Two isolated metallic solid spheres of radii π and 2π are charged such that both have same charge density π.
The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is π $'$ .
The ratio $\frac{π'}{π}$ is :
a.
$\frac{9}{4}$
b.
$\frac{4}{3}$
c.
$\frac{5}{3}$
d.
$\frac{5}{6}$
Correct Answer
No explanation saved for this question yet.
Q2mcq
The magnetic moments associated with two closely wound circular coils π΄and π΅of radius
π $_{π΄}$ = 10 cm and π $_{π΅}$ = 20 cmrespectively are equal if: (Where π $_{π΄}$ , πΌ $_{π΄}$ and π $_{π΅}$ , πΌ $_{π΅}$ are number of
turn and current of π΄ and π΅respectively)
Speed of an electron in Bohrβs 7 $^{th}$ orbit for Hydrogen atom is 3 . 6 $\times$ 10 $^{6}$ m s $^{-1}$ . The corresponding
speed of the electron in 3 $^{rd}$ orbit, in m s $^{-1}$ is :
a.
1 . 8 $\times$ 10 $^{6}$
b.
7 . 5 $\times$ 10 $^{6}$
c.
3 . 6 $\times$ 10 $^{6}$
d.
8 . 4 $\times$ 10 $^{6}$
Correct Answer
No explanation saved for this question yet.
Q4nat
In an experiment for estimating the value of focal length of converging mirror, image of an object placed at
40 cmfrom the pole of the mirror is formed at distance 120 cmfrom the pole of the mirror. These distances
are measured with a modified scale in which there are 20small divisions in 1 cm. The value of error in
measurement of focal length of the mirror is $\frac{1}{πΎ}$ cm. The value of πΎis ______.
✓ Accepted Answer:32
No explanation saved for this question yet.
Q5nat
As per the given figure, if $\frac{dπΌ}{dπ‘}$ = - 1 A s $^{-1}$ , then the value of π $_{AB}$ at this instant will be ______ V.
✓ Accepted Answer:30
No explanation saved for this question yet.
Q6mcq
In a series πΏπ circuit with π $_{πΏ}$ = π , power factor is π $_{1}$ . If a capacitor of capacitance πΆwith π $_{πΆ}$ = π $_{πΏ}$ is added to
the circuit the power factor becomes π $_{2}$ . The ratio of π $_{1}$ to π $_{2}$ will be :
a.
1: 3
b.
1: $\sqrt$2
Correct Answer
c.
1: 1
d.
1: 2
No explanation saved for this question yet.
Q7mcq
Choose the correct relationship between Poisson ratio π, bulk modulus ( πΎ) and modulus of rigidity πof a
given solid object:
A massless square loop, of wire of resistance 10 $\Omega$, supporting a mass of 1 g, hangs vertically with one of its
sides in a uniform magnetic field of 10 $^{3}$ G, directed outwards in the shaded region. A dc voltage πis applied
to the loop. For what value of π, the magnetic force will exactly balance the weight of the supporting mass of
1 g?
(If sides of the loop = 10 cm, π= 10 m s $^{-2}$ )
.
a.
$\frac{1}{10}$ V
b.
100 V
c.
1 V
d.
10 V
Correct Answer
No explanation saved for this question yet.
Q9mcq
A person has been using spectacles of power -1 . 0diopter for distant vision and a separate reading glass of
power 2 . 0diopters. What is the least distance of distinct vision for this person:
a.
10 cm
b.
40 cm
c.
30 cm 50 cm
No explanation saved for this question yet.
Q10nat
The general displacement of a simple harmonic oscillator is π₯= π΄ sin ππ‘. Let πbe its time period. The
slope of its potential energy (π) - time (π‘) curve will be maximum when π‘= $\frac{π}{π½}$ . The value of π½is ______.
✓ Accepted Answer:8
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 horse rider covers half the distance with 5 m s $^{-1}$ speed. The remaining part of the distance was travelled
with speed 10 m s $^{-1}$ for half the time and with speed 15 m s $^{-1}$ for other half of the time. The mean
speed of the rider averaged over the whole time of motion is $\frac{π₯}{7}$ m s $^{-1}$ . The value of π₯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.
