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Question Number 193230    Answers: 1   Comments: 0

Choose the correct option: If a, b and c are consecutive positive integers and log(1 + ac) = 2k then the value of k is: a) log a b) log b c) 2 d) 1 Give the explaination also.

$$\boldsymbol{\mathrm{Choose}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{option}}: \\ $$$$\mathrm{If}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{consecutive}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{and}\:\mathrm{log}\left(\mathrm{1}\:+\:{ac}\right)\:=\:\mathrm{2}{k}\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{is}: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{log}\:{a} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{log}\:{b} \\ $$$$\left.\mathrm{c}\right)\:\mathrm{2} \\ $$$$\left.\mathrm{d}\right)\:\mathrm{1} \\ $$$$\boldsymbol{\mathrm{Give}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{explaination}}\:\boldsymbol{\mathrm{also}}. \\ $$

Question Number 193226    Answers: 1   Comments: 0

(a) 5 out of 12 articles are known to be defective. If three articles are picked, one after the other, without replacement, find the probability that all the three articles are non-defective. (b) Two coins are tossed and a dice is thrown. What is the probability of obtaining a head, a tail and a 4?

$$ \\ $$(a) 5 out of 12 articles are known to be defective. If three articles are picked, one after the other, without replacement, find the probability that all the three articles are non-defective. (b) Two coins are tossed and a dice is thrown. What is the probability of obtaining a head, a tail and a 4?

Question Number 193232    Answers: 0   Comments: 0

Question Number 193222    Answers: 0   Comments: 0

Question Number 193221    Answers: 1   Comments: 0

find the cube root of 9ab^2 + (b^2 +24a^2 )(√(b^2 −3a^2 ))

$$ \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{cube}}\:\boldsymbol{{root}}\:\boldsymbol{{of}} \\ $$$$\mathrm{9}\boldsymbol{{ab}}^{\mathrm{2}} \:+\:\left(\boldsymbol{{b}}^{\mathrm{2}} +\mathrm{24}\boldsymbol{{a}}^{\mathrm{2}} \right)\sqrt{\boldsymbol{{b}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{{a}}^{\mathrm{2}} } \\ $$

Question Number 193214    Answers: 0   Comments: 0

Evaluate Ω=∫_(−∞) ^( ∞) ((e^(x/2) ln((√((3−x)/(3+x)))))/(tanh^(−1) ((x/3))(1+e^x )))dx

$${Evaluate} \\ $$$$\Omega=\int_{−\infty} ^{\:\infty} \frac{{e}^{\frac{{x}}{\mathrm{2}}} {ln}\left(\sqrt{\frac{\mathrm{3}−{x}}{\mathrm{3}+{x}}}\right)}{{tanh}^{−\mathrm{1}} \left(\frac{{x}}{\mathrm{3}}\right)\left(\mathrm{1}+{e}^{{x}} \right)}{dx} \\ $$

Question Number 193213    Answers: 3   Comments: 0

((a^m /a^(−n) ))^(m−n)

$$\left(\frac{{a}^{{m}} }{{a}^{−{n}} }\right)^{{m}−{n}} \\ $$

Question Number 193210    Answers: 1   Comments: 0

Question Number 193205    Answers: 1   Comments: 1

Question Number 193204    Answers: 1   Comments: 0

Question Number 193199    Answers: 1   Comments: 0

a_1 , a_2 ,...,a_n are mutually distinct and is a am sequence . if a_( 1) +a_( 2) +...+a_n =A and a_1 ^( 2) + a_2 ^2 +..+ a_n ^( 2) = B find the am sequence.

$$ \\ $$$$\:\:\:{a}_{\mathrm{1}} \:,\:{a}_{\mathrm{2}} \:,...,{a}_{{n}} \:{are}\:\:{mutually}\:{distinct} \\ $$$$\:\:{and}\:{is}\:{a}\:\:\:\:{am}\:\:{sequence}\:. \\ $$$$\:\:\:{if}\:{a}_{\:\mathrm{1}} \:+{a}_{\:\mathrm{2}} \:+...+{a}_{{n}} \:={A} \\ $$$$\:\:\:{and}\:\: \\ $$$$\:\:\:{a}_{\mathrm{1}} ^{\:\mathrm{2}} \:+\:{a}_{\mathrm{2}} ^{\mathrm{2}} \:+..+\:{a}_{{n}} ^{\:\mathrm{2}} =\:{B} \\ $$$$\:\:\:\:{find}\:\:{the}\:\:{am}\:\:{sequence}. \\ $$

Question Number 193198    Answers: 1   Comments: 0

Question Number 193197    Answers: 0   Comments: 0

(−(3/4))^(666) mod1000=?

$$\left(−\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{666}} {mod}\mathrm{1000}=? \\ $$

Question Number 193195    Answers: 0   Comments: 0

(−3)^(666) mod1000=?

