Match List I and List II
A Gauss’s Law in Electrostatics I $∮ \vec{E}\cdot \vec{d}l= - \frac{d\phi _{B}}{dt}$
B Faraday's Law II
$∮ \vec{B}\cdot d\vec{A}= 0$
C Gauss’s Law in Magnetism III $∮ \vec{B}\cdot d\vec{l}=\mu i \mu \in \frac{d\phi _{E}}{dt}$
$_{0}_{c}+_{0}_{0}$
D Ampere-Maxwell Law IV $∮ \vec{E}\cdot d\vec{s}= \frac{q}{\in _{0}}$
Choose the correct answer from the options given below :
✓ Accepted Answer:400
No explanation saved for this question yet.
Q2mcq
Match List I with List II
List I List II
A Troposphere I Approximate $65 -75\, km$ over Earth’s surface
B E-Part of Stratosphere II Approximate $300\, km$ over Earth’s surface
C $F_{2}$ -Part of Thermosphere III Approximate $10\, km$ over Earth’s surface
D D-Part of Stratosphere IV Approximate $100\, km$ over Earth’s surface
Choose the correct answer from the options given below :
a.
A-III, B-IV, C-II, D-I
b.
A-I, B-II, C-IV, D-III
c.
A-I, B-IV, C-III, D-II
d.
A-III, B-II, C-I, D-IV
Correct Answer
No explanation saved for this question yet.
Q3mcq
A spherical drop of liquid splits into $1000$ identical spherical drops. If $u_{i}$ is the surface energy of the original
drop and $u_{f}$ is the total surface energy of the resulting drops, the (ignoring evaporation), $\frac{u_{f}}{u_{i}} =(\frac{10}{x})$ . Then
value of $x$ is ______:
No explanation saved for this question yet.
Q4mcq
A point charge of $10\,$ µ $C$ is placed at the origin. At what location on the $X$ -axis should a point charge of $40\,$ µ $C$
be placed so that the net electric field is zero at $x= 2\, cm$ on the $X$ -axis ?
a.
$x= 6\, cm$
Correct Answer
b.
$x= 4\, cm$
c.
$x= 8\, cm$
d.
$x= -4\, cm$
No explanation saved for this question yet.
Q5mcq
Match List I with List II
List List II
A Young's Modulus $(Y)$ I $[ML^{-1} \,T\,^{-1}]$
B Co-efficient of Viscosity $(\eta )$ II $[ML^{2} \,T\,^{-1}]$
C Planck's Constant $(h)$ III $[ML^{-1} \,T\,^{-2}]$
D Work Function $(\phi )$ IV $[ML^{2} \,T^{-2}]$
Choose the correct answer from the options given below:
a.
A-II, B-III, C-IV, D-I
b.
A-III, B-I, C-II, D-IV
Correct Answer
c.
A-I, B-III, C-IV, D-II
d.
A-I, B-II, C-III, D-IV
No explanation saved for this question yet.
Q6mcq
A body of mass is taken from earth surface to the height $h$ equal to twice the radius of earth $(R_{e})$ , the increase
in potential energy will be : ( $g\, =$ acceleration due to gravity on the surface of earth)
a.
$3mgR_{e}$
b.
$\frac{1}{3} mgR_{e}$
Correct Answer
c.
$\frac{2}{3} mgR_{e}$
d.
$\frac{1}{2} mgR_{e}$
No explanation saved for this question yet.
Q7mcq
For a moving coil galvanometer, the deflection in the coil is $0. 05\, rad$ when a current of $10\, mA$ is passed
through it. If the torsional constant of suspension wire is $4. 0\, \times \,10^{-5}\,N\,m\, rad^{-1}$ , the magnetic field is $0. 01\,T$
and the number of turns in the coil is $200$ , the area of each turn (in $cm^{2}$ ) is :
a.
$\,2. 0$
b.
$1. 0$
Correct Answer
c.
$\,1. 5$
d.
$0. 5$
No explanation saved for this question yet.
