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Question Number 113928 Answers: 1 Comments: 0

Find the remainder when x^(2006) −1 is divided by x^4 +x^3 +2x^2 +x+1.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:{x}^{\mathrm{2006}} −\mathrm{1}\: \\ $$$$\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} +{x}+\mathrm{1}. \\ $$

Question Number 113919 Answers: 2 Comments: 0

Given a set data : 2,2,3,4,5,5,5,8,8,9,11,14. find the value of Q_1

$${Given}\:{a}\:{set}\:{data}\:\: \\ $$$$:\:\mathrm{2},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{5},\mathrm{5},\mathrm{8},\mathrm{8},\mathrm{9},\mathrm{11},\mathrm{14}. \\ $$$${find}\:{the}\:{value}\:{of}\:{Q}_{\mathrm{1}} \\ $$

Question Number 113913 Answers: 3 Comments: 0

Find the square root of (√(50))+(√(48))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{square}\:\mathrm{root}\:\mathrm{of}\:\sqrt{\mathrm{50}}+\sqrt{\mathrm{48}} \\ $$

Question Number 113910 Answers: 4 Comments: 0

(1)∫_0 ^π ((sin^4 x)/((1+cos x)^2 )) dx ? (2) lim_(x→∞) ((√(1−cos (((2π)/x))))/(1/x)) ?

$$\left(\mathrm{1}\right)\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{sin}\:^{\mathrm{4}} {x}}{\left(\mathrm{1}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:{dx}\:? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{{x}}\right)}}{\frac{\mathrm{1}}{{x}}}\:? \\ $$

Question Number 113907 Answers: 1 Comments: 0

∫ (√x) cos ((√x)) dx

$$\int\:\sqrt{{x}}\:\mathrm{cos}\:\left(\sqrt{{x}}\right)\:{dx} \\ $$

Question Number 113904 Answers: 1 Comments: 0

If { ((f(x)=(√(2x−5)))),((g(x)=x^2 +1)) :} find (f^(−1) ○g)^(−1) (x)

$${If}\:\begin{cases}{{f}\left({x}\right)=\sqrt{\mathrm{2}{x}−\mathrm{5}}}\\{{g}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{1}}\end{cases} \\ $$$${find}\:\left({f}^{−\mathrm{1}} \circ{g}\right)^{−\mathrm{1}} \left({x}\right) \\ $$

Question Number 113901 Answers: 0 Comments: 4

when do I use ∣x∣ for (√x^2 )?

$${when}\:{do}\:{I}\:{use}\:\mid{x}\mid \\ $$$${for}\:\sqrt{{x}^{\mathrm{2}} }? \\ $$

Question Number 113897 Answers: 1 Comments: 0

Question Number 113894 Answers: 2 Comments: 1

Question Number 113885 Answers: 1 Comments: 0

Question Number 113886 Answers: 3 Comments: 0

Question Number 113876 Answers: 4 Comments: 0

If 2^x =4^y =8^z and xyz=288, then find (1/(2x))+(1/(4y))+(1/(8z))

$$\mathrm{If}\:\mathrm{2}^{\mathrm{x}} =\mathrm{4}^{\mathrm{y}} =\mathrm{8}^{\mathrm{z}} \:\mathrm{and}\:\mathrm{xyz}=\mathrm{288},\:\mathrm{then}\:\mathrm{find} \\ $$$$\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{4y}}+\frac{\mathrm{1}}{\mathrm{8z}} \\ $$

Question Number 113868 Answers: 0 Comments: 1

Find the area between the circle ρ=2acosθ and cardiode ρ=a(1+cosθ)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{between}\:\mathrm{the}\:\mathrm{circle}\:\rho=\mathrm{2acos}\theta\:\mathrm{and}\: \\ $$$$\mathrm{cardiode}\:\rho=\mathrm{a}\left(\mathrm{1}+\mathrm{cos}\theta\right) \\ $$

Question Number 113867 Answers: 1 Comments: 0

∫_3 ^6 ((x+1)/(x^3 +x^2 −6x))dx

$$\int_{\mathrm{3}} ^{\mathrm{6}} \frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} −\mathrm{6x}}\mathrm{dx} \\ $$

Question Number 113865 Answers: 0 Comments: 0

Consider the series I_n =∫_1 ^e x(lnx)^n dx and I_0 =∫_1 ^e xdx Which of the following is true ? a\ 0≤I_n ≤(e^2 /(n+2)) b\1≤I_n ≤(e^2 /(n+1)) c\I_n is negative

