AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
A: Tetracyanomethane
B: Carbondioxide
C: Benzene
\( \mathbf{C}: \mathbf{1}, \mathbf{3}-\boldsymbol{b} \boldsymbol{u} \boldsymbol{t} \boldsymbol{a}-\boldsymbol{d} \boldsymbol{i}-\boldsymbol{e} \boldsymbol{n} \boldsymbol{e} \)
Ratio of \( \sigma \) and \( \pi: \)
A . in A and B are equal
B. in C and D are equal
\( c . \) is same in \( A, B, C, \) and \( D \)
D. in B and D are equal
Subject: Physics
A battery of internal resistance \( 4 \Omega \) is
connected tot he network of resistance
as shown. In order to give the maximum power to the network, the value of \( \operatorname{Rin} \Omega \)
should be:
\( A \cdot \frac{4}{9} \)
\( B \cdot \frac{8}{9} \)
\( c \cdot 2 \)
\( D \cdot 18 \)
Subject: Chemistry
The hydrolysis of 1 mol of
peroxodisulphuric acid produces
A. 2 mol of sulphuric acid
B. 2 mol of peroxomonosulphuric acid
c. 1 mol each of sulphuric acid and peroxomonosulphuric acid
D. 1 mol each of sulphuric acid, peroxomonosulphuric acid and hydrogen peroxide
Subject: Physics
Assertion
The universal gravitational constant is same as acceleration due to gravity.
Reason
Gravitational constant and acceleration
due to gravity have same units.
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
Find \( g \) o \( f \) and \( f \circ g \) if \( f: R \rightarrow R \) and \( g: \)
\( R \rightarrow R \) are given by \( f(x)=\cos x \) and
\( g(x)=3 x^{2} . \) Show that \( g \circ f \neq f \circ g \)
Subject: Physics
Three condensers are connected as
shown in series. If the insulated plate of
\( C_{1} \) is at \( 45 V \) one plate of \( C_{3} \) is earthed
find the p.d between the plate of \( C_{2} \)
A . \( 10 V \)
B . \( 20 V \)
\( c .30 V \)
D. \( 45 V \)
Subject: Chemistry
Which of the following is/are correct?
This question has multiple correct options
A. Enthalpy (numerical value) of physisorption is greater than that of chemisorption.
B. Physisorption is not very specific but chemisorption is highly specific.
C. Chemisorption takes place at relatively high temperatures.
D. In physisorption, generally multi - molecular layers are formed on the adsorbent.
Subject: Physics
A uniformly charged solid sphere or
radius \( \boldsymbol{R} \) has potential \( \boldsymbol{V}_{\mathbf{0}} \) (measured
with respect to \( \infty \) ) on its surface. For
this sphere the equipotential surfaces with potentials \( \frac{3 V_{0}}{2}, \frac{5 V_{0}}{4}, \frac{3 V_{0}}{4}, \frac{V_{0}}{4} \)
have radius \( \boldsymbol{R}_{1}, \boldsymbol{R}_{2}, \boldsymbol{R}_{3} \) and \( \boldsymbol{R}_{4} \)
respectively. Then
A \( \cdot R_{1}=0 \) and \( R_{2}\left(R_{4}-R_{3}\right) \)
B . \( R_{1} \neq 0 \) and \( \left(R_{1}-R_{1}\right)>\left(R_{4}-R_{3}\right) \)
c. \( R_{1}=0 \) and \( R_{2}>\left(R_{4}-R_{3}\right) \)
D. none of these
Subject: Physics
Assertion
The value of 1 Micron is equal to \( 10^{-5} m \)
Reason
Micron is the unit for measuring
microscopic distance.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
A man of mass \( 60 \mathrm{kg} \) start falling from
building of height \( 80 m \) with a bag of \( 2 k g \) in his hand. After falling through a
distance \( 20 m \) he throw the bag horizontally with respect to him so that he fail in a pond \( 2 m \) away from the vertical lines of fail. Calculate horizontal
distance of bag from the vertical line of fall where it lands. (take \( \left.g=10 m / s^{2}\right) \)
Subject: Physics
A horizontal parallel beam of light
passes through a vertical convex lens of
focal length \( 20 \mathrm{cm} \) and is then reflected by a titled plane mirror so that it coverages to a point I. The distance Pl is \( 10 \mathrm{cm} \)
M is a point at which the axis of the lens
intersects the mirror. The distance PM
is \( 10 \mathrm{cm} . \) The angle which the mirror makes with the horizontal is
\( \mathbf{A} \cdot 15^{\circ} \)
B. \( 30^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
Subject: Chemistry
Solid Ammonium carbamate
dissociates as:
\( N H_{2} C O O N H_{4}(s) \rightleftharpoons 2 N H_{3}(g)+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) \)
In a closed vessel, solid ammonium
carbonate is in equilibrium with its dissociation products. At equilibrium, ammonia is added such that the partial
pressure of \( N H_{3} \) at new equilibrium
now equals the original total pressure. Calculate the ratio of total pressure at new equilibrium to that of original total
pressure.