A ball of mass 200 grests on a vertical post of height 20 m. A bullet of mass 10 g, travelling in horizontal
direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a
distance 30 mand the bullet at a distance of 120 mfrom the foot of the post. The value of initial velocity of
the bullet will be (if π= 10 m s $^{-2}$ ) :
a.
120 m s $^{-1}$
b.
60 m s $^{-1}$
c.
400 m s $^{-1}$
d.
360 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 charge flowing in a conductor changes with time as ππ‘= πΌπ‘- π½π‘ $^{2}$ + πΎπ‘ $^{3}$ , where πΌ, π½and πΎare constants.
Minimum value of current is:
a.
πΌ- $\frac{3π½2}{πΎ}$
b.
πΌ- $\frac{πΎ2}{3π½}$
c.
π½- $\frac{πΌ2}{3πΎ}$
d.
πΌ- $\frac{π½2}{3πΎ}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The pressure ( π) and temperature ( π) relationship of an ideal gas obeys the equation ππ $^{2}$ = constant. The
volume expansion coefficient of the gas will be :
a.
3π $^{2}$
b.
$\frac{3}{π2}$
c.
$\frac{3}{π3} \frac{3}{π}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A sinusoidal carrier voltage is amplitude modulated. The resultant amplitude modulated wave has maximum
and minimum amplitude of 120 V and 80 Vrespectively. The amplitude of each side band is :
a.
15 V
b.
10 V
c.
20 V
d.
5 V
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If the gravitational field in the space is given as - $\frac{πΎ}{π2}$ . Taking the reference point to be at π= 2 cmwith
gravitational potential π= 10 J kg $^{-1}$ . Find the gravitational potentials at π= 3 cmin SI unit (Given, that
πΎ= 6 J cm kg $^{-1}$ )
a.
9
b.
11
c.
12
d.
10
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
As per the given figure, a small ball πslides down the quadrant of a circle and hits the other ball πof equal
mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the
velocity of ball πafter collision will be : ( π = 10 m s $^{-2}$ )
a.
0
b.
0 . 25 m s $^{-1}$
c.
2 m s $^{-1}$
d.
4 m s $^{-1}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
In Youngβs double slit experiment, two slits π $_{1}$ and π $_{2}$ are πdistance apart and the separation from slits to
screen is π·(as shown in figure). Now if two transparent slabs of equal thickness 0 . 1 mmbut refractive
index 1 . 51and 1 . 55are introduced in the path of beam $\lambda$ = 4000 Γ from π $_{1}$ and π $_{2}$ respectively. The
central bright fringe spot will shift by ________ number of fringes.
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 capacitor of capacitance 900 Β΅ Fis charged by a 100 Vbattery. The capacitor is disconnected from the
battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor
connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged
capacitor. The loss of energy in this process is measured as π₯$\times$ 10 $^{-2}$ J. The value of π₯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.
A thin uniform rod of length 2 m, cross sectional area π΄and density πis rotated about an axis passing
through the centre and perpendicular to its length with angular velocity π. If value of πin terms of its
rotational kinetic energy πΈis $\sqrt$ $\frac{πΌπΈ}{π΄π}$ , then the value of πΌis ______.
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 height of liquid column raised in a capillary tube of certain radius when dipped in liquid π΄vertically is,
5 cm. If the tube is dipped in a similar manner in another liquid π΅of surface tension and density double the
values of liquid π΄, the height of liquid column raised in liquid B would be ______ m.
a.
0 . 20
b.
0 . 5
c.
0 . 05
d.
0 . 10
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a
power of 24 W. The radius of curvature of hemisphere is 10 cmand the inner surface is completely
reflecting. The force on the hemisphere due to the light falling on it is ______ $\times$ 10 $^{-8}$ N.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
In a screw gauge, there are 100divisions on the circular scale and the main scale moves by 0 . 5 mmon a
complete rotation of the circular scale. The zero of circular scale lies 6divisions below the line of graduation
when two studs are brought in contact with each other. When a wire is placed between the studs, 4linear scale
th
divisions are clearly visible while 46 division the circular scale coincide with the reference line. The diameter
of the wire is ______ $\times$ 10 $^{-2}$ mm .
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 small object at rest, absorbs a light pulse of power 20 mWand duration 300 ns. Assuming speed of light
as 3 $\times$ 10 $^{8}$ m s $^{-1}$ . The momentum of the object becomes equal to :
a.
