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Question Number 22177 Answers: 1 Comments: 0

(C_0 /2) − (C_1 /3) + (C_2 /4) − (C_3 /5) + ..........

$$\frac{{C}_{\mathrm{0}} }{\mathrm{2}}\:−\:\frac{{C}_{\mathrm{1}} }{\mathrm{3}}\:+\:\frac{{C}_{\mathrm{2}} }{\mathrm{4}}\:−\:\frac{{C}_{\mathrm{3}} }{\mathrm{5}}\:+\:.......... \\ $$

Question Number 22166 Answers: 1 Comments: 0

If∫_1 ^4 f(x) dx = 5 what is the value of ∫_0 ^1 f(3x +1) dx ?

$$\mathrm{If}\underset{\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\mathrm{5} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{f}\left(\mathrm{3}{x}\:+\mathrm{1}\right)\:{dx}\:? \\ $$

Question Number 22165 Answers: 1 Comments: 0

Question Number 22174 Answers: 1 Comments: 0

Question Number 22154 Answers: 2 Comments: 0

Given a,b,c real and positive numbers, and a + b + c = 1 Find the minimum value of ((a + b)/(abc))

$$\mathrm{Given}\:{a},{b},{c}\:\mathrm{real}\:\mathrm{and}\:\mathrm{positive}\:\mathrm{numbers},\:\mathrm{and} \\ $$$${a}\:+\:{b}\:+\:{c}\:=\:\mathrm{1} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\:\frac{{a}\:+\:{b}}{{abc}} \\ $$

Question Number 22162 Answers: 1 Comments: 0

use the appropite set law to show that (A−B)∪(B−A)=(A∪B)−(A∩B)

$${use}\:{the}\:{appropite}\:{set}\:{law}\:{to}\:{show}\: \\ $$$${that} \\ $$$$\left({A}−{B}\right)\cup\left({B}−{A}\right)=\left({A}\cup{B}\right)−\left({A}\cap{B}\right) \\ $$

Question Number 22151 Answers: 1 Comments: 0

integrate ∫((cosx−cos2x)/(1+cosx))dx

$${integrate} \\ $$$$\int\frac{{cosx}−{cos}\mathrm{2}{x}}{\mathrm{1}+{cosx}}{dx} \\ $$

Question Number 22145 Answers: 1 Comments: 3

A particle P is moving on a circle under the action of only one force acting always towards fixed point O on the circumference. Find ratio of (d^2 φ/dt^2 ) and ((dφ/dt))^2 .

$$\mathrm{A}\:\mathrm{particle}\:{P}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{on}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{under} \\ $$$$\mathrm{the}\:\mathrm{action}\:\mathrm{of}\:\mathrm{only}\:\mathrm{one}\:\mathrm{force}\:\mathrm{acting} \\ $$$$\mathrm{always}\:\mathrm{towards}\:\mathrm{fixed}\:\mathrm{point}\:{O}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{circumference}.\:\mathrm{Find}\:\mathrm{ratio}\:\mathrm{of}\:\frac{{d}^{\mathrm{2}} \phi}{{dt}^{\mathrm{2}} }\:\mathrm{and} \\ $$$$\left(\frac{{d}\phi}{{dt}}\right)^{\mathrm{2}} . \\ $$

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.

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

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