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AllQuestion and Answers: Page 1699
Question Number 32600 Answers: 0 Comments: 6
Question Number 32591 Answers: 0 Comments: 0
Question Number 32590 Answers: 1 Comments: 0
Question Number 32589 Answers: 0 Comments: 0
Question Number 32585 Answers: 3 Comments: 2
$$\boldsymbol{{A}}\:{body}\:{undergoing}\:{SHM}\:{about}\:{the} \\ $$$${origin}\:{has}\:{its}\:{equation}\:{x}=\mathrm{0}.\mathrm{2cos}\:\mathrm{5}\pi{t}. \\ $$$${Find}\:{its}\:{average}\:{speed}\:{from}\:{t}=\mathrm{0}\:{to} \\ $$$${t}=\mathrm{0}.\mathrm{7}\:{sec}. \\ $$
Question Number 32578 Answers: 0 Comments: 1
Question Number 32569 Answers: 0 Comments: 1
$${Compute}\:\:{the}\:\:{number}\:\:{of}\:\:\:{ordered}\:\:{quadruple}\:\:\left({a},\:{b},\:{c},\:{d}\right)\:\:{of}\:\:{distinct}\:\:{positive}\:\:{integers}\:\:\:{so}\:\:{that}\:\:\begin{pmatrix}{\begin{pmatrix}{{a}}\\{{b}}\end{pmatrix}}\\{\begin{pmatrix}{{c}}\\{{d}}\end{pmatrix}}\end{pmatrix}\:\:\:=\:\:\mathrm{21}\:. \\ $$
Question Number 32563 Answers: 2 Comments: 2
$$\boldsymbol{{T}}{he}\:{set}\:{of}\:{values}\:{of}\:'{a}'\:{for}\:{which}\: \\ $$$${all}\:{the}\:{solutions}\:{of}\:{the}\:{equation} \\ $$$$\mathrm{4sin}\:^{\mathrm{4}} {x}+{a}\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{3}=\mathrm{0}\:{are}\:{real}\:{and}\: \\ $$$${distinct}\:{is}\:? \\ $$
Question Number 32584 Answers: 1 Comments: 0
Question Number 32546 Answers: 0 Comments: 1
Question Number 32577 Answers: 0 Comments: 3
Question Number 32543 Answers: 1 Comments: 0
$$\boldsymbol{{T}}{he}\:{coefficient}\:{of}\:{x}^{\mathrm{4}} \:{in}\:{the}\:{expansion} \\ $$$${of}\:\left(\mathrm{1}+\mathrm{5}{x}+\mathrm{9}{x}^{\mathrm{2}} +.....\infty\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{11}} {is} \\ $$$$\left.{a}\right)\:\mathrm{171} \\ $$$$\left.{b}\right)\:\mathrm{172} \\ $$$$\left.{c}\right)\:\mathrm{173} \\ $$$$\left.{d}\right)\:\mathrm{176} \\ $$
Question Number 32541 Answers: 2 Comments: 0
$${Coefficient}\:{of}\:{x}^{\mathrm{5}} \:{in}\:{the}\:{expansion} \\ $$$${of}\:\left({x}^{\mathrm{2}} −{x}−\mathrm{2}\right)^{\mathrm{5}} \:{is} \\ $$
Question Number 32538 Answers: 1 Comments: 1
Question Number 32535 Answers: 0 Comments: 0
$${k}\:\:\leqslant\:\:\mathrm{2018} \\ $$$${f}\:\left({f}\:\left({n}\right)\:\right)\:\:=\:\:\mathrm{2}{n} \\ $$$${f}\:\left({k}\right)\:\:=\:\:\mathrm{2018} \\ $$$${how}\:\:{many}\:\:\:{the}\:{possible}\:{of}\:\:\:\boldsymbol{{k}}\:\:{integers}\:? \\ $$
Question Number 32534 Answers: 1 Comments: 0
Question Number 32532 Answers: 0 Comments: 3
$$\boldsymbol{{I}}{f}\:{a},{b},{c}\:{are}\:\mathrm{3}\:{positive}\:{numbers}\:{in}\:{an} \\ $$$$\boldsymbol{{A}}.\boldsymbol{{P}}\:{and}\: \\ $$$${T}=\:\frac{{a}+\mathrm{8}{b}}{\mathrm{2}{b}−{a}}+\frac{\mathrm{8}{b}+{c}}{\mathrm{2}{b}−{c}}. \\ $$$${Then}\:{the}\:{value}\:{of}\:{T}^{\:\:\mathrm{2}\:} \:{is}\:? \\ $$$${Ans}.\:{given}\:{is}\:\mathrm{361}. \\ $$
Question Number 32529 Answers: 1 Comments: 2
Question Number 32517 Answers: 0 Comments: 1
$${calculatelim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:\frac{{x}^{{sinx}} \:\:−\left({sinx}\right)^{{x}} }{{x}}\:. \\ $$
Question Number 32510 Answers: 2 Comments: 1
Question Number 32508 Answers: 1 Comments: 0
Question Number 32506 Answers: 1 Comments: 0
Question Number 32503 Answers: 0 Comments: 0
$${algebra}\mathrm{1}{ic} \\ $$
Question Number 32501 Answers: 1 Comments: 0
$$\left(\mathrm{x}−\mathrm{2y}+\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{3x}+\mathrm{4y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{100} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ellipse}? \\ $$
Question Number 32500 Answers: 1 Comments: 0
$${proof}:\:\left(−{a}\right)\left(−{b}\right)={ab} \\ $$
Question Number 32499 Answers: 2 Comments: 0
$${proof}:\:{a}\left(−{b}\right)=\left(−{a}\right){b}=−\left({ab}\right) \\ $$
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