A \( \cdot \frac{31}{27} \)
в. \( \frac{17}{7} \)
c. \( \frac{49}{29} \)
D. None of these
Subject: Physics
A ray of light from a denser medium strikes a rarer medium at an angle of incidence \( i . \) If the reflected and
refracted rays are mutually perpendicular to each other then the critical angle is :
\( A \cdot \sin ^{-1}(\tan i) \)
B. \( \cos ^{-1}(\tan i) \)
\( c \cdot \cot ^{-1}(\tan i) \)
D. \( \operatorname{cosec}^{-1}(\tan i) \)
Subject: Maths
\( z_{1} \) and \( z_{2} \) are two distinct points in an
Argand plane. If \( a\left|z_{1}\right|=b\left|z_{2}\right| \) (where \( a, b \)
\( \epsilon \mathrm{R} \) ), then the point \( \left(a z_{1} / b z_{2}\right)+ \)
\( \left(b z_{2} / a z_{1}\right) \) is a point on the
A. Line segment [-2, 2] of the real axis
B. Line segment [-2, 2] of the imaginary axis
c. Unit circle \( |z|=1 \)
D. The line with arg \( z=\tan ^{-1} 2 \)
Subject: Chemistry
Match the following:
List - I List - II
A. Vitamin B \( _{1} \)
1. Riboflavin
B. Vitamin B
2. Pantothenic
acid
C. Vitamin B \( _{3} \)
3. Niacin
D. Vitamin B \( _{5} \)
4. Thiamine
B. A - 4, B -1, C - 2, D - 3
c. \( A-3, B-4, C-2, D-1 \)
D. A - \( 4, \) B- \( 3, \) C-1, D-2
Subject: Physics
A person sitting in the rear end of the compartment throws a ball towards the
front end.The ball follows a parabolic path.The train is moving with velocity of \( 20 m / s . A \) person standing outside on the ground also observes the ball.How
will the maximum heights \( y_{m} \) attained
and the ranges \( R \) seen by the thrower
and the outside observer compare with
each other?
A. same \( y_{m} \) different \( R \)
B. same \( y_{m} \) and \( R \)
C. differently \( y_{m} \) same \( R \)
D. differently \( y_{m} \) and \( R \)
Subject: Physics
For which one of the following input combinations, the given logic circuit
gives the output \( Y=1 ? \)
\( \mathbf{A} \cdot A=0, B=0, C=0 \)
В. \( A=0, B=1, C=0 \)
C \( . A=0, B=1, C=1 \)
D. \( A=1, B=1, C=1 \)
E \( . A=1, B=0, C=1 \)
Subject: Maths
Let \( A \) and \( B \) be two independent events.