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{series}\:\mathrm{I}_{\mathrm{n}} =\int_{\mathrm{1}} ^{\mathrm{e}} \mathrm{x}\left(\mathrm{lnx}\right)^{\mathrm{n}} \mathrm{dx}\:\mathrm{and}\:\mathrm{I}_{\mathrm{0}} =\int_{\mathrm{1}} ^{\mathrm{e}} \mathrm{xdx} \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{true}\:? \\ $$$$\mathrm{a}\backslash\:\mathrm{0}\leqslant\mathrm{I}_{\mathrm{n}} \leqslant\frac{\mathrm{e}^{\mathrm{2}} }{\mathrm{n}+\mathrm{2}}\:\:\:\:\mathrm{b}\backslash\mathrm{1}\leqslant\mathrm{I}_{\mathrm{n}} \leqslant\frac{\mathrm{e}^{\mathrm{2}} }{\mathrm{n}+\mathrm{1}}\:\:\mathrm{c}\backslash\mathrm{I}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{negative} \\ $$

Question Number 113862 Answers: 1 Comments: 0

Question Number 113854 Answers: 1 Comments: 0

if f(x)=2x^2 −12x+10. (i) sketch the graph of y=∣f(x)∣ for −1≤x≤7. (ii) find the set of values of k for which the equation ∣f(x)∣=k has 4 distinct roots.

$${if}\:{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{10}.\: \\ $$$$\left({i}\right)\:{sketch}\:{the}\:{graph}\:{of}\:{y}=\mid{f}\left({x}\right)\mid\:{for} \\ $$$$−\mathrm{1}\leqslant{x}\leqslant\mathrm{7}. \\ $$$$\left({ii}\right)\:{find}\:{the}\:{set}\:{of}\:{values}\:{of}\:{k}\:{for} \\ $$$${which}\:{the}\:{equation}\:\mid{f}\left({x}\right)\mid={k}\:{has}\:\mathrm{4} \\ $$$${distinct}\:{roots}. \\ $$

Question Number 113849 Answers: 0 Comments: 0

A cricket club has 15 members, of whom only 5 can bowl. If the names of 15 members are put into a box and 11 are drawn at random, then the probability of obtaining an 11 containing at least 3 bowlers is

$$\mathrm{A}\:\mathrm{cricket}\:\mathrm{club}\:\mathrm{has}\:\mathrm{15}\:\mathrm{members},\:\mathrm{of}\:\mathrm{whom} \\ $$$$\mathrm{only}\:\mathrm{5}\:\mathrm{can}\:\mathrm{bowl}.\:\mathrm{If}\:\:\mathrm{the}\:\mathrm{names}\:\mathrm{of}\:\mathrm{15} \\ $$$$\mathrm{members}\:\mathrm{are}\:\mathrm{put}\:\mathrm{into}\:\mathrm{a}\:\mathrm{box}\:\mathrm{and}\:\mathrm{11}\:\mathrm{are} \\ $$$$\mathrm{drawn}\:\mathrm{at}\:\mathrm{random},\:\mathrm{then}\:\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{of}\:\mathrm{obtaining}\:\mathrm{an}\:\mathrm{11}\:\mathrm{containing}\:\mathrm{at}\:\mathrm{least} \\ $$$$\mathrm{3}\:\mathrm{bowlers}\:\mathrm{is} \\ $$

Question Number 113848 Answers: 1 Comments: 0

In a △ABC, Σ a^2 (sin^2 B −sin^2 C) =

$$\mathrm{In}\:\mathrm{a}\:\bigtriangleup{ABC},\:\Sigma\:{a}^{\mathrm{2}} \left(\mathrm{sin}^{\mathrm{2}} {B}\:−\mathrm{sin}^{\mathrm{2}} {C}\right)\:= \\ $$

Question Number 113847 Answers: 1 Comments: 0

The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60°. If the third side is 3, the remaining fourth side is

$$\mathrm{The}\:\mathrm{two}\:\mathrm{adjacent}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cyclic} \\ $$$$\mathrm{quadrilateral}\:\mathrm{are}\:\mathrm{2}\:\mathrm{and}\:\mathrm{5}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{between}\:\mathrm{them}\:\mathrm{is}\:\mathrm{60}°.\:\mathrm{If}\:\mathrm{the}\:\mathrm{third} \\ $$$$\mathrm{side}\:\mathrm{is}\:\mathrm{3},\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{fourth}\:\mathrm{side}\:\mathrm{is} \\ $$

Question Number 113846 Answers: 2 Comments: 0

Thr general solution of the equation tan 3x=tan 5x is

$$\mathrm{Thr}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{tan}\:\mathrm{3}{x}=\mathrm{tan}\:\mathrm{5}{x}\:\:\mathrm{is} \\ $$

Question Number 113842 Answers: 0 Comments: 0

If in a triangle a cos^2 ((C/2))+c cos^2 ((A/2))=((3b)/2), then the sides of the triangle are in