Q8nat
A wire of length $1\,m$ moving with velocity $8\,m\,s^{-1}$ at right angles to a magnetic field of $2\,T$ . The magnitude
of induced emf, between the ends of wire will be ___________.
✓ Accepted Answer:5
No explanation saved for this question yet.
Q9nat
Given below are two statements :
Statement I :Stopping potential in photoelectric effect does not depend on the power of the light source.
Statement II :For a given metal, the maximum kinetic energy of the photoelectron depends on the
wavelength of the incident light.
In the light of above statements, choose the most appropriate answer from the options given below.
(1) Statement I is incorrect but statement II is correct (2) Both Statement I and Statement II are incorrect
(3) Statement I is correct but statement II is incorrect (4) Both statement I and statement II are correct
✓ Accepted Answer:68
No explanation saved for this question yet.
Q10mcq
Two objects are projected with same velocity $u$ however at different angles $\alpha$ and $\beta$ with the horizontal. If
$\alpha \, +\beta = \,90^{\circ}$ , the ratio of horizontal range of the first object to the $2^{nd}$ object will be :
a.
$4\, : \,1\,$
b.
$2\, : \,1$
c.
$1\, : \,2$
d.
$\,1\, : \,1$
Correct Answer
No explanation saved for this question yet.
🎉 10 Free Sample Solutions Completed
Unlock All 90 Questions & Solutions
Sign up free in seconds to unlock step-by-step AI answers for the remaining 80 questions.
A series LCR circuit is connected to an AC source of $220\,V$ , $50\, Hz$ . The circuit contains a resistance
$R= 80\,\Omega$ , an inductor of inductive reactance $X_{L} = 70\,\Omega$ , and a capacitor of capacitive reactance $X_{C} = 130\,\Omega$
. The power factor of circuit is $\frac{x}{10}$ . The value of $x$ is:
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where
the molecule has one additional vibrational mode is :-
a.
$\frac{9}{2}R$
b.
$\frac{5}{2}R$
c.
$\frac{3}{2}R$
d.
$\frac{7}{2}R$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Consider a block kept on an inclined plane (inclined at $45^{\circ}$ ) as shown in the figure. If the force required to just
push it up the incline is $2$ times the force required to just prevent it from sliding down, the coefficient of friction
between the block and inclined plane $($ µ $)$ is equal to :
.
a.
$0. 33$
b.
$0. 60$
c.
$0. 25$
d.
$0. 50$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A train blowing a whistle of frequency $320\, Hz$ approaches an observer standing on the platform at a speed of
$66\,m\,s^{-1}$ . The frequency observed by the observer will be (given speed of sound $= 330\,m\,s^{-1}$ ) ______ $Hz$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3 : 2$ . The ratio of their
nuclear sizes will be $( \frac{x}{3})\frac{1}{3}$ . The value of ‘ $x$ ’ is:
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Statement I :When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic it
becomes N-type semi conductor such that P-type has excess holes and N-type has excess electrons.
Statement II :When such P-type and N-type semi-conductors, are fused to make a junction, a current will
automatically flow which can be detected with an externally connected ammeter.
In the light of above statements, choose the most appropriate answer from the options given below.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Every planet revolves around the sun in an elliptical orbit :
A. The force acting on a planet is inversely proportional to square of distance from sun.
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun.
C. The centripetal force acting on the planet is directed away from the sun.
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major
axis of elliptical orbit.
Choose the correct answer from the options given below :
a.
A and D only
b.
C and D only
c.
B and C only
d.
A and C only
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two long parallel wires carrying currents $8\,A$ and $15\,A$ in opposite directions are placed at a distance of $7\, cm$
from each other. A point $P$ is at equidistant from both the wires such that the lines joining the point $P$ to the
wires are perpendicular to each other. The magnitude of magnetic field at $P$ is ______ $\times 10^{-6}\,T$ . (Given:
$\sqrt{2}= 1. 4$ )
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
An object is placed on the principal axis of convex lens of focal length $10\, cm$ as shown. A plane mirror is
placed on the other side of lens at a distance of $20\, cm$ . The image produced by the plane mirror is $5\, cm$ inside
the mirror. The distance of the object from the lens is ____ $cm$ .
