AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
If the escape velocity on earth is 11.2km / sec, its value for a planet having double the radius and 8 times the mass of earth is \( \ldots . \boldsymbol{m} / \boldsymbol{s e c} \)
A . \( 11.2 \mathrm{km} / \mathrm{sec} \)
B. 22.4 km/sec
c. \( 5.6 \mathrm{km} / \mathrm{seco} \)
D. \( 8 \mathrm{km} / \mathrm{sec} \)
Subject: Chemistry
The pressure and temperature of \( 4 d m^{3} \) of carbon dioxide gas are doubled. Then volume of carbon dioxide would be :
\( \mathbf{A} \cdot 2 d m^{3} \)
B. \( 3 d m^{3} \)
\( \mathbf{c} \cdot 4 d m^{3} \)
D. \( 8 d m^{3} \)
Subject: Chemistry
Assertion
An atom is smallest particle in an element that has the properties of the element.
Reason
Molecules are formed by the
combination of two or more atoms
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
2-iodo cyclohexyl acrylate undergoes
acetolysis.Which of the following
statement(s) is/are true?

This question has multiple correct options
A. Trans-isomer of the substrate undergoes acetolysis 670 times faster than that of its cis-isomer.
B. Cis-isomer of the substrate undergoes cytolysis 670 times faster than that of its trans-isomer.
C. Both isomers undergo cytolysis with the same rate.
D. The enhanced rate of this nucleophilic substitution is due to neighbouring group participation.
Subject: Maths
If the length of a rectangle is two times its breadth and area is \( 228 \mathrm{cm}^{2} \), then
length and breadth are respectively
A \( .20 \mathrm{cm}, 10 \mathrm{cm} \)
в. \( 12 \mathrm{cm}, 24 \mathrm{cm} \)
c. \( 24 c m, 12 c m \)
D. \( 16 \mathrm{cm}, 18 \mathrm{cm} \)
Subject: Maths
Factorise \( : 8 x^{3}-27 y^{3}-2 x+3 y \)
A \( \cdot(2 x+3 y)\left(4 x^{2}-x y+9 y^{2}+1\right) \)
В \( \cdot(2 x+y)\left(4 x^{2}-6 x y-9 y^{2}\right) \)
C \( \cdot(x-3 y)\left(4 x^{2}-3 x y+9 y^{2}\right) \)
D \( \cdot(2 x-3 y)\left(4 x^{2}+6 x y+9 y^{2}-1\right) \)
Subject: Maths
The value of the expression \( \mathbf{2}^{k}\left(\begin{array}{l}n \\ \mathbf{0}\end{array}\right)\left(\begin{array}{l}\boldsymbol{n} \\ \boldsymbol{k}\end{array}\right)-\mathbf{2}^{k-1}\left(\begin{array}{l}\boldsymbol{n} \\ \mathbf{1}\end{array}\right)\left(\begin{array}{l}\boldsymbol{n}-\mathbf{1} \\ \boldsymbol{k}-\mathbf{1}\end{array}\right)+ \)
\( 2^{k-2}\left(\begin{array}{l}n \\ 2\end{array}\right)\left(\begin{array}{l}n-2 \\ k-2\end{array}\right) \dots+ \)
\( (-1)^{k}\left(\begin{array}{c}n \\ k\end{array}\right)\left(\begin{array}{c}n-k \\ 0\end{array}\right) \) is
\( A \cdot\left(\begin{array}{l}n \\ k\end{array}\right. \)
\( ^{\mathbf{B}} \cdot\left(\begin{array}{c}n+1 \\ k\end{array}\right) \)
c. \( \left(\begin{array}{c}n+1 \\ k+1\end{array}\right) \)
D. \( \left(\begin{array}{l}n-1 \\ k-1\end{array}\right) \)
Subject: Maths
We know that any odd positive integer
is of the form \( 4 q+1 \) or \( 4 q+3 \) for some
integer \( \boldsymbol{q} \) Thus, we have the following two cases.
