AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A positive point charge is released from
rest at a distance \( r_{0} \) from a positive line charge with uniform density. The speed
(v) of the point charge, as a function of instantaneous distance r from line
charge, is proportional to :-
A \( \cdot v \propto e^{+r / r_{0}} \)
В \( \cdot v \propto \ln \left(\frac{r}{r_{0}}\right) \)
c. \( v \propto\left(\frac{r}{r_{0}}\right) \)
D.
Subject: Physics
Find the distance covered by a particle
during the interval \( t=0 \) to \( t=20 \) s for
which the speed-time graph is shown in
figure.
A . 200 \( \mathrm{m} \)
B. 400 \( m \)
c. \( 100 \mathrm{m} \)
D. 300 \( \mathrm{m} \)
Subject: Physics
Two wires, each of radius \( r, \) but of
different materials are connected
together end to end. If the densities of
charge carriers in the two wires are in the ratio \( 1: 4, \) the ratio of the drift velocity of electrons in the two wires will be \( . . \)
A . 1: 2
B. 2:
\( c \cdot 1: 4 \)
D. 4:
Subject: Biology
Match the following hormones with the respective disease.
(a) Insulin
(i) Addison's disease
(b) Thyroxin
(ii) Diabetes insipidus
(c) Corticoids
(iii) Acromegaly
(d) Growth Hormone
(iv) Goitre
(v) Diabetes mellitus
Select the correct option.
\( A \cdot(a)-(v),(b)-(i),(c)-(i i),(d)-(i i i) \)
B. (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)
\( c \cdot(a)-(v),(b)-(i v),(c)-(i),(d)-(i i i) \)
D. (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)
Subject: Chemistry
Assertion
Statement -1: Coordination isomerism
occurs when both cation and anion are
complex.
Reason
Statement -2: The complexes with coordination number 6 form octahedral
complexes involving either \( s p^{3} d^{2} \) or
\( d^{2} s p^{3} \) hybridization.
A. Statement - 1 is true, Statement - 2 is true and Statement - 2 is correct explanation for Statement -
1.
B. Statement - 1 is true, Statement - 2 is true and Statement - 2 is NOT the correct explanation for Statement - 1
c. Statement -1 is true, Statement -2 is false
D. Statement - 1 is false, Statement - 2 is true
Subject: Maths
A man is know to speak the truth 3 out
of 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: Physics
A charge \( Q \) is located at the centre of a
sphere of radius \( R \) Calculate the flux
going out through the surface of the
sphere
\( ^{A} \cdot \frac{Q}{4 \pi \epsilon_{0} R^{2}} \)
в. \( \frac{Q}{4 \pi \epsilon_{0} R} \)
c. \( \frac{Q}{4 \pi R^{2}} \)
D. \( \underline{Q} \)
Subject: Chemistry
In a constant volume calorimeter, 3.5 g of a gas with molecular weight 28 was
burnt in excess oxygen at 298.0 K. The temperature of the calorimeter was found to increase from \( 298.0 \mathrm{K} \) to
\( 298.45 \mathrm{K} \) due to the combustion
process. Given that the heat capacity of
the calorimeter is \( 2.5 \mathrm{kJ} \mathrm{K}^{-1} \), the
numerical value for the enthalpy of combustion of the gas in \( \mathrm{kJmol}^{-1} \) is:
Subject: Physics
A proton moving with a velocity of \( 1.25 \times 10^{5} \mathrm{m} / \mathrm{s} \) collides with a
stationary helium atom. The velocity of proton after collision is
\( \mathbf{A} \cdot 0.75 \times 10^{5} m s^{-1} \)
B . \( 7.5 \times 10^{5} \mathrm{ms}^{-1} \)
c. \( -7.5 \times 10^{5} \mathrm{ms}^{-1} \)
D. \( 0 m s^{-1} \)
Subject: Maths
There is a right circular cone of height \( h \)
and vertical angle \( 60^{\circ} . \) A sphere when placed inside the cone, it touches the curved surface and the base of the cone.