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A particle executes simple harmonic motion between $x= -A\,and\,x= +A$ . If time taken by particle to go
from $x\, = \,0$ to $\frac{A}{2}$ is $2\,s$ ; then time taken by particle in going from $x= \frac{A}{2}$ to $A$ is:
a.
$3\,s$
b.
$2\,s$
c.
$1. 5\,s$
d.
$4\,s$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A capacitor has capacitance $5\,$ µ $F$ when its parallel plates are separated by air medium of thickness $d$ . A slab of
material of dielectric constant $1. 5$ having area equal to that of plates but thickness $\frac{d}{2}$ is inserted between the
plates. Capacitance of the capacitor in the presence of slab will be ______ µ $F$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two cells are connected between points $A$ and $B$ as shown. Cell 1 has emf of $12\,V$ and internal resistance of
$3\,\Omega$ . Cell 2 has emf of $6\,V$ and internal resistance of $6\,\Omega$ . An external resistor $R$ of $4\,\Omega$ is connected across $A$
and $B$ . The current flowing through $R$ will be ______ $A$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If a solid sphere of mass $5\, kg$ and a disc of mass $4\, kg$ have the same radius, then the ratio of moment of inertia
of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\frac{x}{7}$ . The
value of $x$ is ______.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The energy levels of an atom is shown is figure.
Which one of these transitions will result in the emission of a photon of wavelength $124. 1\, nm$ ?
Given ( $h\, = \,6. 62\, \times \,10^{-34}\,J\,s$ )
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The graph between two temperature scales $P$ and $Q$ is shown in the figure. Between upper fixed point and
lower fixed point there are $150$ equal divisions of scale $P$ and $100$ divisions on scale $Q$ . The relationship for
conversion between the two scales is given by :
.
a.
$\frac{t_{Q}}{150} = \frac{t_{P}-180}{100}$
b.
$\frac{t_{Q}}{100} = \frac{t_{P}-30}{150}$
c.
$\frac{t_{P}}{180} = \frac{t_{Q}-40}{100}$
d.
$\frac{t_{Q}}{100} = \frac{t_{P}-180}{150}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A body of mass $1\, kg$ collides head on elastically with a stationary body of mass $3\, kg$ . After collision, the
smaller body reverses its direction of motion and moves with a speed of $2\,m\,s^{-1}$ . The initial speed of the
smaller body before collision is ______ $m\,s^{-1}$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The light rays from an object have been reflected towards an observer from a standard flat mirror, the image
observed by the observer are :-
A. Real
B. Erect
C. Smaller in size than object
D. Laterally inverted
Choose the most appropriate answer from the options given below:
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Match List I with List II :
List I List II
Isothermal
A I Work done by the gas decreases internal energy
Process
B Adiabatic Process II No change in internal energy
The heat absorbed goes partly to increase internal energy and partly to do
III
C Isochoric Process
work
DIsobaric Process IVNo work is done on or by the gas
Choose the correct answer from the options given below :
a.
A-II, B-I, C-III, D-IV
b.
A-II, B-I, C-IV, D-III
c.
A-I, B-II, C-IV, D-III
d.
A-I, B-II, C-III, D-IV
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Statement I:-Dipole moment is a vector quantity and by convention it is depicted by a small arrow with tail
on the negative centre and head pointing towards the positive centre.
Statement II:-The crossed arrow of the dipole moment symbolizes the direction of the shift of charges in the
molecules.
In the light of the above statements, choose the most appropriate answer from the options given below:-
a.
Both Statement I and Statement II are correct.
b.
Statement I is incorrect but Statement II is
correct.
c.
Both Statement I and Statement II are incorrect.
d.
Statement I is correct but Statement II is
incorrect.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A. Ammonium salts produce haze in atmosphere.
B. Ozone gets produced when atmospheric oxygen reacts with chlorine radicals.
C. Polychlorinated biphenyls act as cleansing solvents.
D. ‘Blue baby’ syndrome occurs due to the presence of excess of sulphate ions in water.
Choose the correct answer from the options given below:-
a.