0 . 5 $\times$ 10 $^{-17}$ kg m s $^{-1}$
b.
2 $\times$ 10 $^{-17}$ kg m s $^{-1}$
c.
3 $\times$ 10 $^{-17}$ kg m s $^{-1}$
d.
1 $\times$ 10 $^{-17}$ kg m s $^{-1}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Heat is given to an ideal gas in an isothermal process.
A. Internal energy of the gas will decrease.
B. Internal energy of the gas will increase.
C. Internal energy of the gas will not change.
D. The gas will do positive work.
E. The gas will do negative work.
Choose the correct answer from the options given below :
a.
A and E only
b.
B and D only
c.
C and E only
d.
C and D only
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The figure represents the momentum time ( π- π‘) curve for a particle moving along an axis under the influence
of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum
respectively ?
If π‘ $_{3}$ - π‘ $_{2}$ < π‘ $_{1}$
a.
c and a
b.
b and c
c.
c and b
d.
a and b
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Match Column-I with Column-II :
Column-I (x-t graphs) Column-II (v-t graphs)
A I
B II
C III
D IV
Choose the correct answer from the options given below:
a.
A- II B-IV, C-III, D-I
b.
A- I. B-II, C-III, D-IV
c.
A- II B-III, C-IV, D-I
d.
A- I, B-III. 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.
If compound Areacts with Bfollowing first order kinetics with rate constant 2 . 011 $\times$ 10 $^{-3}$ s $^{-1}$ . The time
taken by A (in seconds) to reduce from 7 gto 2 gwill be _____ . (Nearest Integer)
log5 = 0 . 698, log7 = 0 . 845, log2 = 0 . 301
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Formation of photochemical smog involves the following reaction in which A, Band Care respectively.
hu
(i) NO $_{2}$ $\longrightarrow$A + B
(ii) B + O $_{2}$ $\rightarrow$C
(iii) A + C $\rightarrow$NO $_{2}$ + O $_{2}$
Choose the correct answer from the options given below:
a.
O, NOand NO $^{-}_{3}$
b.
O, N $_{2}$ Oand NO
c.
N, O $_{2}$ and O $_{3}$
d.
NO, Oand O $_{3}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Which of the following compounds would give the following set of qualitative analysis?
(i) Fehlingβs Test: Positive
(ii) Nafusion extract upon treatment with sodium nitroprusside gives a blood red colour but not prussian blue.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A 300mLbottle of soft drink has 0 . 2MCO $_{2}$ dissolved in it. Assuming CO $_{2}$ behaves as an ideal gas, the volume
of the dissolved CO $_{2}$ at STP is _____ mL. (Nearest integer)
Given: At STP, molar volume of an ideal gas is 22 . 7L mol $^{-1}$
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Consider the cell
Pt $_{s}$ H $_{2}$ g, 1atmH $^{+}$ aq, 1M | Fe $^{3 +}$ aq, Fe $^{2 +}$ aq Pt s
When the potential of the cell is 0 . 712 Vat 298 K, the ratio Fe $^{2 +}$ / Fe $^{3 +}$ is
(Nearest integer)
Given: Fe $^{3 +}$ + e $^{-}$ = Fe $^{2 +}$ , E$^{\circ}$Fe $^{3 +}$ , Fe $^{2 +}$ Pt = 0 . 771 $\frac{2 . 303RT}{F}$ = 0 . 06 V
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):In expensive scientific instruments, silica gel is kept in watch-glasses or in semipermeable
membrane bags.
Reason (R):Silica gel adsorbs moisture from air via adsorption, thus protects the instrument from water
corrosion (rusting) and / or prevents malfunctioning.
In the light of the above statements, choose the correct answer from the options given below:
a.
(A) is false but (R) is true
b.
(A) is true but (R) is false
c.
Both (A) and (R) are true and (R) is the correct
explanation of (A)
d.
Both (A) and (R) are true 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.
Match List I with List II
List II
List I
(No. of lone pairs of e $^{-}$
(molecules/ions)
on central atom)
(A) IF $_{7}$ I. Three
(B) ICl $^{-}_{4}$ II. One
(C) XeF $_{6}$ III. Two
(D) XeF $_{2}$ IV. Zero
Choose the correctanswer from the options given below:
a.
A - II, B - III, C - IV, D - I
b.
A - IV, B - III, C - II, D - I
c.