A \( \cdot n^{2}-1 \) is divisible by 8
B . \( n^{2}+1 \) is divisible by 8
c. \( n-1 \) is divisible by 8
D. \( n+1 \) is divisible by 8
Subject: Physics
Two parallel plate air capacitors of
same capacity' \( C^{\prime} \) are connected in
series to a battery of emf ' \( E^{\prime} . \) Then one
of the capacitors is completely filled
with dielectric material of constant \( ^{\prime} \boldsymbol{K}^{\prime} \)
The change in the effective capacity of
the series combination is
A \( \cdot \frac{C}{2}\left[\frac{K-1}{K+1}\right] \)
B \( \cdot \frac{2}{C}\left[\frac{K-1}{K+1}\right] \)
c. \( \frac{C}{2}\left[\frac{K+1}{K-1}\right] \)
\( ^{\mathrm{D}} \cdot \frac{C}{2}\left[\frac{K-1}{K+1}\right]^{2} \)
Subject: Physics
Three magnets of the same length but
moments \( \mathrm{M}, 2 \mathrm{M} \) and \( 3 \mathrm{M} \) are arranged in the forms of an equilateral triangle with opposite pole nearer, the resultant
magnetic moment of the arrangement is?
A. 6 м
B. zero
c. \( \sqrt{3} \) м
D. \( \frac{\sqrt{3}}{2} \) M
Subject: Physics
Assertion
Heater wire must have high resistance than connecting wires and high metallic point.
Reason
If resistance is high, the electrical
conductivity will be less.
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
Choose the correct relation between \( u, v \)
and \( r \) for a spherical mirror:
A \( \cdot r=\frac{2 u v}{u+v} \)
B. \( r=\frac{2}{u+v} \)
c. \( r=\frac{2(u+v)}{(u v)} \)
D. \( r=\frac{u v}{u+v} \)
Subject: Chemistry
The dissociation of water at \( 25^{\circ} \mathrm{C} \) is
\( 1.9 \times 10^{-7} \% \) and the density of water is
1.0 g/cc. The ionisation constant of water is :
A. \( 3.42 \times 10^{-6} \)
В. \( 3.42 \times 10^{-8} \)
c. \( 1.00 \times 10^{-14} \)
D. \( 2.00 \times 10^{-16} \)
Subject: Chemistry
Consider the following compounds.
\( (i) I C I(i i) I B r(i i i) I C I_{3}(i v) S F_{4} \)
\( (v) B r F_{3}(v i) I F_{3}(v i i) B r F_{5}(v i i i) I F_{7} \)
Calculate the value of \( \left[\frac{\boldsymbol{P}^{2}-\boldsymbol{Q}^{2}}{\boldsymbol{R}+\boldsymbol{S}}\right] \)
Here,
\( \boldsymbol{P}: \) Total number of polar compounds
\( Q: \) Total number of planar compounds
\( R: \) Total number of non polar compounds
\( \boldsymbol{S}: \) Total number of non planar compounds
A. 6
B. 7
\( c \cdot 4 \)
D.
Subject: Maths
Vectors \( \boldsymbol{a} \times(\boldsymbol{b} \times \boldsymbol{c}), \boldsymbol{b} \times(\boldsymbol{c} \times \boldsymbol{a}) \) and
\( \boldsymbol{c} \times(\boldsymbol{a} \times \boldsymbol{b}) \) are
A. linearly dependent vectors
B. equal vectors
c. parallel vectors
D. none of these
Subject: Chemistry
The halogen (Group 17 elements):
A. have an electron configuration of a noble gas less seven electrons
B. are highly electro positive
C. show variable oxidation state of -1,+1,+3,+5 and +7 in their various compounds
D. forms a volatile, covalent hydrides \( H X \) in which the halogen \( (X) \) shows an oxidation state of +1
Subject: Chemistry
Assertion
Pent-1-ene and 2-methylbut-1-ene are position isomers.
Reason
Position isomers have the same
molecular formula but differ in the
position of functional group.
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 and Reason are correct
Subject: Physics
The position of a particle is given by \( \vec{r}=(\hat{i}+2 \hat{j}-\hat{k}) \) and momentum \( \vec{P}= \)
\( (3 \hat{i}+4 \hat{j}-2 \hat{k}) . \) The angular momentum is perpendicular to
A. X-axis
B. Y-axis
c. z-axis
D. Line at equal angles to all the three axes
Subject: Chemistry
According to the Nernst equation, the potential of an electrode changes by
\( \mathbf{5 9 . 2} \boldsymbol{m} \boldsymbol{V} \) whenever the ratio of the
oxidized and the reduced species
changes by a factor of 10 at \( 25^{\circ} \mathrm{C} \). What would be the corresponding change in the electrode potential if the
experiment is carried out at \( 30^{\circ} \mathrm{C} \) ?
