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Question Number 194509 Answers: 2 Comments: 0

Question Number 194500 Answers: 1 Comments: 0

Σ_(0≤i^2 +j^2 ≤16) (i+j)=?

$$\underset{\mathrm{0}\leqslant{i}^{\mathrm{2}} +{j}^{\mathrm{2}} \leqslant\mathrm{16}} {\sum}\left({i}+{j}\right)=? \\ $$

Question Number 194499 Answers: 1 Comments: 3

3^x + 4^x = 5^x find x ?

$$\mathrm{3}^{\mathrm{x}} \:+\:\mathrm{4}^{\mathrm{x}} \:=\:\mathrm{5}^{\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x}\:? \\ $$

Question Number 194491 Answers: 1 Comments: 0

x=(√(4+(√(5(√3) +5(√(48−10(√(7+4(√3))))))))) determinant (((2x−1=?)))

$$\:\:\mathrm{x}=\sqrt{\mathrm{4}+\sqrt{\mathrm{5}\sqrt{\mathrm{3}}\:+\mathrm{5}\sqrt{\mathrm{48}−\mathrm{10}\sqrt{\mathrm{7}+\mathrm{4}\sqrt{\mathrm{3}}}}}}\: \\ $$$$\:\:\:\begin{array}{|c|}{\mathrm{2x}−\mathrm{1}=?}\\\hline\end{array} \\ $$

Question Number 194490 Answers: 1 Comments: 0

A research station supplies three varieties of seeds S1, S2 and S3 in the ratio 4: 2: 1. The probabilities of germination of S1, S2 and S3 are 50%, 60% and 80% respectively. Find the probability that a seed selected at random will germinate.

$$\mathrm{A}\:\mathrm{research}\:\mathrm{station}\:\mathrm{supplies}\:\mathrm{three}\:\mathrm{varieties}\: \\ $$$$\mathrm{of}\:\mathrm{seeds}\:\mathrm{S1},\:\mathrm{S2}\:\mathrm{and}\:\mathrm{S3}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{4}:\:\mathrm{2}:\:\mathrm{1}. \\ $$$$\mathrm{The}\:\mathrm{probabilities}\:\mathrm{of}\:\mathrm{germination}\:\mathrm{of}\: \\ $$$$\mathrm{S1},\:\mathrm{S2}\:\mathrm{and}\:\mathrm{S3}\:\mathrm{are}\:\mathrm{50\%},\:\mathrm{60\%}\:\mathrm{and}\:\mathrm{80\%} \\ $$$$\mathrm{respectively}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{a}\:\mathrm{seed}\:\mathrm{selected}\:\mathrm{at}\:\mathrm{random}\:\mathrm{will}\:\mathrm{germinate}. \\ $$

Question Number 194506 Answers: 0 Comments: 0

Gyanashram classes shivkund(Munger) by−Bittu sir 12 th physics test 1. 2. 3. 4. 5. ? 6. 7. 8. 5 ? 9. 30cm 5T 30^(o ) 10. ? 5 1. , 2. ,

Question Number 194488 Answers: 0 Comments: 0

Question Number 194482 Answers: 1 Comments: 0

determinant (( ),((lim_(x→0) [(1/x^2 ) ((2/(cos x)) + cos x−3)] .)))

$$\:\:\:\:\:\begin{array}{|c|c|}{ }\\{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:\left(\frac{\mathrm{2}}{\mathrm{cos}\:\mathrm{x}}\:+\:\mathrm{cos}\:\mathrm{x}−\mathrm{3}\right)\right]\:.}\\\hline\end{array} \\ $$

Question Number 194475 Answers: 2 Comments: 2

How many sets of two factors of 720 are coprime to each other? (A) 63 (B) 64 (C) 65 (D) 67

$$\mathrm{How}\:\mathrm{many}\:\mathrm{sets}\:\mathrm{of}\:\mathrm{two}\:\mathrm{factors}\:\mathrm{of}\:\mathrm{720}\:\mathrm{are}\: \\ $$$$\mathrm{coprime}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}? \\ $$$$\left(\mathrm{A}\right)\:\mathrm{63}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{64}\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{65}\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{67} \\ $$$$ \\ $$