A, B and C only
b.
B and C only
c.
A and D only
d.
A and C only
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$28. 0$ L of $CO_{2}$ is produced on complete combustion of $16. 8\,L$ gaseous mixture of ethene and methane at
$25^{\circ}C$ and $1$ atm. Heat evolved during the combustion process is $kJ$
Given $: \Delta H_{C}(CH_{4}) = -900\, kJ \, mol^{-1}$
$\Delta H_{C}(C_{2}H_{4}) = -1400\, kJ \, mol^{-1}$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$||$
Based on the given figure, the number of correct statement/s is/are
A. Surface tension is the outcome of equal attractive and repulsion forces acting on the liquid molecule in
bulk.
B. Surface tension is due to uneven forces acting on the molecules present on the surface.
C. The molecule in the bulk can never come to the liquid surface.
D. The molecules on the surface are responsible for vapour pressure if the system is a closed system.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Given below are two statements:-
Statement I:-In froth floatation method a rotating paddle agitates the mixture to drive air out of it.
Statement II:-Iron pyrites are generally avoided for extraction of iron due to environmental reasons.
In the light of the above statements, choose the correct answer from the options given below:-
a.
Both Statement I and Statement II are true
b.
Statement I is false but Statement II is true
c.
Statement I is true but Statement II is false
d.
Both Statement I and Statement II are false
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Match List I with List II
List I List II
A. Cobalt catalyst I. $(H_{2}+ Cl_{2})$ production
B. Syngas II. Water gas production
C. Nickel catalyst III. Coal gasification
D. Brine solution IV. Methanol production
Choose the correct answer from the options given below:-
a.
A-IV, B-I, C-II, D-III
b.
A-IV, B-III, C-I, D-II
c.
A-II, B-III, C-IV, D-I
d.
A-IV, B-III, C-II, D-I
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$Pt(s)H_{2}(\,g)(1 bar)|H^{+}(aq)(1M)| M^{3+}(aq), M^{+}(aq) Pt(s)$
The $E_{cell\,}$ for the given cell is $0. 1115\,V$ at $298\,K$
When $\frac{[M^{+}(aq)]}{[M^{3+}(aq)]} = 10^{a}$
The value of a is ___________
Given : $E^{\theta }_{M^{3+}/M^{+}}= 0. 2\,V$
$\frac{2.303 RT}{F} = 0. 059\,V$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A:-Butylated hydroxyl anisole when added to butter increases its shelf life.
Reason R:-Butylated hydroxyl anisole is more reactive towards oxygen than food.
In the light of the above statements, choose the most appropriate answer from the options given below:-
a.
Both A and R are correct and R is the correct
explanation of A.
b.
A is correct but R is not correct.
c.
A is not correct but R is correct.
d.
Both A and R are correct but R is NOT the
correct explanation of A.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
What is the mass ratio of ethylene glycol ( $C_{2}H_{6}O_{2}$ , molar mass $= 62\,g/ mol$ ) required for making $500\,g$ of
$0. 25$ molal aqueous solution and $250\, mL$ of $0. 25$ molar aqueous solution?
a.
$1 : 1$
b.
$3 : 1$
c.
$2 : 1$
d.
$1 : 2$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The number of pairs of the solution having the same value of the osmotic pressure from the following is
(Assume $100%$ ionization)
A. $0. 500\,M\,C_{2}H_{5}OH(aq)$ and $0. 25\,M\, KBr(aq)$
B. $0. 100\,M\,K_{4}[Fe(CN)_{6}](aq)$ and $0. 100\,M FeSO_{4}(NH_{4})_{2}SO_{4}(aq)$
C. $0. 05\,M\,K_{4}[Fe(CN)_{6}]$ (aq) and $0. 25\,M\, NaCl (aq)$
D. $0. 15\,M\, NaCl(aq)$ and $0. 1\,M\, BaCl_{2}(aq)$
E. $0. 02\,M\, KCl. MgCl_{2}. 6H_{2}O(aq)$ and $0. 05\,M KCl(aq)$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A:-The alkali metals and their salts impart characteristic colour to reducing flame.
