6564 \AA \)
в. 5743 А
c. 3782 ,
D. 7532 月
Subject: Chemistry
Which of the following compound(s) is/are peroxyacids? This question has multiple correct options
A \( . H C l O_{4} \)
в. \( H_{2} S O_{5} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{8} \)
D. \( H_{3} P O_{5} \)
Subject: Physics
A body cools down from \( 80^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in
10 Minutes when the temperature of
surrounding is \( 30^{\circ} \mathrm{C} \). The temperature
of the body after next 10 minutes will be:
A \( \cdot 30^{\circ} \mathrm{C} \)
B . \( 48^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 50^{\circ} C \)
D. \( 52^{\circ} \mathrm{C} \)
Subject: Physics
The energy of a photons is equal to the
kinetic energy of a proton. If \( \lambda_{1} \) is the de
Broglie wavelength of a proton, \( \lambda_{2} \) the wavelength associated with the photon, and if the energy of the photon is \( \mathrm{E} \), then
\( \left(\lambda_{1} / \lambda_{2}\right) \) is proportional to:
\( \mathbf{A} \cdot E^{4} \)
B. \( E^{1 / 2} \)
c. \( E^{2} \)
D. \( E \)
Subject: Physics
A charge \( q \) is released in presence of electric (E) and magnetic field (B) then
after some time its velocity is v then:-
\( A \cdot V \propto E \)
в. \( v \propto \frac{1}{E} \)
\( c \cdot V^{2} \propto E \)
D. \( V \propto B^{\circ} \)
Subject: Physics
A double convex lens has radii of
curvature of \( 1 \mathrm{m} \) and \( 2 \mathrm{m} \), What should
be the refractive index of the material
such that the focal length of the lens is \( 50 \mathrm{cm} ? \)
A \( \cdot 3 \frac{1}{3} \)
B. \( 2 \frac{1}{3} \)
\( c \cdot_{4} \frac{1}{3} \)
D. 1.13
Subject: Physics
When an object is moved along the
principal axis of a thin converging lens of focal length \( 12 \mathrm{cm} \), two images, three times the size of the object are obtained
when the object is at \( x_{1} \) and \( x_{2} \) distance from the lens. Which one of the following
could be the value of the ratio \( \frac{x_{1}}{x_{2}} ? \)
\( A \cdot 3 \)
B. 6
\( c \cdot 4 \)
D. 2
Subject: Physics
Two electric dipoles, \( A, B \) with respective dipole moments \( \overrightarrow{\boldsymbol{d}}_{\boldsymbol{A}}= \) \( -4 q a \hat{i} \) and \( \vec{d}_{B}=-2 q a \hat{i} \) placed on the
x-axis with a separation \( R \), as shown in the figure. The distance from \( A \) at which both of
them produce the same potential is
\( A \)
\[
\frac{\sqrt{2} R}{\sqrt{2}+1}
\]
в.
\[
\frac{R}{\sqrt{2}+1}
\]
\( c \)
\[
\frac{\sqrt{2} R}{\sqrt{2}-1}
\]
\( D \)
\[
\frac{R}{\sqrt{2}-1}
\]
Subject: Chemistry
The reactivity of 2 -bromo- 2 methylbutane \( (I), 1 \) -bromopentane \( (I I) \)
and \( 2- \) bromopentane \( (I I I) \) towards
\( \boldsymbol{S}_{N} 2 \) displacement is such that:
A \( I>I I>I I I \)
\( I \)
В. \( I>I I I>I I \)
c. \( I I>I I I>I \)
D. \( I I>I>I I I \)
Subject: Maths
toppr LoGin 5
Q Type your question
\( \begin{array}{llllll} & 0 & 10 & 20 & 30 & 40 \\ \text { Class } & - & - & - & - & - \\ & 10 & 20 & 30 & 40 & 50\end{array} \)
frequency \( 5 \quad 8 \quad \) 7 \( \quad \) 12
Subject: Maths
In a bolt factory, machines \( A, B \) and \( C \)
manufacture \( 25 \%, 35 \% \) and \( 40 \% \)
respectively of the total number of bolts.
