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AllQuestion and Answers: Page 1956

Question Number 12875 Answers: 0 Comments: 3

Question Number 12874 Answers: 1 Comments: 0

Question Number 12873 Answers: 0 Comments: 0

How many flouride ion are there in 1.46 mole of aluminium flouride Alf_3

$$\mathrm{How}\:\mathrm{many}\:\mathrm{flouride}\:\mathrm{ion}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\mathrm{1}.\mathrm{46}\:\mathrm{mole}\:\mathrm{of}\:\mathrm{aluminium}\:\mathrm{flouride}\:\mathrm{Alf}_{\mathrm{3}} \\ $$

Question Number 12861 Answers: 2 Comments: 0

change0.356^− into p/q form

$${change}\mathrm{0}.\mathrm{35}\overset{−} {\mathrm{6}}\:{into}\:{p}/{q}\:{form} \\ $$$$ \\ $$

Question Number 12859 Answers: 0 Comments: 0

Question Number 12855 Answers: 1 Comments: 0

f(x)=[1−(x−3)^4 ]^(1/7) find f^(−1) (x).

$${f}\left({x}\right)=\left[\mathrm{1}−\left({x}−\mathrm{3}\right)^{\mathrm{4}} \right]^{\mathrm{1}/\mathrm{7}} \\ $$$${find}\:{f}^{−\mathrm{1}} \left({x}\right). \\ $$

Question Number 12846 Answers: 2 Comments: 1

Question Number 12843 Answers: 0 Comments: 0

Let R be a cummutative ring with 1. and a,b member of R. Suppose a is invertible and b is nilpotent. Show that a + b is invertible.

$$\mathrm{Let}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{cummutative}\:\mathrm{ring}\:\mathrm{with}\:\mathrm{1}.\:\mathrm{and}\:\mathrm{a},\mathrm{b}\:\:\mathrm{member}\:\mathrm{of}\:\mathrm{R}.\:\mathrm{Suppose}\:\mathrm{a}\:\mathrm{is} \\ $$$$\mathrm{invertible}\:\mathrm{and}\:\mathrm{b}\:\mathrm{is}\:\mathrm{nilpotent}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{a}\:+\:\mathrm{b}\:\mathrm{is}\:\mathrm{invertible}. \\ $$

Question Number 12841 Answers: 2 Comments: 0

The number of terms in the expansion of (1+5 (√2) x)^9 + (1−5 (√2) x)^9 is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{1}+\mathrm{5}\:\sqrt{\mathrm{2}}\:{x}\right)^{\mathrm{9}} \:+\:\left(\mathrm{1}−\mathrm{5}\:\sqrt{\mathrm{2}}\:{x}\right)^{\mathrm{9}} \:\mathrm{is} \\ $$

Question Number 12881 Answers: 1 Comments: 0

((lim)/(x→0))((√(1−cos x))/x) is equals to.

$$\frac{{lim}}{{x}\rightarrow\mathrm{0}}\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:{x}}}{{x}} \\ $$$${is}\:{equals}\:{to}. \\ $$

Question Number 12830 Answers: 1 Comments: 0

the LCM and HCF of 30 and a certain number are 150 and 5 respectively. find the number please help

$$\mathrm{the}\:\mathrm{LCM}\:\mathrm{and}\:\mathrm{HCF}\:\mathrm{of}\:\mathrm{30}\:\mathrm{and}\:\mathrm{a}\: \\ $$$$\mathrm{certain}\:\mathrm{number}\:\mathrm{are}\:\mathrm{150}\:\mathrm{and}\:\mathrm{5}\: \\ $$$$\mathrm{respectively}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{number} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$

Question Number 12829 Answers: 2 Comments: 0

Question Number 12828 Answers: 1 Comments: 0

The value of the infinite product (√3) ∙ (9)^(1/4) ∙ ((27))^(1/8) ∙ ((81))^(1/(16)) ...to ∞ is equal to ____.