Reason R:-Alkali metals can be detected using flame tests.
In the light of the above statements, choose the most appropriate answer form the options given below
a.
Both A and R are correct but R is NOT the
correct explanation of A.
b.
A is correct but R is not correct.
c.
A is not correct but R is correct
d.
Both A and R are correct and R is the correct
explanation of A.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Match List I with List II.
Choose the correct answer from the options given below :-
List I List II
Isomeric pairs Type of isomers
Propanamine and N-
A I Metamers
Methylethanamine
Hexan-2-one Positional
B II
Hexan-3-one isomers
Ethanamide and
C III Functional isomers
Hydroxyethanimine
D o-nitrophenol and pnitrophenol IV Tautomers
a.
$A -III, \,B -IV, \,C -I, \,D -II$
b.
$A -IV, \,B -III, \,C -I, \,D -II$
c.
$A -II, \,B -III, \,C -I, \,D -IV$
d.
$A -III, \,B -I, \,C -IV, \,D -II$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Total number of moles of AgCl precipitated on addition of excess of $AgNO_{3}$ to one mole each of the following
complexes $[Co (NH_{3})_{4}Cl_{2}] Cl$ , $[Ni (H_{2}O)_{6}] Cl_{2}, [Pt (NH_{3})_{2}Cl_{2}]$ and $[Pd (NH_{3})_{4}] Cl_{2}$ is
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A :- Carbon forms two important oxides $CO$ and $CO_{2}$ . $CO$ is neutral whereas $CO_{2}$ is acidic in
nature.
Reason R: $CO_{2}$ can combine with water in a limited way to form carbonic acid, while $CO$ is sparingly
soluble in water.
In the light of the above statements, choose the most appropriate answer from the options given below :-
a.
Both A and R are correct but R is NOT the
correct explanation of A.
b.
Both A and R are correct and R is the correct
explanation of A.
c.
A is not correct but R is correct.
d.
A is correct but R is not correct.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Match List I with List II
List I List II
Coordination entity Wavelength of light absorbed in nm
A $[CoCl (NH_{3})_{5}]^{2+}$ I. $310$
B $[Co (NH_{3})_{6}]^{3+}$ II. $475$
C $[Co(CN)_{6}]^{3-}$ III. $535$
D $[Cu (H_{2}O)_{4}]^{2+}$ IV. $600$
Choose the correct answer from the options given below :-
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Match List I with List II
List I (Amines) List II $(pKb)$
A. Aniline I. $3. 25$
B. Ethanamine II. $3. 00$
C. N-Ethylethanamine III. $9. 38$
D. N, N-Diethylethanamine IV. $3. 29$
Choose the correct answer from the options given below:-
a.
A-I, B-IV, C-II, D-III
b.
A-III, B-II, C-I, D-IV
c.
A-III, B-II, C-IV, D-I
d.
A-III, B-IV, C-II, D-I
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A chloride salt solution acidified with dil. $HNO_{3}$ gives a curdy white precipitate, $[A]$ , on addition of $AgNO_{3}$ .
[A] on treatment with $NH_{4}OH$ gives a clear solution, B.
a.
$H[AgCl_{3}]&[Ag (NH_{3})_{2}] Cl$
b.
$H[AgCl_{3}]\,&\,(NH_{4})[Ag(OH)_{2}]$
c.
$AgCl \,&\,[Ag (NH_{3})_{2}] Cl$
d.
$AgCl \,&\,(NH_{4})[Ag(OH)_{2}]$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The number of incorrect statement/s from the following is/are
A. Water vapours are adsorbed by anhydrous calcium chloride.
B. There is a decrease in surface energy during adsorption.
C. As the adsorption proceeds, $\Delta H$ becomes more and more negative.
D. Adsorption is accompanied by decrease in entropy of the system.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Match List I with List II
List I (Name of polymer) List II (Uses)
A Glyptal I Flexible pipes
B Neoprene II Synthetic wool
C Acrilan III Paints and Lacquers
D LDP IV Gaskets
Choose the correct answer from the options given below :-
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A first order reaction has the rate constant, $k = 4. 6 \times 10^{-3}\,s^{-1}$ . The number of correct statement/s from the
following is/are Given: $log \,3 = 0. 48$ .