The probability that both \( A \) and \( B \) happen is \( \frac{1}{12} \) and the probability that neither \( A \) nor \( B \) happen is \( 1 / 2 \).If the sum of probabilities of occurence of \( \boldsymbol{A} \) and \( B \) is \( \frac{k}{12}, \) then the value of \( k \) is
Subject: Maths
(a) Differentiate \( \boldsymbol{y}=\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \) with
respect to \( \boldsymbol{x}, \mathbf{0}<\boldsymbol{x}<\mathbf{1} \)
(b) Differentiate \( x^{x}-2^{\sin x} \) with respect
to \( x \)
Subject: Physics
An ac circuit consist of a series
combination of circuit elements \( X \) and
\( Y . \) The Current is ahead of the voltage in phanse by \( \frac{\pi}{4} . \) If element \( X \) is a pure resistor of \( 100 \Omega \)
(a) name the circuit element \( Y \)
(b) calculate the rms value of current, if
rms value of voltage is \( 141 V \)
(c) what will happen if the ac source is replaced by a dc source?
Subject: Physics
At an airport, a bored child starts to walk backwards on a moving platform. The child accelerates relative to the
platform with \( a=-0.5 m / s^{2} \) relative to
the platform. The platform moves with a constant speed \( v=+1.0 m / s \) relative to the
stationary floor In 4.0 seconds, how much will the child have been displaced relative to the floor?
\( A \cdot 8 m \)
в. \( 4 m \)
\( c .3 m \)
D. \( 0 m \)
E. \( -4 m \)
Subject: Physics
14
field intensity at the center of a square having fixed point charges at their
vertices as shown in figure are zero.
Reason

If electric potential at a point is zero
then the magnitude of electric field at that point must be zero.
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
Let \( O \) be the origin and \( P \) be the point at a distance 3 units from origin. If d.x.s' of OP are \( 1,-2,-2, \) then coordinates of \( P \) is
given by
A. 1,-2,-2
в. 3,-6,-6
c. \( \frac{1}{3},-\frac{2}{3},-\frac{2}{3} \)
D. \( \frac{1}{9},-\frac{2}{9},-\frac{2}{9} \)
Subject: Chemistry
Match List-1 with List-2.
List -1
List-2
A) \( C H_{3} C O O N a+C H_{3} C O O H \)
1)Acidic due to cationic hydrolysis
B) \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l}+\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H} \)
2) Basic due to anionic hydrolysis
C) aqueous \( A l C l_{3} \)
Basic buffer solution
D) aqueous \( N a_{2} C O_{3} \)
4)Acidic buffer solution
\( A \cdot A-1 ; B-2 ; C-3 ; D-4 \)
B. \( A-4 ; B-3 ; C-1 ; D-2 \)
c. \( A-2 ; B-3 ; C-1 ; D-4 \)
D. \( A-4 ; B-3 ; C-2 ; D-1 \)
Subject: Maths
Given that both \( x \) and \( y \) are positive
integers. Solve the following systems of equations. \( \boldsymbol{x}^{2}+\boldsymbol{x} \boldsymbol{y}=\mathbf{1 5}, \boldsymbol{y}^{2}+\boldsymbol{x} \boldsymbol{y}=\mathbf{1 0} \)
Subject: Maths
The function has \( \boldsymbol{f}(\boldsymbol{x})= \)
\( (\log (x-1))^{2}(x-1)^{2} \) has
A. local extremum at \( x=1 \)
B. point of inflection at \( x=1 \)
c. local extremum at \( x=2 \)
D. point of inflection at \( x=2 \)
Subject: Physics
A dia-atomic gas undergoes adiabatic expansion as shown in the figure. Find
volume of gas when pressure of gas is
\( 2 \times 10^{5} N / m^{2} \)
A \( \cdot 14 \times 10^{4} m^{3} \)
B . \( 1.4 \times 10^{7} m^{3} \)
c. \( 28 \times 10^{4} m^{3} \)
D. \( 28 \times 10^{3} m^{3} \)
Subject: Physics
An observer is moving away from a
sound source of frequency \( 100 H_{z} \). If the observer is moving with a velocity of \( 49 m / s e c \) and the speed of the speed of the sound in air is \( 330 m / \)sec , then the
apparent frequency is:
A. \( 91 H_{z} \)
в. \( 100 H_{z} \)
\( \mathbf{c} \cdot 85 H_{z} \)
D . \( 149 \mathrm{H}_{2} \)
Subject: Chemistry
(a) The conductivity of \( 0.001 \mathrm{mol} \mathrm{L}^{-1} \)
solution of \( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) is \( 3.905 \times 10^{-5} \)
Scm \( ^{-1} \). Calculate its molar conductivity and degree of dissociation. Given: \( \left(H^{+}\right)=349.6 \mathrm{S} \mathrm{cm}^{2} \mathrm{mol}^{-1} \) and
\( \left(C H_{3} C O O^{-}\right)=40.9 S \mathrm{cm}^{2} m o l^{-1} \)
(b) Define electro chemical cell. What
happens if external potential
applied becomes greater than \( \boldsymbol{E}_{\text {cell}} \) of
electro chemical cell?