The volume of sphere is
A \( \cdot \frac{4}{3} \pi h^{3} \)
В \( \cdot \frac{4}{9} \pi h^{3} \)
c. \( \frac{4}{27} \pi h^{3} \)
D. \( \frac{4}{81} \pi h^{3} \)
Subject: Physics
What is the velocity of the cart just after the first collision?
A \( \cdot \frac{-m v_{0}}{m+M} \)
в. \( \frac{M v_{0}}{m+M} \)
c. \( \frac{M-m}{M+m} v_{0} \)
D. \( \frac{2 M}{m+M} v_{0} \)
Subject: Physics
A conductor is made of an isotropic
material (resistivity \( \rho \) ) has rectangular
cross section. The horizontal
dimensions of the conductor decreases linearly from \( 2 x \) at one end to \( x \) at the
other end and vertical dimensions
increase from y to 2y as shown in the figure. The length of conductor along the axis is equal to I and a battery is connected across the conductor, then
A \cdot resistance of conductor is equal to \( \frac{4 \rho l}{9 x y} \)
B . resistance of conductor is equal to \( \frac{9 \rho l}{4 x y} y \)
c. drift velocity of conduction electrons is maximum at the middle section
D. drift velocity of conduction electrons is minimum at the middle section
Subject: Physics
Assertion
When two unlike charges are brought nearer, their electrostatic potential
energy decreases.
Reason
All conservative forces act in the
direction of decreasing potential
energy.
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
In the formula of brown ring complex
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}(\boldsymbol{N O})\right] \boldsymbol{S} \boldsymbol{O}_{4}, \) the magnetic
moment is 3.87 B.M. The oxidation state
of Fe and number of unpaired electrons present respectively are :
\( \mathbf{A} \cdot 1+, 3 \)
в. \( 2+, 3 \)
c. \( 3+, 3 \)
D. \( 3+, 5 \)
Subject: Maths
: The function \( f(x)=2 x^{3}-3 x^{2}- \)
\( 12 x+8 \) attains minimum value at \( x= \)
2
II: The function of \( f(x)=x^{4}-6 x^{2}+ \)
\( 8 x+11 \) attains minimum value at \( x= \)
2 which of the above statements are
true
A. onlyı
B. only II
c. both I and II
D. neither I nor II
Subject: Maths
\( \int_{0}^{\pi / 2} \frac{d x}{1+\tan x} \)
This question has multiple correct options
A . a multiple of \( \pi / 4 \)
B. a multiple of \( \pi / 2 \)
c. equal to \( \pi / 4 \)
D. a multiple of \( \pi \)
Subject: Physics
Consider a parallelogram \( A B C D, \) with
angle \( \angle B=120^{\circ} . \) A charge \( +Q \) placed
at the corner \( A \) produces field \( E \) and
potential \( V \) at corner \( D \). If we now add
charges \( -2 Q \) and \( +Q \) at corners \( B \) and
\( C \) respectively, the magnitude of field
and potential at \( D \) will become
respectively
\( ^{A} \cdot \frac{\sqrt{3}}{2} E, V \)
в. \( \frac{\sqrt{3}}{2} E, \) о
\( c . E, 0 \)
D. \( \frac{E}{\sqrt{2}}, \frac{V}{\sqrt{2}} \)
Subject: Physics