A. Reaction completes in $1000\,s$ .
B. The reaction has a half-life of $500\,s$ .
C. The time required for $10%$ completion is 25 times the time required for 90% completion.
D. The degree of dissociation is equal to $(1 -e^{-kt})$ .
E. The rate and the rate constant have the same unit.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $A,B,C$ be $3 \times 3$ matrices such that $A$ is symmetric and $B$ and $C$ are skew-symmetric.
Consider the statements
$(S1)\,A^{13} B^{26} - B^{26} A^{13}$ is symmetric
$(S2)\,A^{26}C^{13} - C^{13} A^{26}$ is symmetric
Then,
a.
Only $S2$ is true
b.
Only $S1$ is true
c.
Both $S1$ and $S2$ are false
d.
Both $S1$ and $S2$ are true
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Suppose Anil's mother wants to give $5$ whole fruits to Anil from a basket of $7$ red apples, $5$ white apples and $8$
oranges. If in the selected $5$ fruits, at least $2$ orange, at least one red apple and at least one white apple must be
given, then the number of ways, Anil's mother can offer $5$ fruits to Anil is _____ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If the shortest distance between the line joining the points $(1, 2, 3)$ and $(2, 3, 4)$ , and the line
$\frac{x-1}{2} = \frac{y+1}{-1} = \frac{z-2}{0}$ is $\alpha$ , then $28\alpha ^{2}$ is equal to _____ .
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The foot of perpendicular of the point $(2, 0, 5)$ on the line $\frac{x+1}{2} = \frac{y-1}{5} = \frac{z+1}{-1}$ is $(\alpha ,\beta ,\gamma )$ . Then. Which of the
following is NOT correct?
a.
$\frac{\alpha \beta}{\gamma} = \frac{4}{15}$
b.
$\frac{\alpha}{\beta} = -8$
c.
$\frac{\beta}{\gamma} = -5$
d.
$\frac{\gamma}{\alpha} = \frac{5}{8}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A triangle is formed by $X$ -axis, $Y$ -axis and the line $3x+ 4y= 60$ . Then the number of points $P(a,b)$ which lie
strictly inside the triangle, where $a$ is an integer and $b$ is a multiple of $a$ , is _____ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that
$N -2, , \,N + 2\sqrt{3\,N}$ are in geometric progression be $\frac{k}{48}$ . Then the value of $k$ is
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$\{(1 + | cos \,x|) \frac{\lambda}{|cos \,x|}, 0 <x< \frac{\pi}{2}$
If the function $f(x) = \mu , x= \frac{\pi}{2}$ is continuous at $x= \frac{\pi}{2}$ , then
$\{ \frac{cot \,6x}{cot \,4x,}$
$e \frac{\pi}{2} <x<\pi$
$9\lambda + 6\, log_{c}\mu +\mu ^{6} - e^{6\lambda }$ is equal to
a.
$11$
b.
$8$
c.
$2e^{4} + 8$
d.
$10$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$[ \frac{1}{\sqrt{10}} \frac{3}{\sqrt{10}} ] 1 -i$
Let $A =$ and $B =[ ]$ , where $i = \sqrt{-1}$ . If $M = A^{T} BA$ , then the inverse of the matrix
$[ \frac{-3}{\sqrt{10}} \frac{1}{\sqrt{10}} ] 0 1$
$AM^{2023} \,A^{T}$ is
a.
$1 -2023i$
$[ ]$
$0 1$
b.
$1 0$
$[ ]$
$-2023i 1$
c.
$1 0$
$[ ]$
$2023i 1$
d.
$1 2023i$
$[ ]$
$0 1$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $f(x) = 2x^{n} +\lambda ,\lambda \in R, n \in N$ , and $f(4) = 133$ , $f(5) = 255$ . Then the sum of all the positive integer
divisors of $(f(3) - f(2))$ is
a.