A - II, B - I, C - IV, D - III
d.
A - IV, B - I, C - II, D - III
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-II
LIST-I
(Block of periodic
(Atomic number)
table)
(A) 37 I. p-block
(B) 78 II. d-block
(C) 52 III. f-block
(D) 65 IV. s-block
Choose the correctanswer from the options given below:
a.
A - II, B - IV, C - I, D - III
b.
A - I, B - III, C - IV, D - II
c.
A - IV, B - III, C - II, D - I
d.
A - IV, B - II, C - I, D - III
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 I Fittig reaction
B II Wurtz Fittig reaction
C III Finkelstein reaction
D C $_{2}$ H $_{5}$ Cl + NaI $\rightarrow$C $_{2}$ H $_{5}$ I + Nacl IV Sandmeyer reaction
a.
A-II, B-I, C-III, D-IV
b.
A-III, B-II, C-IV, D-I
c.
A-IV, B-II, C-III, D-I
d.
A-II, B-I, C-IV, D-III
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The energy of one mole of photons of radiation of frequency 2 $\times$ 10 $^{12}$ Hzin Jmol $^{-1}$ is _____ .
(Nearest integer)
(Given: h = 6 . 626 $\times$ 10 $^{-34}$ Js N $_{A}$ = 6 . 022 $\times$ 10 $^{23}$ mol $^{-1}$ )
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):Ketoses give Seliwanoffβs test faster than Aldoses.
Reason (R):Ketoses undergo π½-elimination followed by formation of furfural.
In the light of the above statements, choose the correct answer from the options given below:
a.
(A) is false but (R) is true
b.
Both (A) and (R) are true and (R) is the correct
explanation of (A)
c.
(A) is true but (R) is false
d.
Both (A) and (R) are true 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.
The alkaline earth metal sulphate(s) which are readily soluble in water is/are:
(A) BeSO $_{4}$
(B) MgSO $_{4}$
(C) CaSO $_{4}$
(D) SrSO $_{4}$
(E) BaSO $_{4}$
Choose the correctanswer from the options given below:
a.
A only
b.
B only
c.
A and B
d.
B and C
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
During the qualitative analysis of SO $^{2 -}_{3}$ using dilute H $_{2}$ SO $_{4}$ , SO $_{2}$ gas is evolved which turns K $_{2}$ Cr $_{2}$ O $_{7}$ solution
(acidified with dilute H $_{2}$ SO $_{4}$ ):
a.
Black
b.
Red
c.
Green
d.
Blue
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A solution containing 2 gof a non-volatile solute in 20 gof water boils at 373 . 52 K. The molecular mass
of the solute is _____ gmol $^{-1}$ . (Nearest integer)
Given, water boils at 373 K, K $_{b}$ for water = 0 . 52K kg mol $^{-1}$
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
For OF $_{2}$ molecule consider the following:
(A) Number of lone pairs on oxygen is 2.
(B) FOFangle is less than 104 . 5$^{\circ}$.
(C) Oxidation state of Ois -2.
(D) Molecule is bent 'V' shaped.
(E) Molecular geometry is linear.
Correctoptions are:
a.
C, D, E only
b.
B, E, A only
c.
A, C, D only
d.
A, B, D only
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A trisubstituted compound 'A', C $_{10}$ H $_{12}$ O $_{2}$ gives neutral FeCl $_{3}$ test positive. Treatment of compound 'A' with
NaOHand CH $_{3}$ Brgives C $_{11}$ H $_{14}$ O $_{2}$ , with hydroiodic acid gives methyl iodide and with hot conc. NaOHgives a
compound B, C $_{10}$ H $_{12}$ O $_{2}$ . Compound 'A' also decolorises alkaline KMnO $_{4}$ . The number of πbond/s present in
the compound 'A' 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.
To inhibit the growth of tumours, identify the compounds used from the following:
(A) EDTA
(B) Coordination Compounds of Pt
(C) D-Penicillamine
(D) Cis - Platin
Choose the correct answer from the option given below:
a.
B and D Only
b.
C and D Only
c.
A and B 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.
In the wet tests for identification of various cations by precipitation, which transition element cation doesn't
belong to group IV in qualitative inorganic analysis?
a.
Fe $^{3 +}$
b.
Zn $^{2 +}$
c.