Subject: Physics
A right circular cone has a semi-vertical angle \( \alpha . \) Calculate the solid angle at the
apex P of the cone.
A \( \cdot d \Omega=2 \pi(1-\cos \alpha) \)
в. \( d \Omega=2 \pi(1-\sin \alpha) \)
c. \( d \Omega=2 \pi(\cos \alpha) \)
D. \( d \Omega=2 \pi(\sin \alpha) \)
Subject: Physics
The refractive through the prisms are as shown. Pick out the WRONG statement
from the following. Path of the light ray
in
A \( \cdot \) A is correct if \( n_{2}>n_{1} \) and \( n_{2}>n_{3} \)
B. B is correct if \( n_{1}=n_{2} \) and \( n_{2}>n_{3} \)
c. \( c \) is correct if \( n_{2}<n_{1} \) and \( n_{2}=n_{3} \)
D. D is correct if \( n_{1}>n_{2} \) and \( n_{2}<n_{3} \)
Subject: Maths
Find the geometric mean of the following pairs of numbers:
\( a^{3} b \) and \( a b^{3} \)
\( \mathbf{A} \cdot a^{2} b^{2} \)
B. \( a b \)
\( c \cdot a b^{2} \)
D. \( a^{2} b \)
Subject: Chemistry
Which complex has \( d s p^{2} \) hybridization
and square planar shape?
A \( \cdot\left[N i(C N)_{4}\right]^{2-} \)
B \( \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+} \)
c. \( \left[P t(C l)_{4}\right]^{2-} \)
D. All
Subject: Physics
A particle carrying a charge equal to 100 times the charge on an electron is
rotating one rotation per second in a circular path of radius \( 0.8 \mathrm{m} \). The value of the magnetic field produced at the centre will be:
\( \left(\mu_{0}=\text { permeability for vacuum }\right) \)
\( ^{A} \cdot \frac{10^{-7}}{\mu_{0}} \)
B . \( 10^{-17} \mu_{0} \)
\( \mathbf{c} \cdot 10^{-6} \mu_{0} \)
D. \( 10^{-7} \mu_{0} \)
Subject: Maths
Find matrix \( \boldsymbol{X}, \) if \( \left[\begin{array}{ccc}\mathbf{3} & \mathbf{5} & -\mathbf{9} \\ -\mathbf{1} & \mathbf{4} & -\mathbf{7}\end{array}\right]+\boldsymbol{X}= \)
\( \left[\begin{array}{lll}\mathbf{6} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{8} & \mathbf{6}\end{array}\right] \)
Subject: Chemistry
Match the column I and II and select the
correct option from the codes given below:
(P)
\( (Q) \)
\begin{tabular}{lll} 
Column I & \multicolumn{2}{l} { Column II } \\
Liquid & (i) & Highly compressible \\
Gas & (ii) & Definite volume \\
Plasma & (iii) & Super low density \\
BoseEinstein condensate & (iv) & Super energetic \\
\hline
\end{tabular}
(R)
\( (s) \)
A. \( (P)-(i),(Q)-(i i),(R)-(i i i),(S)-(i v) \)
B. (P)-(ii), (Q)-(i),(R)-(iii),(S)-(iv)
C. (P)-(ii), (Q)-(i),(R)-(iv),(S)-(iii)
D. (P)-(iii), (Q)-(i),(R)-(ii),(S)-(iv)
Subject: Biology
Thoracic chamber is formed dorsally by
the \( _{--}(\mathrm{i})_{--}- \) ventrally by the
(ii) \( _{--\rightarrow} \), laterally by the
(iii) \( _{---} \) and on lower side by the dome shaped (iv)
Select the correct option to complete
the above paragraph.
