Question and Answers Forum

AllQuestion and Answers: Page 1904

Question Number 18614 Answers: 0 Comments: 1

Question Number 18607 Answers: 1 Comments: 1

A block of mass M is pulled vertically upward through a rope of mass m by applying force F on-one end of the rope. What force does the rope exert on the block?

$$\mathrm{A}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:{M}\:\mathrm{is}\:\mathrm{pulled}\:\mathrm{vertically} \\ $$$$\mathrm{upward}\:\mathrm{through}\:\mathrm{a}\:\mathrm{rope}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{by} \\ $$$$\mathrm{applying}\:\mathrm{force}\:{F}\:\mathrm{on}-\mathrm{one}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rope}. \\ $$$$\mathrm{What}\:\mathrm{force}\:\mathrm{does}\:\mathrm{the}\:\mathrm{rope}\:\mathrm{exert}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{block}? \\ $$

Question Number 18606 Answers: 0 Comments: 0

(1/3)+(3/(3×7))+(5/(3×7×11))+(7/(3×7×11×15))+...n terms

$$\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{3}×\mathrm{7}}+\frac{\mathrm{5}}{\mathrm{3}×\mathrm{7}×\mathrm{11}}+\frac{\mathrm{7}}{\mathrm{3}×\mathrm{7}×\mathrm{11}×\mathrm{15}}+...{n}\: \\ $$$$\:{terms} \\ $$

Question Number 18604 Answers: 0 Comments: 0

Question Number 18603 Answers: 0 Comments: 0

The work function of a metal is 4 eV. If light of frequency 2.3 × 10^(15) Hz is incident on metal surface, then, (1) No photoelectron will be ejected (2) 2 photoelectron of zero kinetic energy are ejected (3) 1 photoelectron of zero kinetic energy is ejected (4) 1 photoelectron is ejected, which required the stopping potential of 5.52 volt

$$\mathrm{The}\:\mathrm{work}\:\mathrm{function}\:\mathrm{of}\:\mathrm{a}\:\mathrm{metal}\:\mathrm{is}\:\mathrm{4}\:\mathrm{eV}.\:\mathrm{If} \\ $$$$\mathrm{light}\:\mathrm{of}\:\mathrm{frequency}\:\mathrm{2}.\mathrm{3}\:×\:\mathrm{10}^{\mathrm{15}} \:\mathrm{Hz}\:\mathrm{is} \\ $$$$\mathrm{incident}\:\mathrm{on}\:\mathrm{metal}\:\mathrm{surface},\:\mathrm{then}, \\ $$$$\left(\mathrm{1}\right)\:\mathrm{No}\:\mathrm{photoelectron}\:\mathrm{will}\:\mathrm{be}\:\mathrm{ejected} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2}\:\mathrm{photoelectron}\:\mathrm{of}\:\mathrm{zero}\:\mathrm{kinetic} \\ $$$$\mathrm{energy}\:\mathrm{are}\:\mathrm{ejected} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{1}\:\mathrm{photoelectron}\:\mathrm{of}\:\mathrm{zero}\:\mathrm{kinetic} \\ $$$$\mathrm{energy}\:\mathrm{is}\:\mathrm{ejected} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{1}\:\mathrm{photoelectron}\:\mathrm{is}\:\mathrm{ejected},\:\mathrm{which} \\ $$$$\mathrm{required}\:\mathrm{the}\:\mathrm{stopping}\:\mathrm{potential}\:\mathrm{of}\:\mathrm{5}.\mathrm{52} \\ $$$$\mathrm{volt} \\ $$

Question Number 18611 Answers: 1 Comments: 1

Without using L Hospital′s rule prove that lim_(x→0) ((sin x)/x)=1

$$\mathrm{Without}\:\mathrm{using}\:\mathrm{L}\:\mathrm{Hospital}'\mathrm{s} \\ $$$$\mathrm{rule}\:\mathrm{prove}\:\mathrm{that}\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}=\mathrm{1} \\ $$

Question Number 18593 Answers: 1 Comments: 0

Question Number 18590 Answers: 1 Comments: 0

∫ ((sin x)/(1 + cos^2 x)) dx

$$\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{1}\:+\:\mathrm{cos}^{\mathrm{2}} \:{x}}\:{dx} \\ $$

Question Number 18588 Answers: 1 Comments: 0

sin x = ((2a + 3)/(a + 1)) How many a that can satisfy the equation above?

$$\mathrm{sin}\:{x}\:=\:\frac{\mathrm{2}{a}\:+\:\mathrm{3}}{{a}\:+\:\mathrm{1}} \\ $$$$\mathrm{How}\:\mathrm{many}\:{a}\:\mathrm{that}\:\mathrm{can}\:\mathrm{satisfy}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\mathrm{above}? \\ $$

Question Number 18587 Answers: 0 Comments: 2

lim_(x→0) ((x . tan x)/(x sin x − cos x + 1))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:.\:\mathrm{tan}\:{x}}{{x}\:\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\:+\:\mathrm{1}} \\ $$

