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Question Number 28012    Answers: 1   Comments: 1

1,4,5,16,17,20....... what is the 68th term in this sequnce?

$$\mathrm{1},\mathrm{4},\mathrm{5},\mathrm{16},\mathrm{17},\mathrm{20}.......\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{68th}\:\mathrm{term}\:\mathrm{in}\:\mathrm{this}\:\mathrm{sequnce}? \\ $$

Question Number 27977    Answers: 1   Comments: 0

∣2x+1∣≤2

$$\mid\mathrm{2}{x}+\mathrm{1}\mid\leqslant\mathrm{2} \\ $$

Question Number 27976    Answers: 1   Comments: 1

solve ((2x)/(x^2 +1))<((3x+1)/(2(x^2 +1)))

$${solve} \\ $$$$ \\ $$$$\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} +\mathrm{1}}<\frac{\mathrm{3}{x}+\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{1}\right)} \\ $$$$ \\ $$

Question Number 27975    Answers: 1   Comments: 0

solve the inequality (1/(x^2 +x+1))>0

$${solve}\:{the}\:{inequality} \\ $$$$\frac{\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}>\mathrm{0} \\ $$

Question Number 27974    Answers: 0   Comments: 1

let put f(t)=∫_0 ^∞ ((e^(−ax) − e^(−bx) )/x^2 ) e^(−tx^2 ) dx with t≥0 and a>0 and b>0 find a integral form of f(t).

$${let}\:{put}\:{f}\left({t}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{ax}} \:−\:{e}^{−{bx}} }{{x}^{\mathrm{2}} }\:{e}^{−{tx}^{\mathrm{2}} } \:{dx} \\ $$$${with}\:{t}\geqslant\mathrm{0}\:\:{and}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$$${find}\:{a}\:{integral}\:{form}\:{of}\:{f}\left({t}\right). \\ $$

Question Number 27958    Answers: 1   Comments: 0

For α∈R, cosαcosx+siny≥sinx, ∀x∈R, then find the sum of the possible values of sinα+siny.

$${For}\:\alpha\in{R},\:{cos}\alpha{cosx}+{siny}\geqslant{sinx},\:\forall{x}\in{R}, \\ $$$${then}\:{find}\:{the}\:{sum}\:{of}\:{the}\:{possible}\:{values} \\ $$$${of}\:{sin}\alpha+{siny}. \\ $$

Question Number 27959    Answers: 0   Comments: 6

Question Number 27954    Answers: 0   Comments: 1

Question Number 27951    Answers: 0   Comments: 0

Use the trapezoidal rule with 5 ordinates to evaluate ∫_( 0) ^( 0.8) e^x^2 dx

$$\mathrm{Use}\:\mathrm{the}\:\mathrm{trapezoidal}\:\mathrm{rule}\:\mathrm{with}\:\mathrm{5}\:\mathrm{ordinates}\:\mathrm{to}\:\mathrm{evaluate}\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{0}.\mathrm{8}} \:\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \:\:\mathrm{dx} \\ $$

Question Number 27950    Answers: 0   Comments: 0

Find by the trapezoidal rule the approximate value of ∫_( 0) ^( 1) (dx/(1 + x^2 )). Use ordinates spaced at equal interval of width h = 0.1

$$\mathrm{Find}\:\mathrm{by}\:\mathrm{the}\:\mathrm{trapezoidal}\:\mathrm{rule}\:\mathrm{the}\:\mathrm{approximate}\:\mathrm{value}\:\mathrm{of}\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{dx}}{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} }.\:\:\:\mathrm{Use} \\ $$$$\mathrm{ordinates}\:\mathrm{spaced}\:\mathrm{at}\:\mathrm{equal}\:\mathrm{interval}\:\mathrm{of}\:\mathrm{width}\:\:\mathrm{h}\:=\:\mathrm{0}.\mathrm{1} \\ $$

Question Number 27961    Answers: 0   Comments: 0

A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is

$${A}\:\mathrm{and}\:{B}\:\mathrm{play}\:\mathrm{a}\:\mathrm{game}\:\mathrm{where}\:\mathrm{each}\:\mathrm{is} \\ $$$$\mathrm{asked}\:\mathrm{to}\:\mathrm{select}\:\mathrm{a}\:\mathrm{number}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{25}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{two}\:\mathrm{numbers}\:\mathrm{match},\:\mathrm{both}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{win}\:\mathrm{a}\:\mathrm{prize}.\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{they} \\ $$$$\mathrm{will}\:\mathrm{not}\:\mathrm{win}\:\mathrm{a}\:\mathrm{prize}\:\mathrm{in}\:\mathrm{a}\:\mathrm{single}\:\mathrm{trial}\:\mathrm{is} \\ $$

Question Number 27948    Answers: 0   Comments: 0

what is relation between intensity of diffraction pattern .slit width?

$${what}\:{is}\:{relation}\:{between}\: \\ $$$${intensity}\:{of}\:{diffraction}\: \\ $$$${pattern}\:.{slit}\:{width}? \\ $$

Question Number 27946    Answers: 1   Comments: 0

Q.N− Find the coefficint of x^4 in the expansion of (1+3x+10x^2 )(x+(1/x))^(10)

$$\boldsymbol{\mathrm{Q}}.\boldsymbol{\mathrm{N}}− \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{coefficint}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{x}}^{\mathrm{4}} \\ $$$$\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{expansion}}\:\boldsymbol{\mathrm{of}} \\ $$$$\:\:\:\:\:\left(\mathrm{1}+\mathrm{3}\boldsymbol{\mathrm{x}}+\mathrm{10}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)\left(\boldsymbol{\mathrm{x}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\right)^{\mathrm{10}} \\ $$$$ \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 27944    Answers: 0   Comments: 0