A. (i)vertebral column (ii)sternum (iii)ribs (iv)diaphragm
B. (i)sternum (ii)vertebral column (iii)diaphragm (iv)ribs
c. (i)diaphragm (ii)ribs (iii)vertebral column (iv)sternum
D. (i)ribs (ii)diaphragm (iii)vertebral column (iv)sternum
Subject: Physics
Two thin long wires carry currents \( \boldsymbol{I}_{\mathbf{1}} \)
and \( I_{2} \) along \( x \) -and \( y \) -axes respectively
as shown in figure. Consider the points
only in \( x \) -y plane.
This question has multiple correct options
A. Magnetic field is zero at least at one point in each quadrant
B. Magnetic field can be zero somewhere in the first quadrant
c. Magnetic field can be zero somewhere in the second quadrant
D. Magnetic field is non-zero in second quadrant
Subject: Maths
Find the mean of the following frequency distribution by the assumed
mean method:
\( \begin{array}{lllll}\text { No. of } & \mathbf{5 0}- & \mathbf{5 3 -} & \mathbf{5 6 -} & \mathbf{5 9 -} \\ \text { apples } & \mathbf{5 3} & \mathbf{5 6} & \mathbf{5 9} & \mathbf{6 2}\end{array} \)
No of
boxes 150 115
Subject: Physics
The thickness of a metal sheet is
measured to be \( 326 m m \). Express its
order of magnitude in \( \mathrm{mm} \)
A \( \cdot 10^{\circ} \)
B. \( 10^{\text {। }} \)
\( c \cdot 10^{2} \)
D. \( 10^{3} \)
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{x}^{4} \boldsymbol{e}^{2 x} \) then \( \boldsymbol{y}_{10}(\boldsymbol{0}) \) is equal to
\( A \cdot 2^{10} \)
B . \( 315 \times 2^{10} \)
c. \( 195 \times 2^{10} \)
D. \( 315 \times 2^{8} \)
Subject: Maths
The distance of point (-1,-5,-10) from the point of intersection of \( \frac{x-2}{3}=\frac{y+1}{4}=\frac{-2}{12} \) and plane \( x \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) is :
A . 10
B. 8
\( c \cdot 2 \)
D. 13
Subject: Physics
A man of mass \( m \) starts falling towards
a planet of mass \( M \) and radius R. As he
reaches near to the surface, he realizes that he will pass through a small hole in the planet. As he enters the hole, he sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass \( 2 M / 2 \) and a point
mass \( M / 3 \) at the centre. Change in the force of gravity experienced by the man is
A \( \cdot \frac{2 G M m}{3} \frac{G M m}{R^{2}} \)
B. 0
c. \( \frac{1}{3} \frac{G M m}{R^{2}} \)
D. \( \frac{4 G M m}{3} \frac{G M m}{R^{2}} \)
Subject: Maths
The points \( A(2 a, 4 a), B(2 a, 6 a) \) and
\( \boldsymbol{C}(\mathbf{2} \boldsymbol{a}+\sqrt{\mathbf{3}} \boldsymbol{a}, \mathbf{5} \boldsymbol{a}),(\mathbf{w h e n} \boldsymbol{a}>\boldsymbol{o}) \)
vertices of
Subject: Chemistry
Select the correct I.U.P.A.C. name for
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C o}(\boldsymbol{O} \boldsymbol{N} \boldsymbol{O})_{6}\right] \)
A. Hexaamminecobalt(II) hexanitrito-0 cobalt(II)
B. Hexaamminecobalt(III) hexanitrito-N cobaltate(III)
c. Hexaamminecobaltate(III) hexanitrito-0 cobaltate(II)
D. Hexaamminecobalt(III) hexanitrito-0 cobaltate(III)
Subject: Chemistry
Assertion (A): Ortho phosphoric acid is
tribasic.