Question Number 18584 Answers: 1 Comments: 0

Prove sin (((3π)/(10)))=((1+(√5))/4)

$${Prove} \\ $$$$\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{10}}\right)=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{4}} \\ $$

Question Number 18575 Answers: 1 Comments: 0

If ( ) represents the least integer function, then the value of (10) + (10 + (1/(20))) + (10 + (2/(20))) + ... + (10 + ((19)/(20))) is equal to (1) 219 (2) 200 (3) 220 (4) 221

$$\mathrm{If}\:\left(\:\right)\:\mathrm{represents}\:\mathrm{the}\:\mathrm{least}\:\mathrm{integer}\:\mathrm{function}, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{10}\right)\:+\:\left(\mathrm{10}\:+\:\frac{\mathrm{1}}{\mathrm{20}}\right)\:+ \\ $$$$\left(\mathrm{10}\:+\:\frac{\mathrm{2}}{\mathrm{20}}\right)\:+\:...\:+\:\left(\mathrm{10}\:+\:\frac{\mathrm{19}}{\mathrm{20}}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{219} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{200} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{220} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{221} \\ $$

Question Number 18574 Answers: 1 Comments: 0

The maximum value of f(x) = 2 − ∣x∣^2 − 2x is equal to (1) 6 (2) 4 (3) 5 (4) 3

$$\mathrm{The}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:{f}\left({x}\right)\:=\:\mathrm{2}\:−\:\mid{x}\mid^{\mathrm{2}} \\ $$$$−\:\mathrm{2}{x}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{6} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{4} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{5} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{3} \\ $$

Question Number 18568 Answers: 0 Comments: 0

The energy required to dislodge electron from excited isolated H-atom, IE_1 = 13.6 eV is (1) = 13.6 eV (2) > 13.6 eV (3) < 13.6 eV and > 3.4 eV (4) ≤ 3.4 eV

$$\mathrm{The}\:\mathrm{energy}\:\mathrm{required}\:\mathrm{to}\:\mathrm{dislodge}\:\mathrm{electron} \\ $$$$\mathrm{from}\:\mathrm{excited}\:\mathrm{isolated}\:\mathrm{H}-\mathrm{atom},\:\mathrm{IE}_{\mathrm{1}} \:= \\ $$$$\mathrm{13}.\mathrm{6}\:\mathrm{eV}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:=\:\mathrm{13}.\mathrm{6}\:\mathrm{eV} \\ $$$$\left(\mathrm{2}\right)\:>\:\mathrm{13}.\mathrm{6}\:\mathrm{eV} \\ $$$$\left(\mathrm{3}\right)\:<\:\mathrm{13}.\mathrm{6}\:\mathrm{eV}\:\mathrm{and}\:>\:\mathrm{3}.\mathrm{4}\:\mathrm{eV} \\ $$$$\left(\mathrm{4}\right)\:\leqslant\:\mathrm{3}.\mathrm{4}\:\mathrm{eV} \\ $$

Question Number 18581 Answers: 1 Comments: 0

In moving a body of mass m up and down a rough incline plane of inclination θ, work done is (S is length of the planck, and μ is coefficient of friction).

$$\mathrm{In}\:\mathrm{moving}\:\mathrm{a}\:\mathrm{body}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{up}\:\mathrm{and} \\ $$$$\mathrm{down}\:\mathrm{a}\:\mathrm{rough}\:\mathrm{incline}\:\mathrm{plane}\:\mathrm{of}\:\mathrm{inclination} \\ $$$$\theta,\:\mathrm{work}\:\mathrm{done}\:\mathrm{is}\:\left(\mathrm{S}\:\mathrm{is}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{planck},\right. \\ $$$$\left.\mathrm{and}\:\mu\:\mathrm{is}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\right). \\ $$

Question Number 18561 Answers: 0 Comments: 2

The acceleration of an object is given by a(t) = cos(nπ), and its velocity at time t = 0 is (1/(2π)). Find both the net and the total distance traveled in the first 1.5 seconds.

$$\mathrm{The}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{an}\:\mathrm{object}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\mathrm{a}\left(\mathrm{t}\right)\:=\:\mathrm{cos}\left(\mathrm{n}\pi\right),\:\mathrm{and}\:\mathrm{its}\:\mathrm{velocity} \\ $$$$\mathrm{at}\:\mathrm{time}\:\mathrm{t}\:=\:\mathrm{0}\:\mathrm{is}\:\:\:\frac{\mathrm{1}}{\mathrm{2}\pi}.\:\mathrm{Find}\:\mathrm{both}\:\mathrm{the}\:\mathrm{net}\:\mathrm{and}\:\mathrm{the}\:\mathrm{total}\:\mathrm{distance}\:\mathrm{traveled}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{first}\:\:\mathrm{1}.\mathrm{5}\:\mathrm{seconds}. \\ $$

Question Number 18556 Answers: 1 Comments: 0

Question Number 18551 Answers: 1 Comments: 0

Question Number 18550 Answers: 1 Comments: 1

Question Number 18549 Answers: 0 Comments: 0

A particle of mass 1 gram executes an oscillatory motion on the concave surface of a spherical dish of radius 2 m, placed on a horizontal plane. If the motion of the particle starts from a point on the dish at the height of 1 cm from the horizontal plane and the coefficient of friction is 0.01, how much total distance will be moved by the particle before it comes to rest?