A. \( 59.2 \mathrm{mV} \)
в. \( 71.0 \mathrm{mV} \)
c. \( 60.2 \mathrm{mV} \)
D. None of above
Subject: Maths
Two straight lines \( u=0 \) and \( v=0 \) pass through the origin and angle between them is \( \tan ^{-1}\left(\frac{7}{9}\right) . \) If the ratio of the slope of \( v=0 \) and \( u=0 \) is \( \frac{9}{2} \) then their equations are
This question has multiple correct options
A. \( y+3 x=0 \) and \( 3 y+2 x=0 \)
B. \( 2 y+3 x=0 \) and \( 3 y+x=0 \)
c. \( 2 y=3 x \) and \( 3 y=x \)
D. \( y=3 x \) and \( 3 y=2 x \)
Subject: Physics
A current loop consists of two identical
semicircular parts each of radius \( \mathrm{R} \), one
lying in the \( x \) -y plane and the other in \( x-z \)
plane. If the current in the loop is i., the
resultant magnetic field due to the two
semicircular parts at their common
centre is
A \( \cdot \frac{\mu_{0} i}{\sqrt{2} R} \)
В. \( \frac{\mu_{0} i}{2 \sqrt{2} R} \)
c. \( \frac{\mu_{0} i}{2 R} \)
D. \( \frac{\mu_{0} i}{4 R} \)
Subject: Chemistry
One of the acid listed below is formed
only from \( P_{2} O_{3} \), the rest are formed
from \( P_{2} O_{5} . \) Acid formed from \( P_{2} O_{3} \) is :
A. \( H P O_{3} \)
в. \( H_{2} P_{2} O_{7} \)
c. \( H_{2} P O_{4} \)
D. \( H_{3} P O_{3} \)
Subject: Maths
It is required to fix a pipe such that water flowing through it at a speed of \( 7 m \) per minutes fills a tank of capacity
440 cubic metres in 10 minutes. The
inner radius of the pipe should be:
A. \( \sqrt{2} m \)
в. \( 2 m \)
c. \( \frac{1}{2} m \)
D. \( \frac{1}{\sqrt{2}} m \)
Subject: Physics
Assertion: There exist two angles of
incidence for the same magnitude of deviation (except minimum deviation)
by a prism kept in the air. Reason: In a prism kept in the air, a ray is incident on the first surface and
emerges out of the second surface. Now
if another ray is incident on second. surface (of the prism) along the
previous emergent ray, then this ray emerges out of the first surface along
the previous incident ray. This principle is called the principle of reversibility of light.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Chemistry
\( K F \) combines with \( H F \) to form \( K H F_{2} \)
The compound contains the species:
A \( \cdot K^{+}, F^{-} \) and \( H^{*} \)
B. \( K^{+}, F^{-} \) and \( H F \)
c. \( K^{+} \) and \( \left[H F_{2}\right]^{-} \)
D. \( [K H F]^{+} \) and \( F_{2} \)
Subject: Physics
In the nuclear reaction \( _{1} H^{2}+_{1} H^{2} \rightarrow_{2} \)
\( H e^{3}+_{0} n^{1} \) if the mass of the deuterium
atom \( =2.014741 a m u, \) mass of \( _{2} H e^{3} \)
atom \( =3.016977 a m u, \) and mass of
neutron \( =1.008987 a m u, \) then the \( Q \)
value of the reaction is nearly
A. 0.00352 Mev
B. 3.27 MeV
c. 0.82 Mev
D. 2.45 MeV
Subject: Chemistry
Assertion
Chlorine water must be stored in dark
colored bottles.
Reason
Hypochlorous acid on exposure to
sunlight decomposes to \( H_{2} \) and \( C l_{2} \)
gas.
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
An object is placed at the centre of
curvature of a concave mirror of radius
of curvature \( 20 \mathrm{cm} . \) The nature and
position of the image shall be.