The percentage of defective bolts
among the manufactured bolts is \( 5 \% \)
for \( A, 4 \% \) for \( B \) and \( 2 \% \) for \( C . \) A bolt is
drawn randomly from the manufactured
products and is found to be defective then
This question has multiple correct options
A. the probability that the selected bolt is defective \( = \) 0.0345
B. the probability that the defective bolt was manufactured by machine \( A=\frac{25}{69} \)
C. the probability that the defective bolt was manufactured by machine \( B=\frac{28}{69} \)
D. the probability that the defective bolt was manufactured by machine \( C=\frac{16}{69} \)
Subject: Chemistry
The \( p H \) of \( 0.1 M \) solution of the
following salts increases in the order:
A \( \cdot \operatorname{NaCl}<N H_{4}^{+}<N a C N<H C l \)
в. \( H C l<N H_{4}^{+}<N a C l<N a C N \)
c. \( \operatorname{NaCN}<N H_{4}^{+}<N a C l<H C l \)
D. \( H C l<N a C l<N a C N<N H_{4} \)
Subject: Physics
In the circuit shown the resistance of
voltmeter is 10,000 ohm and that of ammeter reading is 0.10 Amp and
voltmeter reading is 12 volt. Then \( R \) is
equal to
A . \( 120 \Omega \)
в. \( 140 \Omega \)
\( c \cdot 116 \Omega \)
D. 100\Omega
Subject: Maths
If \( \boldsymbol{y}=\sqrt{\frac{1-\sin 2 x}{1+\sin 2 x}}, \) then \( \left(\frac{d y}{d x}\right)_{x=0}= \)
This question has multiple correct options
A \( \cdot \frac{1}{2} \)
B.
c. -2
D.
Subject: Chemistry
Structures of nuclei of three atoms \( A, B \)
and \( C \) are given below-
A has 90 protons and 146 neutrons
B has 92 protons and 146 neutrons
C has 90 protons and 148 neutrons
Based on the above data, which of these
atoms are isotopes and which are
İsobars?
\( A \cdot A \) and \( C \) are isotopes; \( B \) and \( C \) are isobars
B. A and B are isotopes; A and C are isobars
C. \( B \) and \( C \) are isobars; \( A \) and \( B \) are isobars
D. \( A \) and \( C \) are isotopes; \( A \) and \( B \) are isobars
Subject: Physics
A solid sphere of mass \( M \) and radius \( 2 R \) rolls down an inclined plane of
height \( h \) without slipping. The speed of its center of mass when it reaches the
bottom is
A \( \cdot \sqrt{\frac{6}{7} g h} \)
B. \( \sqrt{3 g h} \)
c. \( \sqrt{\frac{10}{7} g h} \)
D. \( \sqrt{\frac{4}{3} g h} \)
Subject: Chemistry
Which is the correct order of bond
energy of single, double and triple bonds between carbon atoms?
A. \( C-C>C=C>C \equiv C \)
в. \( C=C>C \equiv C>C-C \)
c. \( C \equiv C>C-C>C=C \)
D. \( C \equiv C>C=C>C-C \)
\( C \)
Subject: Physics
A cylinder is filled with non-viscous
liquid of density d to a height \( h_{0} \) and \( a \)
hole is made at a height \( h_{1} \) from the
bottom of the cylinder. The velocity of the liquid issuing out of the hole is:
в. \( \sqrt{2 g\left(h_{0}-h_{1}\right)} \)
c. \( \sqrt{d g h_{1}} \)
D. \( \sqrt{d g h_{0}} \)
Subject: Physics
Block A of weight \( 100 \mathrm{N} \) reset on a frictionless inclined plane of slope
angle \( 430^{0} \) as shown in the figure. A
flexible cord attached to A passes over a
frictionless pulley and is connected to
block B of weight W. Find the weight \( \mathbf{W} \) of which the system is in equilibrium.