$$\left(−\mathrm{3}\right)^{\mathrm{666}} {mod}\mathrm{1000}=? \\ $$

Question Number 193192    Answers: 1   Comments: 0

solve and solution Ω=∫(√(sin^(−1) x))dx=?

$$\mathrm{solve}\:\mathrm{and}\:\mathrm{solution} \\ $$$$\Omega=\int\sqrt{\mathrm{sin}^{−\mathrm{1}} \mathrm{x}}\mathrm{dx}=? \\ $$

Question Number 193203    Answers: 1   Comments: 0

Question Number 193183    Answers: 1   Comments: 0

There exists a unique positive integer a for which The sum u = Σ_(n=1) ^(2023) ⌊((n^2 −na)/5)⌋ is an integer strictly between −1000 & 1000 find a+u.

$$ \\ $$$${There}\:{exists}\:{a}\:{unique}\:{positive}\:{integer}\:{a}\:{for} \\ $$$${which}\:{The}\:{sum}\:{u}\:\:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\lfloor\frac{{n}^{\mathrm{2}} −{na}}{\mathrm{5}}\rfloor\:{is}\:{an}\:{integer} \\ $$$${strictly}\:{between}\:−\mathrm{1000}\:\&\:\mathrm{1000}\:{find}\:{a}+{u}. \\ $$

Question Number 193182    Answers: 1   Comments: 0

(x^2 /(2^2 −1^2 ))+(y^2 /(2^2 −3^2 ))+(z^2 /(2^2 −5^2 ))+(w^2 /(2^2 −7^2 ))=1 (x^2 /(4^2 −1^2 ))+(y^2 /(4^2 −3^2 ))+(z^2 /(4^2 −5^2 ))+(w^2 /(4^2 −7^2 ))=1 (x^2 /(6^2 −1^2 ))+(y^2 /(6^2 −3^2 ))+(z^2 /(6^2 −5^2 ))+(w^2 /(6^2 −7^2 ))=1 (x^2 /(8^2 −1^2 ))+(y^2 /(8^2 −3^2 ))+(z^2 /(8^2 −5^2 ))+(w^2 /(8^2 −7^2 ))=1 find (x^2 +y^2 +z^2 +w^2 ).

$$ \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{5}^{\mathrm{2}} }+\frac{{w}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }=\mathrm{1} \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{4}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{\mathrm{4}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}} }{\mathrm{4}^{\mathrm{2}} −\mathrm{5}^{\mathrm{2}} }+\frac{{w}^{\mathrm{2}} }{\mathrm{4}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }=\mathrm{1} \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{6}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{\mathrm{6}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}} }{\mathrm{6}^{\mathrm{2}} −\mathrm{5}^{\mathrm{2}} }+\frac{{w}^{\mathrm{2}} }{\mathrm{6}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }=\mathrm{1} \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{8}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{\mathrm{8}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}} }{\mathrm{8}^{\mathrm{2}} −\mathrm{5}^{\mathrm{2}} }+\frac{{w}^{\mathrm{2}} }{\mathrm{8}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }=\mathrm{1}\: \\ $$$$ \\ $$$${find}\:\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} +{w}^{\mathrm{2}} \right). \\ $$

Question Number 193180    Answers: 3   Comments: 0

If a + b = 1001 & HCF(a, b) = 13 then how many set of a & b.

$$\mathrm{If}\:{a}\:+\:{b}\:=\:\mathrm{1001}\:\&\:\mathrm{HCF}\left({a},\:{b}\right)\:=\:\mathrm{13}\: \\ $$$$\mathrm{then}\:\mathrm{how}\:\mathrm{many}\:\mathrm{set}\:\mathrm{of}\:{a}\:\&\:{b}. \\ $$

Question Number 193179    Answers: 0   Comments: 0

f(θ) = ((v^2 sinθcosθ+vcos (√(v^2 sin^2 θ+Hg )) )/g) f(θ)_(max) =?

$$\:\:{f}\left(\theta\right)\:=\:\frac{{v}^{\mathrm{2}} \mathrm{sin}\theta\mathrm{cos}\theta+{v}\mathrm{cos}\:\sqrt{{v}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \theta+{Hg}\:}\:}{{g}} \\ $$$$\:\:\:{f}\left(\theta\right)_{{max}} =? \\ $$

Question Number 193175    Answers: 3   Comments: 0

please solve for x if 2x^2 =2^x

$${please}\:{solve}\:{for}\:{x}\:{if} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} =\mathrm{2}^{{x}} \\ $$

Question Number 193171    Answers: 0   Comments: 0

Question Number 193170    Answers: 1   Comments: 0

solve : 7^x =−2

$$\mathrm{solve}\::\:\mathrm{7}^{\mathrm{x}} =−\mathrm{2} \\ $$

Question Number 193162    Answers: 1   Comments: 2

Question Number 193161    Answers: 1   Comments: 0

Question Number 193153    Answers: 0   Comments: 0

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