A. Virtual and \( 15 \mathrm{cm} \) from the mirror
B. Real and \( 20 \mathrm{cm} \) from the mirror
c. virtual and \( 20 \mathrm{cm} \) from the mirror
D. Real and \( 10 \mathrm{cm} \) from the mirror
Subject: Maths
Tangent \( 0 A \) and \( O B \) are drawn for
\( O(0,0) \) to the circle \( (x-1)^{2}+(y- \)
1) \( ^{2}=1 \)
Equation of the circumcircle of triangle
OAB is
A \( \cdot x^{2}+y^{2}+x+y=0 \)
B . \( x^{2}+y^{2}-x+y=0 \)
c. \( x^{2}+y^{2}+x-y=0 \)
D. \( x^{2}+y^{2}-x-y=0 \)
Subject: Physics
The Base-Emitter voltage for a CE
transistor used as an amplifier is \( 0.02 \mathrm{V} \) An input signal given to this transistor results in a change of base current by, \( 20 \mu A \) and a changes of \( 2 \mathrm{mA} \) takes
place in the collector current. Calculate the following quantities:
1. Input resistance.
2. A.C. current gain
3. Transconductance.
4. If the load resistance is \( 5 k \Omega \) what will
be the voltage gain.
Subject: Chemistry
An organic compound whose empirical and molecular formula are same.
Contains \( 20 \% \) carbon, \( 6.7 \% \) hydrogen,
\( 46.7 \% \) nitrogen, and the rest oxygen on
heating it yields ammonia, leaving a solid residue. The solid residue gives a violet colour with dilute solution of
alkaline copper sulphate the organic compound is
\( \mathbf{A} \cdot N H_{2} C O O N H_{4} \)
B . \( C H_{3} C O O N H_{4} \)
\( \mathbf{c} \cdot N H_{2} N H C H O \)
D. \( H C O O N H_{4} \)
E \( . N H_{2} C O N H_{2} \)
Subject: Maths
A ladder \( 13 \mathrm{m} \) long leans against a wall. The foot of the ladder is pulled along the
ground away from the wall, at the rate
\( 1.5 \mathrm{m} / \mathrm{sec} . \) How fast is the angle \( \theta \) between the ladder and the ground is changing when the foot of the ladder is
\( 12 \mathrm{m} \) away from the wall.
Subject: Maths
The value of \( \int_{0} \overline{\mathbf{2}} \log \left(\frac{\mathbf{4}+\mathbf{3} \sin \boldsymbol{x}}{\mathbf{4}+\mathbf{3} \cos \boldsymbol{x}}\right) \boldsymbol{d} \boldsymbol{x} \) is
A . 2
B. \( \frac{3}{4} \)
\( c \cdot 0 \)
D. - 2
Subject: Maths
A man travelling east at \( 8 \mathrm{km} \) per hour
find that the wind seems to blow
directly from the north. On doubling the speed, he finds that it appears to come from N-E. Find the velocity of the wind and it's direction.
A. \( 8 \sqrt{2} \), its direction is from \( N-S \). . Its direction is
B. \( 8 \sqrt{2} \), its direction is from \( N-w \)
c. \( 8 \sqrt{2} \), its direction is from s-w.
D. None of these
Subject: Maths
In a game called 'odd man out', \( m(m> \)
2) persons toss a coin to determine who
will buy refreshment for the entire
group. A person who gets an outcome
different from that of the rest of the
members of the group is called the odd man out. The probability that there is a
loser in any game is
A. \( 1 / 2 m \)
в. \( m / 2^{m-1} \)
c. \( 2 / m \)
D. none of these
Subject: Maths
If \( f(x)=\left\{\begin{array}{cl}x-1, & x \geq 1 \\ 2 x^{2}-2, & x<1\end{array}, g(x)=\right. \)
\( \left\{\begin{array}{cl}\boldsymbol{x}+\mathbf{1}, & \boldsymbol{x}>\mathbf{0} \\ -\boldsymbol{x}^{2}+\mathbf{1}, & \boldsymbol{x} \leq \mathbf{0}\end{array}, \text { and } \boldsymbol{h}(\boldsymbol{x})=|\boldsymbol{x}| \), then \right.
\( \lim _{x \rightarrow 0} f(g(h(x))) \) is
A.
B.
