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Question Number 22139 Answers: 0 Comments: 3

The linear mass density, i.e. mass per unit length of the rope, varies from 0 to λ from one end to another. The acceleration of the combined system will be

$$\mathrm{The}\:\mathrm{linear}\:\mathrm{mass}\:\mathrm{density},\:{i}.{e}.\:\mathrm{mass}\:\mathrm{per} \\ $$$$\mathrm{unit}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rope},\:\mathrm{varies}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to} \\ $$$$\lambda\:\mathrm{from}\:\mathrm{one}\:\mathrm{end}\:\mathrm{to}\:\mathrm{another}.\:\mathrm{The} \\ $$$$\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{combined}\:\mathrm{system} \\ $$$$\mathrm{will}\:\mathrm{be} \\ $$

Question Number 22138 Answers: 0 Comments: 0

In the ground state, an element has 13 electrons in its M-shell. The element is

$$\mathrm{In}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{state},\:\mathrm{an}\:\mathrm{element}\:\mathrm{has}\:\mathrm{13} \\ $$$$\mathrm{electrons}\:\mathrm{in}\:\mathrm{its}\:\mathrm{M}-\mathrm{shell}.\:\mathrm{The}\:\mathrm{element}\:\mathrm{is} \\ $$

Question Number 22135 Answers: 1 Comments: 0

A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

$$\mathrm{A}\:\mathrm{mass}\:{m}\:\mathrm{hangs}\:\mathrm{with}\:\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{string}\:\mathrm{wrapped}\:\mathrm{around}\:\mathrm{a}\:\mathrm{pulley}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{frictionless}\:\mathrm{bearing}.\:\mathrm{The}\:\mathrm{pulley}\:\mathrm{has} \\ $$$$\mathrm{mass}\:{m}\:\mathrm{and}\:\mathrm{radius}\:{R}.\:\mathrm{Assuming}\:\mathrm{pulley} \\ $$$$\mathrm{to}\:\mathrm{be}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{uniform}\:\mathrm{circular}\:\mathrm{disc},\:\mathrm{the} \\ $$$$\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{mass}\:{m},\:\mathrm{if}\:\mathrm{the} \\ $$$$\mathrm{string}\:\mathrm{does}\:\mathrm{not}\:\mathrm{slip}\:\mathrm{on}\:\mathrm{the}\:\mathrm{pulley},\:\mathrm{is} \\ $$

Question Number 22133 Answers: 1 Comments: 1

If f : R^+ → R^+ is a polynomial function which satisfy the equation f(f(x)) + f(x) = 12x ∀ x ∈ R^+ , then find f(x).

$$\mathrm{If}\:{f}\::\:{R}^{+} \:\rightarrow\:{R}^{+} \:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{function} \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\:{f}\left({f}\left({x}\right)\right)\:+ \\ $$$${f}\left({x}\right)\:=\:\mathrm{12}{x}\:\forall\:{x}\:\in\:{R}^{+} ,\:\mathrm{then}\:\mathrm{find}\:{f}\left({x}\right). \\ $$

Question Number 22120 Answers: 0 Comments: 2

hi, i′m new here.

$$\mathrm{hi},\:{i}'{m}\:{new}\:{here}. \\ $$

Question Number 22128 Answers: 0 Comments: 2

Question Number 22116 Answers: 1 Comments: 1

Question Number 22251 Answers: 1 Comments: 0

Reversible melting of solid benzene at 1 atm and normal melting point correspond to (1) q > 0 (2) w < 0 (3) ΔE > 0 (4) All of these

$$\mathrm{Reversible}\:\mathrm{melting}\:\mathrm{of}\:\mathrm{solid}\:\mathrm{benzene}\:\mathrm{at} \\ $$$$\mathrm{1}\:\mathrm{atm}\:\mathrm{and}\:\mathrm{normal}\:\mathrm{melting}\:\mathrm{point} \\ $$$$\mathrm{correspond}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{q}\:>\:\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{w}\:<\:\mathrm{0} \\ $$$$\left(\mathrm{3}\right)\:\Delta\mathrm{E}\:>\:\mathrm{0} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{All}\:\mathrm{of}\:\mathrm{these} \\ $$

Question Number 22112 Answers: 1 Comments: 0

A boy ran around a circular part of radius 14m in 15s. Calculate the average velocity and the average speed.

$$\mathrm{A}\:\mathrm{boy}\:\mathrm{ran}\:\mathrm{around}\:\mathrm{a}\:\mathrm{circular}\:\mathrm{part}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{14m}\:\mathrm{in}\:\mathrm{15s}.\:\mathrm{Calculate}\:\mathrm{the}\: \\ $$$$\mathrm{average}\:\mathrm{velocity}\:\mathrm{and}\:\mathrm{the}\:\mathrm{average}\:\mathrm{speed}. \\ $$

Question Number 22105 Answers: 1 Comments: 0

use the first principle to find value of f(x)=(x)^(1/3)

$${use}\:{the}\:{first}\:{principle}\:{to}\:{find} \\ $$$${value}\:{of} \\ $$$${f}\left({x}\right)=\left({x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$