A . 25 N
в. 50 N
\( c .75 \mathrm{N} \)
D. 100 N
Subject: Maths
An example of the even number of terms
in an arithmetic progression written in a symmetrical format is?
A. \( a-d, a+d, a+2 d, a+4 d \)
B. \( a-2 d, a+d, a+2 d, a+3 d \)
c. \( a-3 d, a-d, a+d, a+3 d \)
D. \( a-2 d, a-d, a, a+d, a+2 d \)
Subject: Chemistry
The \( \left[A g^{+}\right] \) in a saturated solution of
\( A g_{2} C r O_{4} \) is \( 1.5 \times 10^{-4} M . \) What is the
solubility product of \( A g_{2} C r O_{4} ? \)
A \( \cdot 3.375 \times 10^{-12} \)
B. \( 1.6875 \times 10^{-10} \)
C \( .1 .6875 \times 10^{-11} \)
D. \( 1.6875 \times 10^{-12} \)
Subject: Physics
A person wants to drive on the vertical surface of a large cylindrical wooden 'well' commonly known as'death well' in a circus. The radius of the well is
2 meter, and the coefficient of friction
between the tyres of the motorcycle and
the wall of the well is \( 0.2, \) the minimum
speed the motorcyclist must have in order to prevent slipping should be
A. \( 10 \mathrm{m} / \mathrm{s} \)
в. \( 15 \mathrm{m} / \mathrm{s} \)
\( c .1 .98 m / s \)
D. \( 25 \mathrm{m} / \mathrm{s} \)
Subject: Maths
If \( \boldsymbol{y}=[\log (\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}+\mathbf{1}})]^{2} \)
Prove that \( \left(\mathbf{1}+\boldsymbol{x}^{2}\right) \frac{d^{2} \boldsymbol{y}}{d x^{2}}+\boldsymbol{x} \frac{d \boldsymbol{y}}{d \boldsymbol{x}}=\mathbf{2} \)
Subject: Chemistry
Observe the following statements:
1. Heavy water is harmful to the growth of animals.
2. Heavy water reacts with \( A l_{4} C l_{3} \) and
forms deuterated acetylene.
3. \( B a C l_{2} .2 D_{2} O \) is an example of interstitial deuterate
The correct statements are:
A. 1 and 3
B. 1 and 2
c. 1,2 and 3
D. 2 and 3
Subject: Physics
In Millikan oil drop experiment a charged drop falls with a terminal velocity V. If an electric field E is applied vertically upwards it moves with terminal velocity \( 2 V \) in upward
direction. If electric field reduces to \( \boldsymbol{E} / \mathbf{2} \)
then its terminal velocity will be-
A \( \cdot \frac{V}{2} \)
B.
c. \( \frac{3 V}{2} \)
D. \( 2 V \)
Subject: Physics
Two particles, A and B having equal charges, after being accelerated through the same potential difference enter into a region of uniform magnetic field and the particles describe circular
paths of radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) respectively.
The ratio of the masses of \( A \) and \( B \) is:
\( \mathbf{A} \cdot \sqrt{R_{1} / R_{2}} \)
в. \( R_{1} / R_{2} \)
c. \( \left(R_{1} / R_{2}\right)^{2} \)
\( \mathbf{D} \cdot\left(R_{2} / R_{1}\right)^{2} \)
Subject: Maths
Let \( A \) and \( B \) be two independent event then show that \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{1}- \)
\( \boldsymbol{P}\left(\boldsymbol{A}^{\prime}\right) \boldsymbol{P}\left(\boldsymbol{B}^{\prime}\right) \)
Subject: Chemistry
A lead storage battery has initially \( 200 g \) of lead and \( 200 g \) of \( P b O_{2}, \) plus
excess \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \) How long could this cell deliver a current of 10 amp, without
recharging, if it was possible to operate it so that the reaction goes to completion?