\( c \cdot 2 \)
\( D \)
Subject: Physics
A convex lens of focal length \( 20 \mathrm{cm} \) is placed coaxially with a concave mirror of focal length \( 10 \mathrm{cm} \) at a distance of
\( 50 c m \) apart from each other. A beam of
light coming parallel to the principal axis is incident on the convex lens. Find
the position of the final image formed by this combination. Draw the ray diagram showing the formation of the image.
Subject: Chemistry
Which of the following statements
is/are correct?
This question has multiple correct options
A. \( 4- \) Chlorophenol \( (I) \) will dissolve in \( N a O H \) but \( 4- \)
chloro \( -1- \) methyl benzene (II) will not.
B. \( 4- \) Methylbenzoic \( (I I I) \) acid will dissolve in
aq.NaHCO\( _{3} \) ) but \( 4- \) methylphenol(\( I V \) ) will not.
C \( .2,4,6- \) Trinitrophenol \( (V) \) will dissolve in
aq.NaHCO\( _{3} \) ) but \( 4- \) methylphenol \( (V I) \) will not
D. \( 4- \) Ethylphenol \( (V I I) \) will dissolve in aq. \( N a O H \) but
ethyl phenyl ether \( (V I I) \) will not.
Subject: Physics
Assertion
\( 1 m m^{2}=10^{-6} m^{2} \)
Reason
The numerical value of physical quantity is less for a smaller unit.
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
If \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \) and \( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})>\mathbf{0} \) for all \( \boldsymbol{x}>\mathbf{0} \)
then \( \frac{\boldsymbol{f}(\boldsymbol{x})}{\boldsymbol{x}} \)
A \( \cdot \) decreases on \( (0, \infty) \)
B . increases on \( (0, \infty) \)
c. decreases on \( (1, \infty) \)
D. neither increases nor decreases on \( (0, \infty) \)
Subject: Biology
Match the correct one
A. A: afferent arteriole, B: Proximal convoluted tubule, C
Henle's loop, D: Distal convoluted tubule, E: Peritubular
capillaries, F: collecting duct
B. F: efferent arteriole, B: PCT, C: Henle's loop, D: DCT, E:
peritubular capillaries, F: collecting duct
C. A: afferent arteriole, B: peritubular capillaries, C:
Henle's loop, D: DCT, E: PCT, F: collecting duct
D. A: afferent arteriole, B: Henle's loop, C: collecting ductt
D: PCT, E: DCT, F: peritubular capillaries
Subject: Maths
\( \int_{0}^{\pi / 2} \sin 2 x \tan ^{-1}(\sin x) d x= \)
A. \( \frac{\pi}{2}-1 \)
B. \( \frac{\pi}{2}+1 \)
c. \( \frac{3 \pi}{2}+1 \)
D. \( \frac{3 \pi}{2}-1 \)
Subject: Chemistry
The concentration of a solution is
\( \mathbf{1 0}^{-4} \boldsymbol{M} \) for \( \boldsymbol{C l}^{-}, \mathbf{1 0}^{-\mathbf{5}} \boldsymbol{M} \) for \( \boldsymbol{B r}^{-} \) and
\( 10^{-3} \mathrm{M} \) for \( I^{-} . A g N O_{3}(s) \) is added slowly to the solution. If the minimum
concentration of \( \boldsymbol{A} \boldsymbol{g}^{+} \) required to start
precipitation of all three ions is \( 10^{-x} \)
then the value of \( x \) is
\( \left[\text { Given, } \boldsymbol{K}_{s p(A g C l)}=\mathbf{1 0}^{-\mathbf{1 0}}, \boldsymbol{K}_{s p(A g B r)}=\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{1 3}}, \boldsymbol{K}_{\boldsymbol{s p}(\boldsymbol{A g I})}=\mathbf{1 0}^{-\mathbf{1 7}}\right] \)
Subject: Physics
By which factor the magnetic field produced by a wire at distance \( 2 \mathrm{cm} \) from the wire than at \( 4 \mathrm{cm} \) from the wire
is stronger if wire length is \( 2 \mathrm{m} \) and carries a 10 -amp current :
A .2
B. \( 2 \sqrt{2} \)
\( c \cdot 4 \)
D. \( 4 \sqrt{2} \)
\( E \)
Subject: Physics
A mass of \( 2.0 \mathrm{kg} \) is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and
released the mass executes a simple harmonic motion. The spring constant is \( 200 \mathrm{N} / \mathrm{m} \). What should be the
minimum amplitude of the motion, so
that the mass gets detached from the
pan?