Question Number 22103 Answers: 1 Comments: 2

cos(^ 15)

$$\mathrm{cos}\overset{} {\left(}\:\mathrm{15}\right) \\ $$

Question Number 22102 Answers: 1 Comments: 0

cosh (15)

$$\mathrm{cosh}\:\left(\mathrm{15}\right) \\ $$

Question Number 22090 Answers: 2 Comments: 0

Question Number 26917 Answers: 1 Comments: 2

Given a^2 + b^2 = 1 and c^2 + d^2 = 1 The minimum value of ac + bd − 2 is ...

$$\mathrm{Given}\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:=\:\mathrm{1}\:\mathrm{and}\:{c}^{\mathrm{2}} \:+\:{d}^{\mathrm{2}} \:=\:\mathrm{1} \\ $$$$\mathrm{The}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:{ac}\:+\:{bd}\:−\:\mathrm{2}\:\mathrm{is}\:... \\ $$

Question Number 22295 Answers: 1 Comments: 0

The ionization potential of hydrogen is 13.6 eV/mole. Calculate the energy in kJ required to produce 0.1 mole of H^+ ions. Given, 1 eV = 96.49 kJ mol^(−1) )

$$\mathrm{The}\:\mathrm{ionization}\:\mathrm{potential}\:\mathrm{of}\:\mathrm{hydrogen}\:\mathrm{is} \\ $$$$\mathrm{13}.\mathrm{6}\:\mathrm{eV}/\mathrm{mole}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{energy}\:\mathrm{in} \\ $$$$\mathrm{kJ}\:\mathrm{required}\:\mathrm{to}\:\mathrm{produce}\:\mathrm{0}.\mathrm{1}\:\mathrm{mole}\:\mathrm{of}\:\mathrm{H}^{+} \\ $$$$\left.\mathrm{ions}.\:\mathrm{Given},\:\mathrm{1}\:\mathrm{eV}\:=\:\mathrm{96}.\mathrm{49}\:\mathrm{kJ}\:\mathrm{mol}^{−\mathrm{1}} \right) \\ $$

Question Number 22276 Answers: 1 Comments: 0

Question Number 22082 Answers: 1 Comments: 0

If A is a fifty-element subset of the set {1, 2, 3, ...., 100} such that no two numbers from A add up to 100 show that A contains a square.

$$\mathrm{If}\:{A}\:\mathrm{is}\:\mathrm{a}\:\mathrm{fifty}-\mathrm{element}\:\mathrm{subset}\:\mathrm{of}\:\mathrm{the}\:\mathrm{set} \\ $$$$\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:....,\:\mathrm{100}\right\}\:\mathrm{such}\:\mathrm{that}\:\mathrm{no}\:\mathrm{two} \\ $$$$\mathrm{numbers}\:\mathrm{from}\:{A}\:\mathrm{add}\:\mathrm{up}\:\mathrm{to}\:\mathrm{100}\:\mathrm{show} \\ $$$$\mathrm{that}\:{A}\:\mathrm{contains}\:\mathrm{a}\:\mathrm{square}. \\ $$

Question Number 22080 Answers: 0 Comments: 1

Given any positive integer n show that there are two positive rational numbers a and b, a ≠ b, which are not integers and which are such that a − b, a^2 − b^2 , a^3 − b^3 , ....., a^n − b^n are all integers.

$$\mathrm{Given}\:\mathrm{any}\:\mathrm{positive}\:\mathrm{integer}\:{n}\:\mathrm{show} \\ $$$$\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{two}\:\mathrm{positive}\:\mathrm{rational} \\ $$$$\mathrm{numbers}\:{a}\:\mathrm{and}\:{b},\:{a}\:\neq\:{b},\:\mathrm{which}\:\mathrm{are}\:\mathrm{not} \\ $$$$\mathrm{integers}\:\mathrm{and}\:\mathrm{which}\:\mathrm{are}\:\mathrm{such}\:\mathrm{that}\:{a}\:−\:{b}, \\ $$$${a}^{\mathrm{2}} \:−\:{b}^{\mathrm{2}} ,\:{a}^{\mathrm{3}} \:−\:{b}^{\mathrm{3}} ,\:.....,\:{a}^{{n}} \:−\:{b}^{{n}} \:\mathrm{are}\:\mathrm{all} \\ $$$$\mathrm{integers}. \\ $$

Question Number 22079 Answers: 0 Comments: 1

Let ABC be a triangle and h_a the altitude through A. Prove that (b + c)^2 ≥ a^2 + 4h_a ^2 . (As usual a, b, c denote the sides BC, CA, AB respectively.)

$$\mathrm{Let}\:{ABC}\:\mathrm{be}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{and}\:{h}_{{a}} \:\mathrm{the} \\ $$$$\mathrm{altitude}\:\mathrm{through}\:{A}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\left({b}\:+\:{c}\right)^{\mathrm{2}} \:\geqslant\:{a}^{\mathrm{2}} \:+\:\mathrm{4}{h}_{{a}} ^{\mathrm{2}} . \\ $$$$\left(\mathrm{As}\:\mathrm{usual}\:{a},\:{b},\:{c}\:\mathrm{denote}\:\mathrm{the}\:\mathrm{sides}\:{BC},\right. \\ $$$$\left.{CA},\:{AB}\:\mathrm{respectively}.\right) \\ $$

