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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