(Take \( \left.g=10 m / s^{2}\right) \)
A. \( 8.0 \mathrm{cm} \)
B. 10.0 \( \mathrm{cm} \)
c. Any values less than \( 12.0 \mathrm{cm} \)
D. 4.0 \( \mathrm{cm} \)
Subject: Maths
The value of \( \lim _{x \rightarrow 0} \frac{1-\cos ^{3} x}{x \sin x \cos x} \) is?
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{3}{2} \)
D.
Subject: Biology
In the given figure, \( A, B, C, D, E \) and \( F \)
represent some stages of hydrosere.
Select the correct statement regarding
these.
A. Hydrilla and Potamogeton occur in stage \( A \); Nymphaea and Nelumbo occur in stage B
B. Phragmites and Typha occur in stage \( C ; \) Carex and Cyperus occur in stage \( \mathrm{D} \)
C. Aluns and Populus occur in stage \( \mathrm{E} \); Acer and Quercus occur in stage \( F \)
D. All of these
Subject: Physics
If \( \overrightarrow{\boldsymbol{A}}=(1,1,1), \vec{C}=(0,1,-1) \) are given
vectors, then a vector \( \vec{B} \) satisfying the equation \( \overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}=\overrightarrow{\boldsymbol{C}} \) and
\( \vec{A} \cdot \vec{B}=3 \) is :
\( A \cdot(5,2,2) \)
B. \( \left(\frac{5}{3}, \frac{2}{3}, \frac{2}{3}\right) \)
c. \( \left(\frac{2}{3}, \frac{5}{3}, \frac{2}{3}\right) \)
D. \( \left(\frac{2}{3}, \frac{2}{3}, \frac{5}{3}\right) \)
Subject: Physics
A particle is projected at an angle of \( 30^{\circ} \) with the horizontal with a momentum \( \boldsymbol{P} \)
At the highest point its momentum is
A \( \cdot \frac{\sqrt{3}}{2} P \)
в. \( \frac{2}{\sqrt{3}} P \)
\( c . P \)
D. \( \frac{1}{2} P \)
Subject: Maths
The sum \( \frac{3}{1.2}, \frac{3}{1.2}, \frac{1}{2}, \frac{4}{2.3}\left(\frac{1}{2}\right)^{2}+\frac{5}{3.4}\left(\frac{1}{2}\right)^{2} \)
A \( \cdot 1-\frac{1}{(n+1) 2^{n}} \)
B. \( 1-\frac{1}{n .2^{n-1}} \)
\( \mathbf{C} \cdot 1=\frac{1}{(n+1) 2^{n}} \)
D. \( \frac{1}{(n-1) 2^{n-1}} \)
Subject: Maths
\( \operatorname{Let} f(x)=\left\{\begin{array}{l}x+1, x>0 \\ 2-x, x \leq 0\end{array} \text { and } g(x)=\right. \)
\( \left\{\begin{array}{c}x+1, x<1 \\ x^{2}-2 x-2,1 \leq x<2 \\ x-5, x \geq 2\end{array}\right. \)
Find the LHL and RHLof \( g(f(x)) \) at \( x=0 \) lim
and, hence, find \( _{\boldsymbol{x} \rightarrow 0} g(f(x)) \)
Subject: Maths
What is \( \tan ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1}\left(\frac{1}{3}\right) \) equa
to?
A \( \cdot \frac{\pi}{2} \)
в. \( \frac{\pi}{3} \)
c. \( \frac{\pi}{4} \)
D.
Subject: Physics
An electric dipole of momentum \( \vec{p} \) is placed in a uniform electric field. The
dipole is rotated through a very smal angle from equilibrium and is released. Prove that it executes simple harmonic motion with frequency \( f=\frac{1}{2 \pi} \sqrt{\frac{p E}{I}} \)
Where, \( I= \) moment of inertia of the
dipole.