Did anybody give Silverzone iOM of class 11?

$${Did}\:{anybody}\:{give}\:{Silverzone}\:{iOM}\:{of} \\ $$$${class}\:\mathrm{11}? \\ $$

Question Number 27942    Answers: 1   Comments: 1

Question Number 27939    Answers: 0   Comments: 1

Question Number 27936    Answers: 2   Comments: 1

Question Number 27930    Answers: 0   Comments: 2

Question Number 27920    Answers: 1   Comments: 0

∫(((x−1)dx)/((x+1)(√(x^3 +x^2 +x))))

$$\int\frac{\left({x}−\mathrm{1}\right){dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}}} \\ $$

Question Number 27922    Answers: 0   Comments: 4

a,b & c are distinct primes and x,y,z∈{0,1,2,...}. What is the number of divisors, common to the numbers a^x b^y c^z , a^x b^z c^y ,a^y b^x c^z ,a^y b^z c^x ,a^z b^x c^y & a^z b^y c^z .

$$\mathrm{a},\mathrm{b}\:\&\:\mathrm{c}\:\mathrm{are}\:\boldsymbol{\mathrm{distinct}}\:\boldsymbol{\mathrm{primes}}\:\mathrm{and} \\ $$$$\mathrm{x},\mathrm{y},\mathrm{z}\in\left\{\mathrm{0},\mathrm{1},\mathrm{2},...\right\}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\boldsymbol{\mathrm{divisors}}, \\ $$$$\boldsymbol{\mathrm{common}}\:\mathrm{to}\:\mathrm{the}\:\boldsymbol{\mathrm{numbers}}\:\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{y}}} \boldsymbol{\mathrm{c}}^{\boldsymbol{\mathrm{z}}} , \\ $$$$\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{z}}} \boldsymbol{\mathrm{c}}^{\boldsymbol{\mathrm{y}}} ,\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{y}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{c}}^{\boldsymbol{\mathrm{z}}} ,\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{y}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{z}}} \boldsymbol{\mathrm{c}}^{\boldsymbol{\mathrm{x}}} ,\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{z}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{c}}^{\boldsymbol{\mathrm{y}}} \:\&\:\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{z}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{y}}} \boldsymbol{\mathrm{c}}^{\boldsymbol{\mathrm{z}}} \:. \\ $$

Question Number 27909    Answers: 0   Comments: 1

Question Number 27908    Answers: 1   Comments: 1

IF a_(1,) a_2 ,.....,a_(n−1) ,a_n are in AP then prove that 1/a_1 .a_n + 1/a_2 .a_(n−1) + 1/a_3 .a_(n−2) +...+1/a_n .a_1 = 2/a_1 +a_(n ) [1/a_(1 ) +1/a_2 +....+1/a_n ]

$${IF}\:\:{a}_{\mathrm{1},} {a}_{\mathrm{2}} ,.....,{a}_{{n}−\mathrm{1}} ,{a}_{{n}} \:{are}\:{in}\:{AP}\:{then}\:{prove}\:{that} \\ $$$$\mathrm{1}/{a}_{\mathrm{1}} .{a}_{{n}} +\:\mathrm{1}/{a}_{\mathrm{2}} .{a}_{{n}−\mathrm{1}} +\:\mathrm{1}/{a}_{\mathrm{3}} .{a}_{{n}−\mathrm{2}} +...+\mathrm{1}/{a}_{{n}} .{a}_{\mathrm{1}} = \\ $$$$\mathrm{2}/{a}_{\mathrm{1}} +{a}_{{n}\:} \left[\mathrm{1}/{a}_{\mathrm{1}\:} +\mathrm{1}/{a}_{\mathrm{2}} +....+\mathrm{1}/{a}_{{n}} \right] \\ $$

Question Number 27899    Answers: 2   Comments: 0

Question Number 27888    Answers: 1   Comments: 4

a and b are distinct primes and x,y∈{0,1,2,...}. What is the number of divisors common to the numbers (a^x b^y ) and (a^y b^x )?

$$\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{are}\:\boldsymbol{\mathrm{distinct}}\:\boldsymbol{\mathrm{primes}}\:\mathrm{and} \\ $$$$\mathrm{x},\mathrm{y}\in\left\{\mathrm{0},\mathrm{1},\mathrm{2},...\right\}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{divisors}} \\ $$$$\boldsymbol{\mathrm{common}}\:\mathrm{to}\:\mathrm{the}\:\boldsymbol{\mathrm{numbers}}\:\left(\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{y}}} \right) \\ $$$$\boldsymbol{\mathrm{and}}\:\left(\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{y}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{x}}} \right)? \\ $$

Question Number 27885    Answers: 0   Comments: 1

(4) Find the term indepen− dent of x in the expansion of (x^2 −2+(1/x^2 ))^6

$$\left(\mathrm{4}\right)\:\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{term}}\:\boldsymbol{\mathrm{indepen}}− \\ $$$$\boldsymbol{\mathrm{dent}}\:\boldsymbol{\mathrm{of}}\:\:\:\:\boldsymbol{\mathrm{x}}\:\:\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{expansion}}\:\boldsymbol{\mathrm{of}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{2}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right)^{\mathrm{6}} \\ $$

Question Number 27884    Answers: 2   Comments: 0

(3) Find the term independ− ent of x in the expansion of ( x+(1/x))^2 (x−(1/x))^(12)

$$\left(\mathrm{3}\right)\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{term}}\:\boldsymbol{\mathrm{independ}}− \\ $$$$\boldsymbol{\mathrm{ent}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{x}}\:\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{expansion}}\:\boldsymbol{\mathrm{of}} \\ $$$$\:\:\:\left(\:\boldsymbol{\mathrm{x}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\right)^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}−\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\right)^{\mathrm{12}} \\ $$

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