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Question Number 113825 Answers: 1 Comments: 0

The greatest and least values of (sin^(−1) x)^3 + (cos^(−1) x)^3 are

$$\mathrm{The}\:\mathrm{greatest}\:\mathrm{and}\:\mathrm{least}\:\mathrm{values}\:\mathrm{of} \\ $$$$\left(\mathrm{sin}^{−\mathrm{1}} {x}\right)^{\mathrm{3}} +\:\left(\mathrm{cos}^{−\mathrm{1}} {x}\right)^{\mathrm{3}} \:\:\mathrm{are} \\ $$

Question Number 113824 Answers: 1 Comments: 0

If 4 sin^(−1) x+cos^(−1) x= π, then x equals

$$\mathrm{If}\:\mathrm{4}\:\mathrm{sin}^{−\mathrm{1}} {x}+\mathrm{cos}^{−\mathrm{1}} {x}=\:\pi,\:\mathrm{then}\:{x}\:\mathrm{equals} \\ $$

Question Number 113823 Answers: 1 Comments: 0

A solution of the equation tan^(−1) (1+x)+tan^(−1) (1−x) = (π/2) is

$$\mathrm{A}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{1}+{x}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{1}−{x}\right)\:=\:\frac{\pi}{\mathrm{2}}\:\:\mathrm{is} \\ $$

Question Number 113822 Answers: 1 Comments: 0

If in a △ABC, 3a=b+c, then the value of cot (B/2) cot (B/2) is

$$\mathrm{If}\:\:\mathrm{in}\:\mathrm{a}\:\bigtriangleup{ABC},\:\mathrm{3}{a}={b}+{c},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\mathrm{cot}\:\frac{{B}}{\mathrm{2}}\:\mathrm{cot}\:\frac{{B}}{\mathrm{2}}\:\mathrm{is} \\ $$

Question Number 113821 Answers: 3 Comments: 1

∫_0 ^(π/2) ln(2−sinx)dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{2}−\mathrm{sinx}\right)\mathrm{dx} \\ $$

Question Number 113816 Answers: 1 Comments: 1

0.095=h∙((h/(1+2h)))^(2/3) h=? & show the practice

$$\mathrm{0}.\mathrm{095}={h}\centerdot\left(\frac{{h}}{\mathrm{1}+\mathrm{2}{h}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} \:\:\:\:\:\:\:\:\:{h}=?\:\: \\ $$$$\&\:{show}\:{the}\:{practice} \\ $$

Question Number 113812 Answers: 1 Comments: 0

lim_(x→0) xlnx=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}xlnx}=? \\ $$

Question Number 113811 Answers: 1 Comments: 0

If log_(12) 27=a, express log_6 16 in terms of a.

$$\mathrm{If}\:\mathrm{log}_{\mathrm{12}} \mathrm{27}=\mathrm{a},\:\mathrm{express}\:\mathrm{log}_{\mathrm{6}} \mathrm{16}\:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{a}. \\ $$

Question Number 113808 Answers: 0 Comments: 0

In a △ABC , ∠B=(π/3) and ∠C=(π/4). Let D divide BC internally in the ratio 1 : 3. Then ((sin ∠BAD)/(sin ∠CAD)) equals

$$\mathrm{In}\:\mathrm{a}\:\bigtriangleup{ABC}\:,\:\angle{B}=\frac{\pi}{\mathrm{3}}\:\mathrm{and}\:\angle{C}=\frac{\pi}{\mathrm{4}}.\:\mathrm{Let} \\ $$$${D}\:\mathrm{divide}\:{BC}\:\mathrm{internally}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\mathrm{1}\::\:\mathrm{3}.\:\mathrm{Then}\:\frac{\mathrm{sin}\:\angle{BAD}}{\mathrm{sin}\:\angle{CAD}}\:\mathrm{equals} \\ $$

Question Number 113803 Answers: 3 Comments: 0

If a=log_(24) 12, b=log_(36) 24 and c=log_(48) 36, then 1+abc is equal to (A) 2ab (B) 2ac (C) 2bc (D) 0

$$\mathrm{If}\:\mathrm{a}=\mathrm{log}_{\mathrm{24}} \mathrm{12},\:\mathrm{b}=\mathrm{log}_{\mathrm{36}} \mathrm{24}\:\mathrm{and} \\ $$$$\mathrm{c}=\mathrm{log}_{\mathrm{48}} \mathrm{36},\:\mathrm{then}\:\mathrm{1}+\mathrm{abc}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$ \\ $$$$\left(\mathrm{A}\right)\:\mathrm{2ab}\:\left(\mathrm{B}\right)\:\mathrm{2ac}\:\left(\mathrm{C}\right)\:\mathrm{2bc}\:\left(\mathrm{D}\right)\:\mathrm{0} \\ $$