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{t} & \boldsymbol{t}+\mathbf{1} \\ \boldsymbol{t}-\mathbf{1} & \boldsymbol{t}\end{array}\right] \) is a matrix such
that \( A A^{T}=I_{2} \) then trace of the matrix
is
A . 2
B. 0
\( c \cdot 4 \)
\( D \)
Subject: Maths
f \( \boldsymbol{x}=\sin t, \boldsymbol{y}=\sin \boldsymbol{k} \boldsymbol{t} \) satisfies
\( \left(1-x^{2}\right) y_{2}-x y_{1}+A y=0 \) then \( A \) is
Equal to
\( A \cdot k \)
B.
\( \mathbf{c} \cdot k^{2} \)
D. \( 1+k \)
Subject: Maths
If \( y=\tan ^{-1}\left(\frac{4 x}{1+5 x^{2}}\right)+ \)
\( \tan ^{-1}\left(\frac{2+3 x}{2-3 x}\right), \) then \( \frac{d y}{d x} \) is
\( \frac{1}{1+4 x^{2}} \)
- s. \( \frac{3}{1+4 x^{2}} \)
\( \frac{5}{1+25 x^{2}} \)
\( \frac{5}{\left(1+25 x^{2}\right)}-\frac{1}{\left(1+x^{2}\right)}-\frac{1.5}{\left(1+2.25 x^{2}\right)} \)
Subject: Maths
\( \operatorname{Let} \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1 \) for \( x>0, y>0, z>0 \)
Which of the following sets could be the possible values of \( (x-1)(y-1)(z-1) ? \) This question has multiple correct options
B. \( [11, \infty) \)
\( c \cdot[7, \infty) \)
D. \( [6, \infty) \)
Subject: Physics
A dipole consisting of \( +10 n C \) and \( -10 n C \) separated by a distance of \( 2 \mathrm{cm} \) oscillates in an electric filed of strength \( 60,000 \mathrm{Vm}^{-1} . \) The frequency of its
oscillation is (Moment of inertia about the axis of oscillations is \( 3 \times 10^{-10} \mathrm{kgm}^{2} \) ):
A . \( 20.2 \mathrm{Hz} \)
в. \( 25.4 \mathrm{Hz} \)
c. \( 31.38 H z \)
D. \( 37.1 \mathrm{Hz} \)
Subject: Chemistry
The disintegration energy \( Q \) for the change \( _{Z}^{A} \mathbf{X} \stackrel{-\alpha}{\longrightarrow} \underset{Z-2}{A-4} \mathbf{D}+Q \) is given by
\( \boldsymbol{Q}=\left[\boldsymbol{M}\left(\begin{array}{l}A \mathbf{X} \\ Z\end{array}\right)-\boldsymbol{M}\left(\begin{array}{l}\boldsymbol{A}-\mathbf{4} \\ \boldsymbol{Z}-\mathbf{2}\end{array} \mathbf{D}\right)-\right. \)
\( \left.M\left(_{2}^{4} \mathbf{H e}\right)\right] C^{2}, \) where \( M \) represents the
mass of respective nuclei reported in
paranthesis and \( C \) is speed of light. For
\( \alpha \) -decay :
A. \( Q=+v e \)
В. \( Q=-v e \)
c. \( Q=0 \)
D. not related with \( Q \)
Subject: Physics
If the ratio of lengths, radii and Youngs
modulii of steel and brass wires in the
figure are a, b and c respectively. Then the corresponding ratio of increase in
their lengths would be:
A \( \cdot \frac{2 a}{h^{2}} \)
в. \( \frac{3 a}{2 b^{2} c} \)
c. \( \frac{3 c}{2 a b^{2}} \)
D. \( \frac{2 a^{2}}{b} \)
Subject: Chemistry
A \( 5.25 \% \) solution of a substance is isotonic with a \( 1.5 \% \) solution of urea
(molar mass \( =60 g m o l^{-1} \) ) in the same
solvent. If the densities of both the
solutions are assumed to be equal to \( 1.0 g c m^{-3}, \) molar mass of the substance will be:
A . \( 105.0 g \) mol \( ^{-1} \)
B. \( 210.0 g \) mol \( ^{-1} \)
c. \( 90.0 g \) mol \( ^{-1} \)
D. \( 15.0 g m o l^{-1} \)