The amount of heat required to convert 1 g of ice at \( -10^{0} C \) into steam at \( 100^{0} C \) is (approximately): (specific
heat of water \( =4.187 \mathrm{J} / \mathrm{g}^{0} \mathrm{C}, \) latent heat of fusion \( =334 \) J/g , latent heat of
vaporization \( =2260 \) J/g, specific heat of ice \( =\mathbf{2 . 0 3} \mathrm{J} / \mathrm{g} \) ):
A . 3034 J
B. 735 J
c. 1000
D. 4200 J
Subject: Maths
Assertion
In a triangle \( A B C \) if \( \tan A: \tan B: \)
\( \tan C=1: 2: 3 \) then \( A=45^{\circ} \)
Reason
If \( p: q: r=1: 2: 3 \) then \( p=1 \)
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
The self-inductance of an air core
solenoid of 100 turns is 1 m \( H \). The self-
inductance of another Solenoid of 50
turns (with the same length and crosssectional area) with a core having relative permeability 500 is
A . \( 125 \mathrm{mH} \)
B. 24 mH
c. \( 60 \mathrm{mH} \)
D. 30 mH
E. \( 45 \mathrm{mH} \)
Subject: Physics
A hot body is allowed to cool. The surrounding temperature is constant at
\( 30^{\circ} \mathrm{C} . \) The body takes time \( t_{1} \) to cool
from \( 90^{\circ} \mathrm{C} \) to \( 89^{\circ} \mathrm{C} \) and time \( t_{2} \) to cool
from \( 60^{\circ} \mathrm{C} \) to \( 59.5^{\circ} \mathrm{C} \). Then
A \( \cdot t_{2}=2 t_{1} \)
B. \( t_{2}=\frac{t_{1}}{2} \)
c. \( t_{2}=4 t \)
D. \( t_{2}=t_{1} \)
Subject: Physics
Assertion
Sound waves do not travel through
vacuum
Reason
Sound waves are mechanical waves,
which require a medium for their
propagation
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
Factors of \( (\boldsymbol{a}+\boldsymbol{b})^{3}-(\boldsymbol{a}-\boldsymbol{b})^{3} \) are
A \( \cdot 2 a b\left(3 a^{2}+b^{2}\right) \)
B . \( a b\left(3 a^{2}+b^{2}\right) \)
c. \( 2 b\left(3 a^{2}+b^{2}\right) \)
D. \( 3 a^{2}+b^{20} \)
Subject: Physics
If position vector of a point varies with time " \( \boldsymbol{t}^{\prime \prime} \) as \( \overrightarrow{\boldsymbol{r}}=\left(\boldsymbol{t}+\boldsymbol{t}^{2}\right)(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}) \) meter
then velocity at time \( t=4 s \) will be
A \( \cdot(6 \hat{i}+6 \hat{j}) m / s \)
B . \( (6 \hat{i}+9 \hat{j}) m / s \)
c. \( (9 \hat{i}+6 \hat{j}) m / s \)
D. \( (9 \hat{i}+9 \hat{j}) m / s \)
Subject: Physics
Four identical charges each of charge
are placed at the corners of a square.
Then at the centre of the square the
resultant electric intensity E and the net electric potential V are
A. \( E \neq 0, V=0 \)
B. \( E=0, V=0 \)
c. \( E=0, V \neq 0 \)
D. \( E \neq 0, V \neq 0 \)
Subject: Physics
The plates of a parallel plate condenser are pulled apart with a velocity v. If at any instant their mutual distance of
separation is \( x, \) the magnitude of the time of rate of change of capacity depends on \( x \) as follows:
\( A \cdot 1 / x \)
B . \( 1 / x^{2} \)
c. \( x^{2} \)
D.