Question Number 113801 Answers: 0 Comments: 3

what is the number that is evenly divisible by 3 and 6 and but not divisible by 2?

$${what}\:{is}\:{the}\:{number}\:{that}\:{is}\:{evenly}\: \\ $$$${divisible}\:{by}\:\mathrm{3}\:{and}\:\mathrm{6}\:{and}\:{but}\:{not}\:{divisible} \\ $$$${by}\:\mathrm{2}? \\ $$

Question Number 113800 Answers: 1 Comments: 0

log (ab)−log∣b∣ = A. log(a) B. log ∣a∣ C. −log(a) D. None of these.

$$\mathrm{log}\:\left(\mathrm{ab}\right)−\mathrm{log}\mid\mathrm{b}\mid\:= \\ $$$$ \\ $$$$\mathrm{A}.\:\mathrm{log}\left(\mathrm{a}\right)\:\mathrm{B}.\:\mathrm{log}\:\mid\mathrm{a}\mid\:\mathrm{C}.\:−\mathrm{log}\left(\mathrm{a}\right)\:\mathrm{D}. \\ $$$$\mathrm{None}\:\mathrm{of}\:\mathrm{these}. \\ $$

Question Number 113796 Answers: 1 Comments: 0

find the greatest coeeficient in the expansion (6−4x)^(−3)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coeeficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\: \\ $$$$\left(\mathrm{6}−\mathrm{4x}\right)^{−\mathrm{3}} \\ $$

Question Number 113794 Answers: 1 Comments: 0

find the largest coeeficient in (3x−2)^3

$$\mathrm{find}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{coeeficient}\:\mathrm{in}\:\left(\mathrm{3x}−\mathrm{2}\right)^{\mathrm{3}} \\ $$

Question Number 113793 Answers: 0 Comments: 0

prove Σ_(k=1) ^∞ ((sin^2 (πk)−πk sin(kx) cos(πk))/k^2 )=(π/4)

$${prove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}^{\mathrm{2}} \left(\pi{k}\right)−\pi{k}\:{sin}\left({kx}\right)\:{cos}\left(\pi{k}\right)}{{k}^{\mathrm{2}} }=\frac{\pi}{\mathrm{4}} \\ $$

Question Number 113807 Answers: 1 Comments: 0

In any △ABC, if the angles are in the ratio 1 : 2 : 3, then the ratio of corresponding sides is

$$\mathrm{In}\:\mathrm{any}\:\bigtriangleup{ABC},\:\mathrm{if}\:\mathrm{the}\:\mathrm{angles}\:\mathrm{are}\:\mathrm{in}\: \\ $$$$\mathrm{the}\:\mathrm{ratio}\:\mathrm{1}\::\:\mathrm{2}\::\:\mathrm{3},\:\mathrm{then}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of} \\ $$$$\mathrm{corresponding}\:\mathrm{sides}\:\mathrm{is} \\ $$

Question Number 113789 Answers: 2 Comments: 0

Σ_(n=1) ^∝ (3/(n(n+3)))=?

$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\propto} {\sum}}\frac{\mathrm{3}}{\mathrm{n}\left(\mathrm{n}+\mathrm{3}\right)}=? \\ $$

Question Number 113786 Answers: 2 Comments: 0

Question Number 113781 Answers: 4 Comments: 0

Question Number 113771 Answers: 1 Comments: 0

Question Number 113770 Answers: 0 Comments: 0

Question Number 113769 Answers: 2 Comments: 0

prove that, tan (7(1/2))°=(√6)−(√3)+(√2)−2

$${prove}\:{that},\:\mathrm{tan}\:\left(\mathrm{7}\frac{\mathrm{1}}{\mathrm{2}}\right)°=\sqrt{\mathrm{6}}−\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}−\mathrm{2} \\ $$

Question Number 113775 Answers: 0 Comments: 1

Question Number 113767 Answers: 0 Comments: 1

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Question Number 113766 Answers: 1 Comments: 0

I=∫_0 ^∞ ((π/(1+π^2 x^2 ))−(1/(1+x^2 )))lnx dx put πx=tanA, x =tanB I=∫_0 ^(π/2) (ln(tanA)−lnπ)dA−∫_0 ^(π/2) ln(tanB)dB I=((−π)/2)lnπ

$$ \\ $$$${I}=\int_{\mathrm{0}} ^{\infty} \left(\frac{\pi}{\mathrm{1}+\pi^{\mathrm{2}} {x}^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right){lnx}\:{dx} \\ $$$${put}\:\pi{x}={tanA},\:{x}\:={tanB} \\ $$$${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\left({ln}\left({tanA}\right)−{ln}\pi\right){dA}−\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {ln}\left({tanB}\right){dB} \\ $$$${I}=\frac{−\pi}{\mathrm{2}}{ln}\pi \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 113763 Answers: 0 Comments: 0

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