Question Number 194467 Answers: 2 Comments: 0

f(x)= (√(8x−x^2 )) −(√(14x−x^2 −48))

$$\:\: \\ $$$$ \mathrm{f}\left(\mathrm{x}\right)=\:\sqrt{\mathrm{8x}−\mathrm{x}^{\mathrm{2}} }\:−\sqrt{\mathrm{14x}−\mathrm{x}^{\mathrm{2}} −\mathrm{48}} \\ $$

Question Number 194466 Answers: 2 Comments: 0

lim_(n→∞) Π_(k=1) ^n (1+(1/n)+(k/n^2 ))=?

$$\:\:\: \underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{n}}+\frac{\mathrm{k}}{\mathrm{n}^{\mathrm{2}} }\right)=? \\ $$

Question Number 194464 Answers: 1 Comments: 0

Question Number 194463 Answers: 1 Comments: 0

Question Number 194462 Answers: 1 Comments: 0

Prove that ∫^( +∞^ ) _( 0) ((1−e^(−x^2 ) )/x^2 )dx=(√𝛑)

$$\mathrm{Prove}\:\mathrm{that}\:\:\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}^{\:+\infty^{} } \frac{\mathrm{1}−\boldsymbol{{e}}^{−\boldsymbol{{x}}^{\mathrm{2}} } }{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}=\sqrt{\boldsymbol{\pi}} \\ $$

Question Number 194456 Answers: 2 Comments: 0

∫ ((x^8 −1)/( (√(x^(14) +x^6 )))) dx

$$\:\:\:\:\: \\ $$$$\:\:\:\int\:\frac{\mathrm{x}^{\mathrm{8}} −\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{14}} +\mathrm{x}^{\mathrm{6}} }}\:\mathrm{dx} \\ $$

Question Number 194455 Answers: 1 Comments: 0

Question Number 194451 Answers: 1 Comments: 0

lim_(x→0) ((1−(1/2)x^2 +(1/3)x^4 −cos (x))/(4x^4 +x^5 ))

$$\:\:\:\:\: \\ $$$$ \underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{3}}\mathrm{x}^{\mathrm{4}} −\mathrm{cos}\:\left(\mathrm{x}\right)}{\mathrm{4x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{5}} } \\ $$

Question Number 194448 Answers: 0 Comments: 0

If a , b , c >0 , such that a+b+c=3 prove that (1/(1+ab))+(1/(1+ac))+(1/(1+bc))≥(9/(2((√a)+(√b)+(√c))))

$${If}\:{a}\:,\:{b}\:,\:{c}\:>\mathrm{0}\:,\:{such}\:{that}\:{a}+{b}+{c}=\mathrm{3} \\ $$$${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{ab}}+\frac{\mathrm{1}}{\mathrm{1}+{ac}}+\frac{\mathrm{1}}{\mathrm{1}+{bc}}\geqslant\frac{\mathrm{9}}{\mathrm{2}\left(\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}\right)} \\ $$

Question Number 194446 Answers: 0 Comments: 0

Question Number 194445 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (1/(n^2 (n+a)))=¿ (a≠0)

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+{a}\right)}=¿ \\ $$$$\left({a}\neq\mathrm{0}\right) \\ $$

Question Number 194444 Answers: 1 Comments: 0

Question Number 194436 Answers: 1 Comments: 0

Question Number 194434 Answers: 1 Comments: 0

calcul e^(2ln(1+u) ) −e^(−2ln(1+u)) =?

$${calcul} \\ $$$${e}^{\mathrm{2}{ln}\left(\mathrm{1}+{u}\right)\:} −{e}^{−\mathrm{2}{ln}\left(\mathrm{1}+{u}\right)} \:=? \\ $$

Question Number 194431 Answers: 0 Comments: 0

Question Number 194426 Answers: 0 Comments: 0

Question Number 194425 Answers: 1 Comments: 0

lim_(x→0^+ ) ((((√(sin x)) +tan x)/( (√x) + x)) )

$$\:\:\:\:\:\: \underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\left(\frac{\sqrt{\mathrm{sin}\:\mathrm{x}}\:+\mathrm{tan}\:\mathrm{x}}{\:\sqrt{\mathrm{x}}\:+\:\mathrm{x}}\:\right) \\ $$$$ \\ $$

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