Subject: Maths
Statement I: The function \( f(x) \) in the
figure is differentiable at \( x=a \)
Statement II: The function \( f(x) \)
continuous at \( x=a \)
A. Both Statement I and Statement II are true and the
Statement II is the correct explanation of the Statement I
B. Both Statement I and Statement II are true and the Statement II is not the correct explanation of the Statement I
c. Statement l is true but Statement II is false
Statement I is false but Statement II is true
Subject: Maths
The equation \( \frac{x^{2}}{8-t}+\frac{y^{2}}{t-4}=1 \) will
represent an ellipse if
A. \( t \in(1,5) \)
B. \( t \in(2,8) \)
c. \( t \in(4,8)-\{6\} \)
D. \( t \in(4,10)-\{6\} \)
Subject: Physics
If you leave the saddle when it is moving upward. The magnitude of down ward acceleration of the saddle is - - - - when
you lose contact with it:
\( A \cdot 6 m s^{-2} \)
B. 7.2 \( m s^{-2} \)
c. \( 9.8 \mathrm{ms}^{-2} \)
D. 12.2 \( m s^{-2} \)
Subject: Physics
In common emitter amplifier, the current gain is \( 62 . \) The collector resistance and input resistance are \( 5 k \Omega \) an \( 500 \Omega \)
respectively. If the input voltage is \( 0.01 V, \) the output voltage is
A. \( 0.62 V \)
V
B. \( 6.2 V \)
\( c .62 V \)
D. \( 620 V \)
Subject: Chemistry
A mixture of ethane and neon having a volume of \( 20 \mathrm{ml} \), requires \( 49 \mathrm{ml} \) of
oxygen for complete combustion. The percentage of ethane in the mixture is:
A . \( 70 \% \)
B. 30\%
c. \( 35 \% \)
D. \( 64 \% \)
Subject: Maths
In \( \triangle A B C, \angle B \) is a right angle. The median AD and BE are at right angles. Then angle \( C \) is
A . 60
B. \( \tan ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)
c. \( \tan ^{-1} \sqrt{2} \)
D. 90
Subject: Chemistry
Amphetamine \( \left(C_{3} H_{13} N\right) \) is a weak
base with \( p K_{b} \) of \( 4.2 . \) Calculate the \( p H \) of a solution containing an amphetamine concentration of \( 220 m g / L \)
A . 3.49
B. 5.21
c. 10.5
D. 13.7
Subject: Maths
In the complex numbers, where \( i= \)
\( \sqrt{-1}, \) the conjugate of any value \( a+b i \)
is \( a- \) ib. What is the result when you
multiply \( 2+7 i \) by its conjugate?
A . 45
в. -45
\( c .45 i \)
D. 53
E. 53
Subject: Physics
Modern vacuum pumps can evacuate a
vessel down to a pressure of \( 4.0 \times \) \( 10^{-15} a t m . \) at room temperature (300
K). Taking \( \boldsymbol{R}= \)
\( 8.3 K J^{-1} \) mole \( ^{-1}, 1 a t m=10^{5} \) Pa and
\( N_{\text {Avogradro}}=6 \times 10^{23} \)mole\( ^{-1}, \) the mean
distance between molecules of gas in an evacuated vessel will be of the order
of
A. \( 0.2 \mu m \)
B. \( 0.2 \mathrm{mm} \)
c. \( 0.2 \mathrm{cm} \)
D. 0.2 nm
Subject: Physics
Two identical charged spheres are suspended by strings of equal lengths.
The strings make an angle of \( 30^{\circ} \) with each other. When suspended in a liquid of density \( 0.8 g c m^{-3} \) the angle remains
the same. If density of the material of the sphere is \( 1.6 g c m^{-3}, \) the dielectric constant of the liquid is
A . 1
B. 4
\( c \cdot 3 \)
D.
Subject: Maths
If \( a, b, c \) are positive such that \( a b^{2} c^{3}= \)
64 then least value of \( \left(\frac{1}{a}+\frac{2}{b}+\frac{3}{c}\right) \)
is
\( A \cdot 6 \)
B. 2
\( c \cdot 3 \)
D. 32
Subject: Maths
Find the inverse of the following
matrices:
(a) \( \left[\begin{array}{ccc}\mathbf{1} & \mathbf{4} & \mathbf{0} \\ {[\mathbf{0 . 3 e m}]-\mathbf{1}} & \mathbf{2} & \mathbf{2} \\ {[\mathbf{0 . 3 e m}] \mathbf{0}} & \mathbf{0} & \mathbf{2}\end{array}\right] \)
(b) \( \left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0 \\ {[0.3 e m] \sin \theta} & \cos \theta & 0 \\ {[0.3 e m] 0} & 0 & 1\end{array}\right] \)
(c) \( \left[\begin{array}{ccc}2 & 2 & 2 \\ {[0.3 e m] 2} & 5 & 5 \\ {[0.3 e m] 2} & 5 & 11\end{array}\right] \)
(d) \( \left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ {[\mathbf{0 . 3 e m}] \mathbf{2}} & \mathbf{4} & \mathbf{5} \\ {[\mathbf{0 . 3 e m}] \mathbf{3}} & \mathbf{5} & \mathbf{6}\end{array}\right] \)
(e) \( \left[\begin{array}{ccc}\mathbf{1} & \mathbf{4} & \mathbf{0} \\ {[\mathbf{0 . 3 e m}]-\mathbf{1}} & \mathbf{2} & \mathbf{2} \\ {[\mathbf{0 . 3 e m}] \mathbf{0}} & \mathbf{0} & \mathbf{2}\end{array}\right] \)
Subject: Chemistry
Strength of an acid solution or a basic solution can be determined by knowing the hydrogen ion concentrations in
them, using a pH scale.
