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AllQuestion and Answers: Page 1316

Question Number 81731 Answers: 0 Comments: 1

If a, b, c are in AP; p, q, r are in HP and ap, bq, cr are in GP, then (p/r)+(r/p) is equal to

$$\mathrm{If}\:\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP};\:\:{p},\:{q},\:{r}\:\mathrm{are}\:\mathrm{in}\:\mathrm{HP}\: \\ $$$$\mathrm{and}\:\:{ap},\:{bq},\:{cr}\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP},\:\mathrm{then}\:\frac{{p}}{{r}}+\frac{{r}}{{p}} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 81725 Answers: 0 Comments: 1

If 7 points out of 12 are in the same straight line, then the number of triangles formed is

$$\mathrm{If}\:\:\mathrm{7}\:\mathrm{points}\:\mathrm{out}\:\mathrm{of}\:\mathrm{12}\:\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{straight}\:\mathrm{line},\:\mathrm{then}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{triangles}\:\mathrm{formed}\:\mathrm{is} \\ $$

Question Number 81724 Answers: 0 Comments: 2

The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{an} \\ $$$$\mathrm{examiner}\:\mathrm{can}\:\mathrm{assign}\:\mathrm{30}\:\mathrm{marks}\:\mathrm{to}\:\mathrm{8} \\ $$$$\mathrm{questions},\:\mathrm{giving}\:\mathrm{not}\:\mathrm{less}\:\mathrm{than}\:\mathrm{2}\:\mathrm{marks} \\ $$$$\mathrm{to}\:\mathrm{any}\:\mathrm{question}\:\mathrm{is} \\ $$

Question Number 81704 Answers: 0 Comments: 0

find Γ((1/3)) and Γ((2/3))

$${find}\:\Gamma\left(\frac{\mathrm{1}}{\mathrm{3}}\right)\:{and}\:\Gamma\left(\frac{\mathrm{2}}{\mathrm{3}}\right) \\ $$

Question Number 81698 Answers: 1 Comments: 1

Question Number 81692 Answers: 0 Comments: 1

Question Number 81684 Answers: 1 Comments: 1

∫ (dx/(x^3 + 1)) = ...

$$\int\:\:\:\frac{{dx}}{{x}^{\mathrm{3}} \:+\:\mathrm{1}}\:\:=\:\:... \\ $$

Question Number 81720 Answers: 0 Comments: 2

let f(x)=arctan(1+x^2 ) 1) calculate f^((n)) (x) and f^((n)) (0) 2) developpf at integr serie

$${let}\:{f}\left({x}\right)={arctan}\left(\mathrm{1}+{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developpf}\:{at}\:{integr}\:{serie} \\ $$

Question Number 81719 Answers: 0 Comments: 1

1) find ∫ (dx/((x+2)^5 (x−3)^9 )) 2) calculate ∫_4 ^(+∞) (dx/((x+2)^5 (x−3)^9 ))

$$\left.\mathrm{1}\right)\:{find}\:\int\:\:\:\frac{{dx}}{\left({x}+\mathrm{2}\right)^{\mathrm{5}} \left({x}−\mathrm{3}\right)^{\mathrm{9}} } \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{4}} ^{+\infty} \:\frac{{dx}}{\left({x}+\mathrm{2}\right)^{\mathrm{5}} \left({x}−\mathrm{3}\right)^{\mathrm{9}} } \\ $$

Question Number 81674 Answers: 2 Comments: 3

Question Number 81672 Answers: 0 Comments: 3

If x ∈ R, the least value of the expression ((x^2 −6x+5)/(x^2 +2x+1)) is

$$\mathrm{If}\:{x}\:\in\:{R},\:\mathrm{the}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{expression}\:\frac{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{5}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}}\:\mathrm{is} \\ $$

Question Number 81664 Answers: 0 Comments: 4

∫_(−π/4) ^(π/4) e^(−x) sin x dx =

$$\underset{−\pi/\mathrm{4}} {\overset{\pi/\mathrm{4}} {\int}}\:{e}^{−{x}} \:\mathrm{sin}\:{x}\:{dx}\:= \\ $$

Question Number 81663 Answers: 0 Comments: 2

∫_( 0) ^1 x (1−x)^n dx =

$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:{x}\:\left(\mathrm{1}−{x}\right)^{{n}} \:{dx}\:= \\ $$

Question Number 81657 Answers: 0 Comments: 2

∫_0 ^3 ((x+1)/((x^2 +2x)^(15) ))=....