Reason (R): Orthophosphoric acid forms three series of salts
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
c. (A) is true and (R) is false
D. (A) is false but (R) is true
Subject: Maths
If \( \boldsymbol{A}^{-1}=\left[\begin{array}{cc}1 & -2 \\ -2 & 2\end{array}\right], \) then what is
\( \operatorname{det}(A) \) equal to \( ? \)
\( A \cdot 2 \)
B. -2
c. \( 1 / 2 \)
D. \( -1 / 2 \)
Subject: Chemistry
Statement 1: A solution of NaCl will
conduct electricity.
Statement 2: NaCl will not form ions in
Solution.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and
Statement 2 is not the correct explanation of Statement 1.
C. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.
Subject: Maths
A man is know to speak the truth 3 out if 4 times. He throws a die and reports
that it is a six. The probability that it is actually a six is:
A \( \cdot \frac{3}{8} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{3}{4} \)
D. None of these
Subject: Maths
f \( A=\{1,2,3\} \) and \( B=\{3,4\} \) and
\( \boldsymbol{C}=\{\mathbf{1}, \mathbf{3}, \mathbf{5}\} . \) Find \( \boldsymbol{A} \times(\boldsymbol{B} \cup \boldsymbol{C}) \)
Subject: Maths
In following symbol series, some of the symbols are missing which are given in that order as one of the alternatives
below it. Choose the correct alternative.
\( \$ \$ \operatorname{ltex} t\left\{x+_{-} x x_{-}+++x x_{-}+++x\right\} \$ \$ \)
\( A \cdot x++x \)
B. \( +x x+ \)
\( c \cdot x x x+ \)
D. \( x+x+ \)
\( E \cdot x+x x \)
Subject: Chemistry
Study the given statements and select
the correct answer.
(I) Lipids are macromolecules but obtained under-macromolecular
fraction due to their insoluble nature in
the aqueous medium of a cell.
(II) Water is the most abundant
chemical in a living organism.
(III) The first respiratory substrate is lipid.
(IV) Dihydroxyacetone occurs in d and I form.
A. I, II and IV are correct
B. I, II \& III are correct
c. I, I lare correct
D. III and IV are correct
Subject: Maths
\( \frac{\boldsymbol{x}^{\boldsymbol{4}}+\boldsymbol{2} \boldsymbol{4} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{8}}{\left(\boldsymbol{x}^{2}+\mathbf{1}\right)^{3}}= \)
A. \( \frac{1}{x^{2}+1}+\frac{22}{\left(x^{2}+1\right)^{2}}+\frac{5}{\left(x^{2}+1\right)^{3}} \)
B. \( \frac{1}{x^{2}+1}-\frac{22}{\left(x^{2}+1\right)^{2}}+\frac{5}{\left(x^{2}+1\right)^{3}} \)
C \( \frac{1}{x^{2}+1}+\frac{22}{\left(x^{2}+1\right)^{2}}+\frac{28}{\left(x^{2}+1\right)^{3}} \)
D. \( \frac{1}{x^{2}+1}+\frac{23}{\left(x^{2}+1\right)^{2}}+\frac{4}{\left(x^{2}+1\right)^{3}} \)
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{m} \sin ^{-1} \boldsymbol{x}} \)
Then \( \left(1-x^{2}\right)\left(\frac{d y}{d x}\right)^{2}=A y^{2}, \) then \( A= \)
?