(i) Neutral solution has pH 7.
(ii) Acidic solution has pH less than 7 .
(iii) Basic solution has pH more than 7 .
The pH of a solution is inversely proportional to hydrogen(H+) ion concentration in it.
Teacher told three students Renuka,
Bhawna and Seema to test their saliva
with pH paper before and after having their lunch. Identify the correct observation from the following.
A. Bhawna observed that pH paper turned red and recorded pH value of \( 2.3-2.5 \) after having lunch
B. Seema observed that pH paper turned yellow and recorded pH value of \( 5.6-5.8 \) before having lunch
c. Renuka observed that pH paper turned green and recorded pH value of 7.4-7.9 before having lunch
D. observations made by both Renuka and Seema were correct
Subject: Maths
Evaluate the left hand limit of the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\frac{|\boldsymbol{x}-\mathbf{4}|}{\boldsymbol{x}-\mathbf{4}}, \boldsymbol{x} \neq \mathbf{4} \\ \mathbf{0} \quad, \boldsymbol{x}=\mathbf{4}\end{array}\right. \)
Subject: Physics
An observer whose least distance of
distinct vision is 'd', views his own face
in a convex mirror or radius or
curvature 'r'. The magnification produced cannot exceed \( \frac{\boldsymbol{k} \boldsymbol{r}}{\boldsymbol{d}+\sqrt{\boldsymbol{d}^{2}+\boldsymbol{r}^{2}}} \)
Find \( k \)
\( A \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Maths
A tyre manufacturing company kept a record of the distance covered before a
tyre needed to be replaced. The table
show the result of 1000 cases :
Distance in \( K m \quad \) Frequency
Less than 4000 20
4000 to 9000 210
9000 to 14000 325
More than 14000 445
If you buy a tyre of this company what is the probability that it will need to be replaced after it has covered somewhere between \( 4000 \mathrm{km} \) and \( 14000 \mathrm{km} \) ?
A . 0.65
B. 0.625
c. 0.125
D. None of these
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x}) \) denotes the fractional part of \( \mathbf{a} \) real number \( x \). Then the value of
\( \int_{0}^{\sqrt{3}} f\left(x^{2}\right) d x \)
A \( \cdot 2 \sqrt{3}-\sqrt{2}-1 \)
1 1
в. \( 0(z e r o) \)
c. \( \sqrt{2}-\sqrt{3}+1 \)
D. \( \sqrt{3}-\sqrt{2}+1 \)
Subject: Maths
Sum the series:
\( 1-\frac{1}{3}+\frac{1}{3^{2}}-\frac{1}{3^{3}}+\frac{1}{3^{4}} \dots \dots \infty \)
\( A \cdot \frac{3}{4} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{2}{3} \)
D. 3
Subject: Physics
A cricket ball of mass 150 gram moving with a velocity of \( 12 \mathrm{m} / \mathrm{s} \) strikes against the bat. It rebounces with a velocity of \( 20 \mathrm{m} / \mathrm{s} . \) The ball remains in touch with the batfor 0.01 second. The average force
applied by the bat on the ball is
A. 840 Newton
B. 480 Newton
c. 804 Newton
D. 408 Newton
Subject: Chemistry
STATEMENT-1: Dumas method is more
applicable to nitrogen containing
organic compounds than Kjeldahl's
method.