$$\:\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\frac{\mathrm{x}+\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}\right)^{\mathrm{15}} }=.... \\ $$

Question Number 81655 Answers: 0 Comments: 0

Question Number 81654 Answers: 0 Comments: 6

Question Number 81649 Answers: 0 Comments: 6

Question Number 81648 Answers: 0 Comments: 2

A team of 8 couples, (husband and wife) attend a lucky draw in which 4 persons picked up for a prize. Then the probability that there is at least one couple is

$$\mathrm{A}\:\mathrm{team}\:\mathrm{of}\:\mathrm{8}\:\mathrm{couples},\:\left(\mathrm{husband}\:\mathrm{and}\:\mathrm{wife}\right) \\ $$$$\mathrm{attend}\:\mathrm{a}\:\mathrm{lucky}\:\mathrm{draw}\:\mathrm{in}\:\mathrm{which}\:\mathrm{4}\:\mathrm{persons} \\ $$$$\mathrm{picked}\:\mathrm{up}\:\mathrm{for}\:\mathrm{a}\:\mathrm{prize}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{there}\:\mathrm{is}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{couple}\:\mathrm{is} \\ $$

Question Number 81647 Answers: 0 Comments: 8

how to prove that the number is divisible by 3, then the number of numbers is a multiple of 3

$$\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{number}\: \\ $$$$\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3},\:\mathrm{then}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3} \\ $$

Question Number 81636 Answers: 0 Comments: 4

∫ ((x(tan^(−1) (x))^2 )/((1+x^2 )^(3/2) )) dx =

$$\int\:\frac{{x}\left(\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\right)^{\mathrm{2}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:{dx}\:=\: \\ $$

Question Number 81629 Answers: 1 Comments: 0

Given vectors x=3i−6j−k, y=i+4j−3k and z=3i−4j+12k, then the projection of X×Y on vector Z is

$$\mathrm{Given}\:\mathrm{vectors}\:\boldsymbol{\mathrm{x}}=\mathrm{3}\boldsymbol{\mathrm{i}}−\mathrm{6}\boldsymbol{\mathrm{j}}−\boldsymbol{\mathrm{k}},\:\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{i}}+\mathrm{4}\boldsymbol{\mathrm{j}}−\mathrm{3}\boldsymbol{\mathrm{k}} \\ $$$$\mathrm{and}\:\boldsymbol{\mathrm{z}}=\mathrm{3}\boldsymbol{\mathrm{i}}−\mathrm{4}\boldsymbol{\mathrm{j}}+\mathrm{12}\boldsymbol{\mathrm{k}},\:\mathrm{then}\:\mathrm{the}\:\mathrm{projection} \\ $$$$\mathrm{of}\:\boldsymbol{\mathrm{X}}×\boldsymbol{\mathrm{Y}}\:\mathrm{on}\:\mathrm{vector}\:\boldsymbol{\mathrm{Z}}\:\mathrm{is} \\ $$

Question Number 81615 Answers: 1 Comments: 0

∫_( 0) ^3 x (√(1+x)) dx =

$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:{x}\:\sqrt{\mathrm{1}+{x}}\:{dx}\:= \\ $$

Question Number 81610 Answers: 1 Comments: 0

Question Number 81598 Answers: 0 Comments: 5

fog(x)=8x+3 g(x)=2x−1 f(x)=.....? gof(x)=6x+1 g(x)=5x+1 f(x)=.....? gof(x)=7x+9 f(x)=5x+2 g(x)=.....? f(x)=3x−8 gof(x)=8x+3 g(x)=.....? gof(x)=5x+1 f(x)=3x g(x)=....?

Question Number 81597 Answers: 0 Comments: 2

fog(x)=5x+6 f(x)=2x+1 g(x)=.....?

$$\mathrm{fog}\left(\mathrm{x}\right)=\mathrm{5x}+\mathrm{6} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{1} \\ $$$$\mathrm{g}\left(\mathrm{x}\right)=.....? \\ $$

Question Number 81596 Answers: 0 Comments: 2

f(x)=3x+1 , g(x)=2x+3 a). fog(x)=.... b). gof(x)=....

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3x}+\mathrm{1}\:,\:\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{3} \\ $$$$\left.\mathrm{a}\right).\:\mathrm{fog}\left(\mathrm{x}\right)=.... \\ $$$$\left.\mathrm{b}\right).\:\mathrm{gof}\left(\mathrm{x}\right)=.... \\ $$

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