$61$
b.
$60$
c.
$58$
d.
$59$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If $\int \frac{1}{3}^{3}|log_{e}x|dx = \frac{m}{n} log_{e}(\frac{n^{2}}{e} )$ , where $m$ and $n$ are coprime natural numbers, then $m^{2} + n^{2} -5$ is equal to
_____ .
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let the function $f(x)= 2x^{3} +(2p-7)x^{2} + 3(2p-9)x-6$ have a maxima for some value of $x < 0$ and a
minima for some value of $x> 0$ . Then, the set of all values of $p$ is
a.
$(\frac{9}{2} , \infty )$
b.
$(0, \frac{9}{2})$
c.
$(-\infty , \frac{9}{2} )$
d.
$(-\frac{9}{2} , \frac{9}{2})$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $f :R\rightarrow \rightarrow R$ be a function defined by $f(x) = log_{\sqrt{m}} {\sqrt{2}(sinx-cosx) +m-2}$ , for some $m$ , such that
the range of $f$ is $[0, 2]$ . Then the value of $m$ is _____ .
a.
$5$
b.
$3$
c.
$2$
d.
$4$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
For the two positive numbers $a,b$ , if $a,b$ and $\frac{1}{18}$ are in a geometric progression, while $\frac{1}{a} , 10$ and $\frac{1}{b}$ are in an
arithmetic progression, then, $16a+ 12b$ is equal to _____ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $y=y(t)$ be a solution of the differential equation $\frac{dy}{dt} +\alpha y=\gamma e^{-\beta t}$ Where, $\alpha > 0,\beta > 0$ and $\gamma > 0$ . Then
$Lim_{t\rightarrow \infty \rightarrow } y(t)$
a.
is $0$
b.
does not exist
c.
is $1$
d.
is $-1$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Points $P(-3, 2),Q(9, 10)$ and $R($ $\alpha$ $, 4)$ lie on a circle $C$ with $PR$ as its diameter. The tangents to $C$ at the
points $Q$ and $R$ intersect at the point $S$ . If $S$ lies on the line $2x- ky= 1$ , then $k$ is equal to _____ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$25%$ of the population are smokers. A smoker has $27$ times more chances to develop lung cancer then a non-
smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is $\frac{k}{10}$ .Then the
value of $k$ is _____ .
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $T$ and $C$ respectively, be the transverse and conjugate axes of the hyperbola
$16x^{2} - y^{2} + 64x+ 4y+ 44 = 0$ . Then the area of the region above the parabola $x^{2} =y+ 4$ , below the
transverse axis $T$ and on the right of the conjugate axis $C$ is:
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If $m$ and $n$ respectively are the numbers of positive and negative value of $\theta$ in the interval $[-\pi ,\pi ]$ that satisfy
the equation $cos 2\theta cos \frac{\theta}{2} = cos 3\theta cos \frac{9\theta}{2}$ , then $mn$ is equal to _____ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $a\in R$ and let $\alpha ,\beta$ be the roots of the equation $x^{2} + 60\frac{1}{4}x+a= 0$ . If $\alpha ^{4} +\beta ^{4} = -30$ , then the product of
all possible values of $a$ is _____ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If the four points, whose position vectors are $3ˆi -4ˆj + 2ˆk,ˆi + 2ˆj - ˆk, -2ˆi -ˆj + 3ˆk\,\,$ and $5ˆi -2\alpha ˆj + 4ˆk$ are
coplanar, then $\alpha$ is equal to
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$|$
The equations of two sides of a variable triangle are $x = 0$ and $y = 3$ , and its third side is a tangent to the
parabola $y^{2} = 6x$ . The locus of its circumcentre is :
a.
$4y^{2} -18y-3x-18 = 0$
b.
$4y^{2} + 18y+ 3x+ 18 = 0$
c.
$4y^{2} -18y+ 3x+ 18 = 0$
d.
$4y^{2} -18y-3x+ 18 = 0$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