STATEMENT-2:Kjeldahl's method does
not give satisfactory results for compounds in which nitrogen is linked
to oxygen.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Chemistry
\( \ln \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C l}_{2}\right], \boldsymbol{P} \boldsymbol{t}-\boldsymbol{C l} \) bond length
is \( 2 A \) and \( C I-C I \) distance is \( 2.88 A \) then
the compound is:
A. tetrahedral
B. square pyramidal
c. cis-square planar
D. trans-square planar
Subject: Physics
A thin rod of negligible mass and area of cross-section \( 4 \times 10^{-6} m^{2} \)
suspended vertically from one end, has
a length of \( 0.5 \mathrm{m} \) at \( 100^{\circ} \mathrm{C} \). The rod is
cooled to \( 0^{\circ} \mathrm{C} ; \) but prevented from
contracting by attaching a mass at the
lower end. Find (i) this mass, and (ii)
the energy stored in the rod. Given for
the rod, Young's modulus \( =10^{11} N / m^{2} \)
coefficient of linear expansion \( 10^{-5} K^{-1} \)
and \( g=10 m / s^{2} \)
A . (i) \( 60 \mathrm{kg} \), (ii) \( 0.1 \mathrm{J} \)
B. (i) 40kg, (ii) 0.1J
c. (i) 560kg, (ii) 0.1]
D. (i) \( 490 \mathrm{kg}, \) (ii) 10.1
Subject: Maths
If \( \vec{a}+\vec{b}+\vec{c}=\overrightarrow{0} \) show that \( \vec{a} \times \vec{b}=\vec{b} \times \)
\( \overrightarrow{\boldsymbol{c}}=\overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{a}} \)
Subject: Biology
Consider the following statement regarding human.
a. Duodenum is the longest part of small intestine
b. Hepatic and cystic ducts release their
secretions into common bile duct
whose opening is controlled by
sphincter of Oddi
c. Ileocaecal valve is present at the
junction of small intestine and large intestine
d. Mechanical digestion and chemical digestion of food occurs in buccal cavity, stomach and small intestine Which of the following choices is
correct?
A. A and B only
B. B and C only
C. \( \mathrm{C} \) and \( \mathrm{D} \) only
D. \( A, B, C \) and \( D \)
Subject: Chemistry
In the reaction \( C_{(g)}+C O_{2(g)} \rightleftharpoons 2 C O_{(g)} \)
the equilibrium pressure is 12 atm. IF
\( 50 \% \) of \( C O_{2} \) reacts, \( K_{p} \) for the change
is:
A . 12 atm
B. 32 atm
\( c .64 a t m \)
D. 16 atm
Subject: Maths
Assertion
Let \( \boldsymbol{f}:[\mathbf{8} \boldsymbol{\pi}, \mathbf{9} \boldsymbol{\pi}] \rightarrow[-\mathbf{1}, \mathbf{1}], \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{\operatorname { c o s } \boldsymbol { x }} \)
then
Statement-1: \( \boldsymbol{f}^{-1}(-1)=\mathbf{9} \boldsymbol{\pi} \) because
Reason
Statement-2 : \( \boldsymbol{f}^{-1}(\boldsymbol{x})=\mathbf{1 0} \boldsymbol{\pi}- \)
\( \cos ^{-1} x \forall x \infty[-1,1] \)
A. Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-
B. Statement-1 is true, Statement-2 is true and Statement-2 is NOT correct explanation for Statement-
c. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true
Subject: Chemistry
Which of the following explains the
reason why atomic radii decrease
across a period?
A. As you move across the period, the number of protons increases, which increases the nuclear charge. The number of electrons remains the same creating a larger Coulombic attraction and decreasing the radii
B. As you move across the period, the number of protons and electrons increases. The increased Coulombic attraction decreases the overall size of the atom.
C. As you move across the period, the number of protons remains constant while the number of electrons
increases. The decreased Coulombic attraction
decreases the overall size of the atom.