A . \( m \)
B. \( -m \)
\( \mathrm{c} \cdot m^{2} \)
D. \( -m^{2} \)
Subject: Chemistry
Assertion
\( Y b^{+2} \) is more stable in compare to
\( G d^{+2} \)
Reason
The electron configuration of \( G d \) is
\( [\boldsymbol{X} \boldsymbol{e}] \boldsymbol{4} \boldsymbol{f}^{7} \boldsymbol{5} \boldsymbol{d}^{2} \boldsymbol{6} \boldsymbol{s}^{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
Structural isomerism and
stereoisomerism should be considered
in answering this question. Compound is reacted with KOH dissolved in
ethanol. Three isomeric alkenes with
molecular formula \( C_{4} H_{8} \) are formed.
What is J?
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{2}-C H_{2}-B r \)
B. \( C H_{3}-_{I}^{C H}-C H_{2}-C H_{3} \)
\( \mathbf{c} . C H_{3}-C H-C H_{2}-B r \)
\( _{C H_{3}} \)
D. \( C H_{3} \)
\( C H_{3}-C-B r \)
\( _{C H_{3}} \)
Subject: Physics
If a \( 3 c m \) tall object placed
perpendicular to principal axis of a convex lens of focal length \( 15 \mathrm{cm} \)
produces a real invented image of height \( 15 c m, \) then its object distance
\( (u) \) is and image distance \( (v) \) is
A. \( u=-18 m, v=+90 m \)
в. \( u=+18 \mathrm{cm}, v=-90 \mathrm{cm} \)
c. \( u=-18 \mathrm{cm}, V=+90 \mathrm{cm} \)
D. \( y=+18 c m, v=+90 \mathrm{cm} \)
Subject: Maths
Suppose a machine produces metal parts that contain some defective parts
with probability \( 0.05 . \) How many parts should be produced in order that the probability of atleast one part being defective is \( \frac{1}{2} \) or more?
(Given that, log \( _{10} 95=1.977 \) and
\( \left.\log _{10} 2=0.3\right) \)
This question has multiple correct options
A . 11
в. 12
\( c \cdot 15 \)
D. 14
Subject: Chemistry
Assertion: The Gibbs free-energy equation can be used to predict the solubility of a solute. Reason: The solubility of most salts increases as temperature increases.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Physics
Electric charges are distributed in a small volume. The flux of the electric
field through a spherical surface of radius \( 10 \mathrm{cm} \) surrounding the total charge is 25 V-m. The flux over
concentric sphere of radius \( 20 \mathrm{cm} \) will
be:
\( A \cdot 25 \vee m \)
B. \( 50 \mathrm{Vm} \)
\( c .100 \mathrm{vm} \)
D. \( 200 \mathrm{vm} \)
Subject: Physics
A rigid spherical body is spinning
around an axis without any external
torque. Due to change in temperature, the
volume increases by \( 1 \% . \) Its angular speed
A. Will increase approximately by \( 1 \% \)
B. Will decrease approximately by 1 \%
C. Will decrease approximately by 0.67 \%
D. Will increase approximately by 0.33 \%
Subject: Physics
A wire \( \left(Y=2 \times 10^{11} N / m\right) \) has length
\( 1 m \) and area \( 1 m m^{2} . \) The work required
to increased its length by \( 2 m m \) is
A. \( 400 J \)
B. \( 40 J \)
c. \( 0.4 J \)
D. \( 0.04 J \)
Subject: Physics
The elastic limit of an elevator cable is
\( 2 \times 10^{9} N / m^{2} . \) The maximum upward
acceleration that an elevator of mass
\( 2 \times 10^{3} k g \) can have when supported by
a cable whose cross-sectional area is
\( 10^{-4} m^{2}, \) provided the stress in cable would not exceed half of the elastic
limit would be
A \( \cdot 10 m s^{-2} \)
B. \( 50 m s^{-2} \)
\( \mathrm{c} \cdot 40 \mathrm{ms}^{-2} \)
D. Not possible to move up