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{infinite}\:\mathrm{product} \\ $$$$\sqrt{\mathrm{3}}\:\centerdot\:\sqrt[{\mathrm{4}}]{\mathrm{9}}\:\centerdot\:\sqrt[{\mathrm{8}}]{\mathrm{27}}\:\centerdot\:\sqrt[{\mathrm{16}}]{\mathrm{81}}\:...\mathrm{to}\:\infty\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\_\_\_\_. \\ $$

Question Number 12827 Answers: 2 Comments: 0

Sum of three numbers in GP be 14. If one is added to first and second and 1 is subtracted from the third, the new numbers are in AP. The smallest of them is

$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{three}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{be}\:\mathrm{14}.\:\mathrm{If}\:\mathrm{one}\:\mathrm{is} \\ $$$$\mathrm{added}\:\mathrm{to}\:\mathrm{first}\:\mathrm{and}\:\mathrm{second}\:\mathrm{and}\:\mathrm{1}\:\mathrm{is}\:\mathrm{subtracted} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{third},\:\mathrm{the}\:\mathrm{new}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}. \\ $$$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{of}\:\mathrm{them}\:\mathrm{is} \\ $$

Question Number 12826 Answers: 0 Comments: 0

prove that 1: 0<∫_0 ^(π/4) x(√(tan x)) dx< (π^2 /(32)) 2: (1/2)<∫_(π/4) ^(π/2) ((sin x)/x) dx <((√2)/2) 3: 0<∫_(100π) ^(200π) ((cos x)/x) dx <(1/(100π))

$$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{1}:\:\:\mathrm{0}<\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\mathrm{x}\sqrt{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}<\:\frac{\pi^{\mathrm{2}} }{\mathrm{32}} \\ $$$$\mathrm{2}:\:\frac{\mathrm{1}}{\mathrm{2}}<\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\:\mathrm{dx}\:<\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$$\mathrm{3}:\:\mathrm{0}<\int_{\mathrm{100}\pi} ^{\mathrm{200}\pi} \:\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{x}}\:\mathrm{dx}\:<\frac{\mathrm{1}}{\mathrm{100}\pi} \\ $$

Question Number 12822 Answers: 1 Comments: 0

prove by contradiction 9+13(√(3 )) is irrational

$${prove}\:{by}\:{contradiction}\:\mathrm{9}+\mathrm{13}\sqrt{\mathrm{3}\:} \\ $$$${is}\:{irrational} \\ $$

Question Number 12814 Answers: 1 Comments: 2

Question Number 12812 Answers: 1 Comments: 0

Question Number 12804 Answers: 1 Comments: 3

Question Number 12801 Answers: 1 Comments: 0

Question Number 12797 Answers: 1 Comments: 2

1 + x + x^2 + ... x^(49) = (1/2)(x^(49) − (1/x)) Find the value of x

$$\mathrm{1}\:+\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{2}} \:+\:...\:\mathrm{x}^{\mathrm{49}} \:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{x}^{\mathrm{49}} \:−\:\frac{\mathrm{1}}{\mathrm{x}}\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$

Question Number 12796 Answers: 1 Comments: 0

The sum of two positive numbers is 20. find the numbers (i) If their product is maximum (ii) If the sum of their square is maximum (iii) If the product of the square of one and the cube of the other is maximum

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two}\:\mathrm{positive}\:\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{20}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{numbers} \\ $$$$\left(\mathrm{i}\right)\:\:\mathrm{If}\:\mathrm{their}\:\mathrm{product}\:\mathrm{is}\:\mathrm{maximum} \\ $$$$\left(\mathrm{ii}\right)\:\:\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{square}\:\mathrm{is}\:\mathrm{maximum} \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{If}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{one}\:\mathrm{and}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{is}\:\mathrm{maximum} \\ $$

Question Number 12794 Answers: 0 Comments: 0

Let R be a cummutative ring with 1, and a,b∈R. suppose a is ivertible and b is nilpotent. Show that a + b is ivertible.

$$\mathrm{Let}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{cummutative}\:\mathrm{ring}\:\mathrm{with}\:\mathrm{1},\:\mathrm{and}\:\:\mathrm{a},\mathrm{b}\in\mathrm{R}.\:\mathrm{suppose}\:\mathrm{a}\:\mathrm{is}\:\mathrm{ivertible}\:\mathrm{and} \\ $$$$\mathrm{b}\:\mathrm{is}\:\mathrm{nilpotent}.\:\mathrm{Show}\:\mathrm{that}\:\:\mathrm{a}\:+\:\mathrm{b}\:\:\mathrm{is}\:\mathrm{ivertible}. \\ $$

Question Number 12773 Answers: 1 Comments: 0

Question Number 12768 Answers: 1 Comments: 0

∫ ((sec x)/(tan^2 x)) dx

$$\int\:\frac{\mathrm{sec}\:{x}}{\mathrm{tan}^{\mathrm{2}} \:{x}}\:{dx} \\ $$

Question Number 12766 Answers: 1 Comments: 0

∫ (dx/(1 + tan x))

$$\int\:\frac{{dx}}{\mathrm{1}\:+\:\mathrm{tan}\:{x}} \\ $$

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