D. The atomic radii do not decrease across a period. It actually increases, duh!
Subject: Maths
If \( \boldsymbol{x}=\boldsymbol{y} \cos \frac{\boldsymbol{2} \boldsymbol{\pi}}{\mathbf{3}}=\boldsymbol{z} \cos \frac{\boldsymbol{4} \boldsymbol{\pi}}{\boldsymbol{3}}, \) then \( \boldsymbol{x} \boldsymbol{y}+ \)
\( y z+z x \) is equal to
\( \mathbf{A} \cdot-4 x^{2} \)
B.
\( c \cdot 1 \)
D.
Subject: Chemistry
The energy required to excite the electron in the atom from \( n=1 \) to \( n= \)
2, when the ionization enthalpy of a
hydrogen atom is \( 1.312 \times 10^{6} J / \) mol
will be:
(in the unit of \( 10^{5} \) ).
A . 8.53
B. 7.51
c. 8.92
D. 9.86
Subject: Chemistry
Why nascent hydrogen is more reactive
than molecular hydrogen?
A. The production of nascent hydrogen is associated with the release of high energy. This released energy activates the nascent hydrogen and makes it more energy rich than that of ordinary occurring molecular hydrogen. Because more energy means more reactivity, nascent hydrogen is more reactive than molecular hydrogen.
B. In the time of formation nascent hydrogen is in the form of minute bubbles with high internal pressure which makes it more reactive.
C. both \( A \) and \( B \)
D. none of these
Subject: Maths
If \( \sin ^{-1}\left(\frac{1}{3}\right)+\sin ^{-1}\left(\frac{2}{3}\right)=\sin ^{-1} x, \) then
\( x \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{\sqrt{5}+4 \sqrt{2}}{9} \)
c. \( \frac{5 \sqrt{2}-4 \sqrt{5}}{9} \)
D.
Subject: Physics
A lift in which a man is standing, is moving upwards with a speed of \( 10 \mathrm{m} / \mathrm{s} \) The man drops a coin from a height of \( 4.9 m \) and if \( g=9.8 m / s^{2}, \) then the coin
reaches the floor of the lift after a time
A \( \cdot \sqrt{2} s \)
B. \( 1 s \)
c. \( \frac{1}{2} s \)
D. \( \frac{1}{\sqrt{2}} s \)
Subject: Physics
Four metallic plates each with a surface area of one side \( A \) are placed at a
distance \( d \) from each other as shown in
figure. Then the capacitance of the
system between \( X \) and \( Y \) is
A.
B. \( \frac{2 \epsilon_{0} A}{3 d} \)
c. \( \frac{3 \epsilon_{0} A}{d} \)
D.
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x}) \) be a continuous function
whose range is \( [2,6,5] . \) If \( h(x)= \) \( \left[\frac{\cos x+f(x)}{\lambda}\right], \lambda \in N \) be continuous
where [.] denotes the greatest integer
function, then the least value of \( \lambda \) is
\( A \cdot 6 \)
B. 7
c. 8
D. None of these
Subject: Maths
If \( I_{n}=\int x^{n} e^{a x} d x, \) then \( I_{n}-\frac{x^{n} e^{a x}}{a}= \)
A. \( \frac{n}{a} I_{n-2} \)
B. \( -\frac{n}{a} I_{n-2} \)
c. \( \frac{n}{a} I_{n-1} \)
D. \( -\frac{n}{a} I_{n-1} \)
Subject: Physics
A stream of electrons and protons are
directed towards a narrow slit in a
screen (see figure). The intervening region has a uniform electric field \( \boldsymbol{E} \)
(vertically downwards) and a uniform
magnetic field \( B \) (out of the plane of the
figure) as shown. Then:
This question has multiple correct options
A \( \cdot \) electron and protons with speed \( \frac{|E|}{|B|} \) will pass through
the slitt
B. protons with speed \( \frac{|E|}{|B|} \) will pass through the slit.
electrons of the same speed will not
c. neither electrons nor protons will go through the slitt irrespective of their speed
D. electrons will always be deflected upwards irrespective of their speed