Question Number 22076 Answers: 0 Comments: 3

find approximately and quickly without calculator ((54329)/(2467)) .

$${find}\:{approximately}\:{and}\:{quickly} \\ $$$${without}\:{calculator}\:\frac{\mathrm{54329}}{\mathrm{2467}}\:. \\ $$

Question Number 22161 Answers: 0 Comments: 1

The students were asked whether they had dictionary(D) or thesau rus(T) in their room.the results showed that 650 students had dict ionary,150 did not had dictionary, 175 had a thesaurus,and 50 had neither a dictionary nor a thesaur us,fimd the number of student who (i)live in domitory ( ii)have both dictionary and thesaurus (iii)have only thesaurus

$${The}\:{students}\:{were}\:{asked}\:{whether} \\ $$$${they}\:{had}\:{dictionary}\left({D}\right)\:{or}\:{thesau} \\ $$$${rus}\left({T}\right)\:{in}\:{their}\:{room}.{the}\:{results}\: \\ $$$${showed}\:{that}\:\mathrm{650}\:{students}\:{had}\:{dict} \\ $$$${ionary},\mathrm{150}\:{did}\:{not}\:{had}\:{dictionary}, \\ $$$$\mathrm{175}\:{had}\:{a}\:{thesaurus},{and}\:\mathrm{50}\:{had} \\ $$$${neither}\:{a}\:{dictionary}\:{nor}\:{a}\:{thesaur} \\ $$$${us},{fimd}\:{the}\:{number}\:{of}\:{student}\:{who} \\ $$$$\:\:\left({i}\right){live}\:{in}\:{domitory} \\ $$$$\:\:\:\left(\:{ii}\right){have}\:{both}\:{dictionary}\:{and}\:{thesaurus} \\ $$$$\:\:\left({iii}\right){have}\:{only}\:{thesaurus} \\ $$$$ \\ $$

Question Number 22071 Answers: 1 Comments: 4

STATEMENT-1 : If an object is at rest then there should not be any friction on it. STATEMENT-2 : If an object is moving then the friction acting on it has to be kinetic. STATEMENT-3 : If an object is at rest then kinetic friction cannot act on it.

$$\mathrm{STATEMENT}-\mathrm{1}\::\:\mathrm{If}\:\mathrm{an}\:\mathrm{object}\:\mathrm{is}\:\mathrm{at} \\ $$$$\mathrm{rest}\:\mathrm{then}\:\mathrm{there}\:\mathrm{should}\:\mathrm{not}\:\mathrm{be}\:\mathrm{any}\:\mathrm{friction} \\ $$$$\mathrm{on}\:\mathrm{it}. \\ $$$$\mathrm{STATEMENT}-\mathrm{2}\::\:\mathrm{If}\:\mathrm{an}\:\mathrm{object}\:\mathrm{is}\:\mathrm{moving} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{friction}\:\mathrm{acting}\:\mathrm{on}\:\mathrm{it}\:\mathrm{has}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{kinetic}. \\ $$$$\mathrm{STATEMENT}-\mathrm{3}\::\:\mathrm{If}\:\mathrm{an}\:\mathrm{object}\:\mathrm{is}\:\mathrm{at}\:\mathrm{rest} \\ $$$$\mathrm{then}\:\mathrm{kinetic}\:\mathrm{friction}\:\mathrm{cannot}\:\mathrm{act}\:\mathrm{on}\:\mathrm{it}. \\ $$

Question Number 26924 Answers: 1 Comments: 0

Question Number 22062 Answers: 1 Comments: 1

Question Number 22061 Answers: 1 Comments: 0

If 9x^2 +6xy+4y^2 is a factor of 27x^3 −8y^3 . find the other factor.

$$\mathrm{If}\:\mathrm{9x}^{\mathrm{2}} +\mathrm{6xy}+\mathrm{4y}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of} \\ $$$$\mathrm{27x}^{\mathrm{3}} −\mathrm{8y}^{\mathrm{3}} .\:\mathrm{find}\:\mathrm{the}\:\mathrm{other}\:\mathrm{factor}. \\ $$

Question Number 22059 Answers: 1 Comments: 0

A flywheel whose diameter is 1.5m decrease uniformly from 240rad/min until it came to rest 10s. Find the number of revolution made.

$$\mathrm{A}\:\mathrm{flywheel}\:\mathrm{whose}\:\mathrm{diameter}\:\mathrm{is}\:\mathrm{1}.\mathrm{5m}\:\mathrm{decrease}\:\mathrm{uniformly}\:\mathrm{from}\:\mathrm{240rad}/\mathrm{min} \\ $$$$\mathrm{until}\:\mathrm{it}\:\mathrm{came}\:\mathrm{to}\:\mathrm{rest}\:\mathrm{10s}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{revolution}\:\mathrm{made}. \\ $$

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