A. 2.48 hour
B. 3.48 hour
c. 4.48 hour
D. 6.48 hour
Subject: Maths
Differentiate
\( 2 x^{3 / 2}+2 x^{5 / 2}+C \)
A \( \cdot \frac{d y}{d x}=\sqrt{x}(3+5 x) \)
B. \( \frac{d y}{d x}=\sqrt{x}(3-5 x) \)
c. \( \frac{d y}{d x}=-\sqrt{x}(3+5 x) \)
D. None of these
Subject: Physics
A circular plate of diameter \( ^{\prime} \boldsymbol{d}^{\prime} \) is kept
in contact with a square plate of edge
\( d^{\prime} \) as shown in figure. The density of material and thickness are same
everywhere. The center of mass of the
composite system will be
A. inside the circular plate
B. inside the square plate
c. at the point of contact
D. outside the syestem
Subject: Chemistry
The Born Haber cycle below represents the energy changes occurring at \( 298 \mathrm{K} \) when \( \mathrm{KH} \) is formed from its elements
\( \mathbf{v}: \Delta \boldsymbol{H}_{\text {atomisation}} \mathrm{K}=\mathbf{9 0} \mathrm{kJ} / \mathrm{mol} \)
\( \mathbf{w}: \Delta \boldsymbol{H}_{\text {ionisation}} \mathbf{K}=\mathbf{4 1 8} \mathbf{k J} / \mathrm{mol} \)
\( \mathbf{x}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {dissociation}} \mathrm{H}=436 \mathrm{kJ} / \mathrm{mol} \)
\( \mathbf{y}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {electronaffinity}} \mathbf{H}=\mathbf{7 8} \mathbf{k} \mathbf{J} / \mathrm{mol} \)
\( \mathbf{z}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {lattice}} \mathrm{KH}=710 \mathrm{kJ} / \mathrm{mol} \)
In terms of the letters \( v \) to \( z \)
the expression for \( \Delta \boldsymbol{H}_{i} \) of \( \mathrm{K} \) is \( \boldsymbol{\Delta} \boldsymbol{H}_{i}=\boldsymbol{w} / 2 \)
If true enter 1 , else enter 0
A. 0
B. 1
\( c \cdot 2 \)
D. 3
Subject: Physics
Which of the following relation is true?
A. \( 3 Y=K(1+\sigma) \)
в. \( _{K}=\frac{9 \eta Y}{Y+\eta} \)
\( \mathbf{c} \cdot \sigma=(6 K+\eta) Y \)
D. \( \sigma=\frac{0.5 Y-\eta}{\eta} \)
Subject: Physics
A closely wound solenoid \( 80 \mathrm{cm} \) long
has 5 layers of winding of 400 turns each. The diameter of the solenoid is
1.8 \( c m . \) If the current \( 8.0 A \) flows in it
the magnitude of magnetic field inside the solenoid near its centre will be
\( \mathbf{A} \cdot 8 \pi \times 10^{-3} T \)
В . \( 6 \pi \times 10^{-3} T \)
c. \( 4 \pi \times 10^{-3} T \)
D. \( 3 \pi \times 10^{-3} T \)
Subject: Physics
The magnetic force acting on a charged particle of charge \( -2 \mu C \) in a magnetic
field of \( 2 T \) acting in y-direction, when the particle velocity is \( (2 \check{i}+3 j) \)
\( \times 10^{6} m s^{-1} \) is :
A. \( 8 \mathrm{N} \) in \( \mathrm{z} \) -direction
B. 4 N in Z-direction
c. 8 N in y-direction
D. 4 N in Y-direction
Subject: Chemistry
Which substance is wrongly paired
with the bonding found between the
molecules of that substance?
\( \mathbf{A} \cdot N H_{3}- \) hydrogen bonding
B. \( F_{2} \) -van der waals (dispersion) forces
c. \( H C l \) - dipoles
D. \( C H_{4} \) - dipoles
E . \( N a C l(a q) \) - molecule-ion attraction