Co $^{2 +}$
d.
Ni $^{2 +}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Among the statements:
π1: π$\vee$π$\Rightarrow$π$\Leftrightarrow$π$\Rightarrow$π
π2: π$\vee$π$\Rightarrow$π$\Leftrightarrow$π$\Rightarrow$π$\vee$π$\Rightarrow$π
a.
Only ( π1 ) is a tautology
b.
Neither ( π1 ) nor ( π2 ) is a tautology
c.
Only ( π2 ) is a tautology
d.
Both ( π1 ) and ( π2 ) are tautologies
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let π¦= π₯+ 2, 4π¦= 3π₯+ 6and 3π¦= 4π₯+ 1be three tangent lines to the circle ( π₯- β) $^{2}$ + ( π¦- π) $^{2}$ = π $^{2}$ .
Then β+ πis equal to :
a.
5
b.
5 ( 1 + $\sqrt$2 )
c.
6
d.
5$\sqrt$2
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If π $_{1}$ < π $_{2}$ are two values of πsuch that the angle between the planes π $_{1}$ : $^{$\rightarrow$}$ π(3 $^{^}$ i - 5 $^{^}$ π+ π) $^{^}$ = 7and
π $_{2}$ : $^{$\rightarrow$}$ πΒ· (π $^{^}$ π+ $^{^}$ π- 3π) $^{^}$ = 9is sin $\frac{-12$\sqrt{\,}$6}{5}$ , then the square of the length of perpendicular from the point
38π $_{1}$ , 10π $_{2}$ , 2to the plane π $_{1}$ 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 the equation of the plane passing through the point ( 1, 1, 2 )and perpendicular to the line
π₯- 3π¦+ 2π§- 1 = 0 = 4π₯- π¦+ π§is π΄π₯+ π΅π¦+ πΆπ§= 1, then 140 ( πΆ- π΅+ π΄) 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.
If π( β, π) be point on the parabola π₯= 4π¦ $^{2}$ , which is nearest to the point π( 0, 33 ), then the distance of π
from the directrix of the parabola π¦ $^{2}$ = 4 ( π₯+ π¦) is equal to:
a.
2
b.
4
c.
8
d.
6
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The line π $_{1}$ passes through the point 2, 6, 2and is perpendicular to the plane 2π₯+ π¦- 2π§= 10. Then the
shortest distance between the line π $_{1}$ and the line $\frac{π₯+ 1}{2}$ = $\frac{π¦+ 4}{-3}$ = $\frac{π§}{2}$ is:
a.
7
b.
$\frac{19}{3}$
c.
$\frac{19}{2}$
d.
9
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let πΌbe the area of the larger region bounded by the curve π¦ $^{2}$ = 8π₯and the lines π¦= π₯and π₯= 2, which lies
in the first quadrant. Then the value of 3πΌis 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.
If the coefficient of π₯ $^{15}$ in the expansion of ππ₯ $^{3}$ + $\frac{1}{1}^{15}$ is equal to the coefficient of π₯ $^{-15}$ in the expansion of
ππ₯3
15
ππ₯ $\frac{1}{3}$ - $\frac{1}{ππ₯3}$ , where πand πare positive real numbers, then for each such ordered pair π, π:
a.
π= π
b.
ππ= 1
c.
π= 3π
d.
ππ= 3
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The mean and variance of 7observations are 8and 16respectively. If one observation 14is omitted, πand π
are respectively mean and variance of remaining 6observation, then π+ 3 π- 5is 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.
If an unbiased die, marked with -2, - 1, 0, 1, 2, 3on its faces is thrown five times, then the probability that the
product of the outcomes is positive, is :
a.
$\frac{881}{2592}$
b.
$\frac{521}{2592}$
c.
$\frac{440}{2592}$
d.
$\frac{27}{288}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let the system of linear equations
π₯+ π¦+ ππ§= 2
2π₯+ 3π¦- π§= 1
3π₯+ 4π¦+ 2π§= π
have infinitely many solutions. Then the system
π+ 1 π₯+ 2π- 1 π¦= 7
2π+ 1π₯+ π+ 5π¦= 10has :
a.
infinitely many solutions
b.
unique solution satisfying π₯- π¦= 1
c.
no solution
d.
unique solution satisfying π₯+ π¦= 1
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let a unit vector $^{$\rightarrow$}$ ππmake angle πΌ, π½, πΎwith the positive directions of the co-ordinate axes OX, OY, OZ
respectively, where π½$\in$0, $\frac{π}{2}$ . $^{$\rightarrow$}$ ππis perpendicular to the plane through points 1, 2, 3, 2, 3, 4and 1, 5, 7, then
which one of the following is true ?