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}\:\mathrm{gram}\:\mathrm{executes}\:\mathrm{an} \\ $$$$\mathrm{oscillatory}\:\mathrm{motion}\:\mathrm{on}\:\mathrm{the}\:\mathrm{concave} \\ $$$$\mathrm{surface}\:\mathrm{of}\:\mathrm{a}\:\mathrm{spherical}\:\mathrm{dish}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{2}\:\mathrm{m}, \\ $$$$\mathrm{placed}\:\mathrm{on}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{plane}.\:\mathrm{If}\:\mathrm{the} \\ $$$$\mathrm{motion}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{dish}\:\mathrm{at}\:\mathrm{the}\:\mathrm{height}\:\mathrm{of}\:\mathrm{1}\:\mathrm{cm} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{plane}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{is}\:\mathrm{0}.\mathrm{01},\:\mathrm{how}\:\mathrm{much} \\ $$$$\mathrm{total}\:\mathrm{distance}\:\mathrm{will}\:\mathrm{be}\:\mathrm{moved}\:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{particle}\:\mathrm{before}\:\mathrm{it}\:\mathrm{comes}\:\mathrm{to}\:\mathrm{rest}? \\ $$

Question Number 18546 Answers: 0 Comments: 2

In ΔABC, tan(A/2) + tan(B/2) + tan(C/2) = (√3), then Δ must be (1) Equilateral (2) Isosceles (3) Acute angled

$$\mathrm{In}\:\Delta{ABC},\:\mathrm{tan}\frac{{A}}{\mathrm{2}}\:+\:\mathrm{tan}\frac{{B}}{\mathrm{2}}\:+\:\mathrm{tan}\frac{{C}}{\mathrm{2}}\:=\:\sqrt{\mathrm{3}}, \\ $$$$\mathrm{then}\:\Delta\:\mathrm{must}\:\mathrm{be} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Equilateral} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Isosceles} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Acute}\:\mathrm{angled} \\ $$

Question Number 18545 Answers: 1 Comments: 0

The number of solutions of sin3x + cos2x = 0 in [0, ((3π)/2)] is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mathrm{sin3}{x}\:+\:\mathrm{cos2}{x}\:=\:\mathrm{0}\:\mathrm{in}\:\left[\mathrm{0},\:\frac{\mathrm{3}\pi}{\mathrm{2}}\right]\:\mathrm{is} \\ $$

Question Number 18543 Answers: 1 Comments: 0

Question Number 18538 Answers: 0 Comments: 0

Question Number 18530 Answers: 1 Comments: 0

In an atom the last electron is present in f-orbital and for its outermost shell the graph of Ψ^2 has 6 maximas. What is the sum of group and period of that element?

$$\mathrm{In}\:\mathrm{an}\:\mathrm{atom}\:\mathrm{the}\:\mathrm{last}\:\mathrm{electron}\:\mathrm{is}\:\mathrm{present} \\ $$$$\mathrm{in}\:{f}-\mathrm{orbital}\:\mathrm{and}\:\mathrm{for}\:\mathrm{its}\:\mathrm{outermost}\:\mathrm{shell} \\ $$$$\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\Psi^{\mathrm{2}} \:\mathrm{has}\:\mathrm{6}\:\mathrm{maximas}.\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{group}\:\mathrm{and}\:\mathrm{period}\:\mathrm{of}\:\mathrm{that} \\ $$$$\mathrm{element}? \\ $$

Question Number 19238 Answers: 0 Comments: 4

Let ABCD be a parallelogram. Two points E and F are chosen on the sides BC and CD, respectively, such that ((EB)/(EC)) = m, and ((FC)/(FD)) = n. Lines AE and BF intersect at G. Prove that the ratio ((AG)/(GE)) = (((m + 1)(n + 1))/(mn)).

$$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{parallelogram}.\:\mathrm{Two} \\ $$$$\mathrm{points}\:{E}\:\mathrm{and}\:{F}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{on}\:\mathrm{the}\:\mathrm{sides} \\ $$$${BC}\:\mathrm{and}\:{CD},\:\mathrm{respectively},\:\mathrm{such}\:\mathrm{that} \\ $$$$\frac{{EB}}{{EC}}\:=\:{m},\:\mathrm{and}\:\frac{{FC}}{{FD}}\:=\:{n}.\:\mathrm{Lines}\:{AE}\:\mathrm{and}\:{BF} \\ $$$$\mathrm{intersect}\:\mathrm{at}\:{G}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\frac{{AG}}{{GE}}\:=\:\frac{\left({m}\:+\:\mathrm{1}\right)\left({n}\:+\:\mathrm{1}\right)}{{mn}}. \\ $$

Pg 1899 Pg 1900 Pg 1901 Pg 1902 Pg 1903 Pg 1904 Pg 1905 Pg 1906 Pg 1907 Pg 1908

Contact: info@tinkutara.com