Let π= {1, 2, 3, 4, 5, 6} . Then the number of oneone functions π: π$\rightarrow$π( π), where π( π) denote the power
set of π, such that π( π) $\subset$π( π) where π< πis
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 [ denotes the greatest integer , then the value of $^{2}$ π₯2 $^{π₯+ π₯3}$ is :
π‘ $\leq$1 $\frac{3π- 1}{π}$ $\int$ $_{1}$ π ππ₯
a.
π $^{9}$ - π
b.
π $^{8}$ - π
c.
π $^{7}$ - 1
d.
π $^{8}$ - 1
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Suppose π: π $\rightarrow$0, $\infty$ be a differentiable function such that 5ππ₯+ π¦= ππ₯Β· ππ¦, $\forall$ π₯, π¦$\in$π , If π3 = 320,
then $\sum$ $_{π= 0}^{5}$ ππis equal to:
a.
6875
b.
6575
c.
6825
d.
6528
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If the solution of the equation log $_{cosπ₯}$ cotπ₯+ 4log $_{sinπ₯}$ tanπ₯= 1, π₯$\in$0, $\frac{π}{2}$ is sin $\frac{-1πΌ+ $\sqrt{\,}$π½}{2}$ , where πΌ, π½are integers,
then πΌ+ π½is equal to:
a.
3
b.
5
c.
6
d.
4
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A straight line cuts off the intercepts $\mathrm{OA}=\mathrm{a}$ and $\mathrm{OB}=\mathrm{b}$ on the
positive directions of $\mathrm{x}$-axis and $\mathrm{y}-$ axis respectively. If the perpendicular from
origin $\mathrm{O}$ to this line makes an angle of $\frac{\pi}{6}$ with positive direction of $y$-axis and the
area of $\triangle \mathrm{OAB}$ is $\frac{98}{3} \sqrt{3}$, then $\mathrm{a}^2-\mathrm{b}^2$ is equal
to:
a.
$\frac{392}{3}$
b.
196
c.
$\frac{196}{3}$
d.
98
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The number of points on the curve π¦= 54π₯ $^{5}$ - 135π₯ $^{4}$ - 70π₯ $^{3}$ + 180π₯ $^{2}$ + 210π₯at which the normal lines are
parallel to π₯+ 90π¦+ 2 = 0is:
a.
2
b.
3
c.
4
d.
0
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If $^{$\rightarrow$}$ π, $^{$\rightarrow$}$ π, $^{$\rightarrow$}$ πare three non-zero vectors and π $^{^}$ is a unit vector perpendicular to $^{$\rightarrow$}$ πsuch that $^{$\rightarrow$}$ π= πΌ $^{$\rightarrow$}$ π- π, πΌ$\neq$0 $^{^}$
and $^{$\rightarrow$}$ πΒ· $^{$\rightarrow$}$ π= 12, then $^{$\rightarrow$}$ π$\times$ $^{$\rightarrow$}$ π$\times$ $^{$\rightarrow$}$ πis equal to:
a.
15
b.
9
c.
12
d.
6
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let the solution curve π¦= π¦( π₯) of the differential equation $\frac{ππ¦}{ππ₯}$ - $\frac{3π₯5tan-1π₯3}{3}$ π¦= 2π₯ exp $\frac{π₯3- tan-1π₯3}{( 1 + π₯)6}$ pass through
1 + π₯62 $\sqrt$
the origin. Then π¦( 1 )is equal to:
a.
exp $\frac{4 - π}{4$\sqrt{\,}$2}$
b.
exp $\frac{π- 4}{4$\sqrt{\,}$2}$
c.
exp $\frac{1 - π}{4$\sqrt{\,}$2}$
d.
exp $\frac{4 + π}{4$\sqrt{\,}$2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The minimum number of elements that must be added to the relation π = ( π, π) , ( π, c ) on the set {a, b, c}
so that it becomes symmetric and transitive is:
a.
4
b.
7
c.
5
d.
3
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
