Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1697

Question Number 38044    Answers: 2   Comments: 1

Question Number 38032    Answers: 1   Comments: 1

Question Number 38025    Answers: 1   Comments: 0

An AP has 41 terms.The sum of the first five terms of this AP is 35 and the sum of the last five terms of the same AP is 395. find the common difference and the first term.

$$\boldsymbol{\mathrm{An}}\:\boldsymbol{\mathrm{AP}}\:\boldsymbol{\mathrm{has}}\:\mathrm{41}\:\boldsymbol{\mathrm{terms}}.\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{five}} \\ $$$$\boldsymbol{\mathrm{terms}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{AP}}\:\boldsymbol{\mathrm{is}}\:\mathrm{35}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{last}}\:\boldsymbol{\mathrm{five}}\:\boldsymbol{\mathrm{terms}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{same}}\:\boldsymbol{\mathrm{AP}}\:\boldsymbol{\mathrm{is}}\:\mathrm{395}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{common}}\:\boldsymbol{\mathrm{difference}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{term}}. \\ $$

Question Number 38024    Answers: 1   Comments: 0

Question Number 38015    Answers: 0   Comments: 6

Question Number 38012    Answers: 3   Comments: 1

The roots of the equation 2x^2 − x + 3 = 0 are α and β if the roots of 3x^2 + px + q=0 are α + (1/α) and β + (1/(β )) find the value of p and q.

$${The}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} \:−\:{x}\:+\:\mathrm{3}\:=\:\mathrm{0}\:{are}\:\alpha\:{and}\:\beta \\ $$$${if}\:{the}\:{roots}\:{of}\:\mathrm{3}{x}^{\mathrm{2}} \:+\:{px}\:+\:{q}=\mathrm{0}\: \\ $$$${are}\:\alpha\:+\:\frac{\mathrm{1}}{\alpha}\:{and}\:\beta\:+\:\frac{\mathrm{1}}{\beta\:}\:{find}\:{the}\:{value} \\ $$$${of}\:{p}\:{and}\:{q}. \\ $$$$\: \\ $$

Question Number 38011    Answers: 2   Comments: 0

Show that ((sin2A)/(1+ cos2A)) = TanA

$${Show}\:{that}\: \\ $$$$\:\:\frac{{sin}\mathrm{2}{A}}{\mathrm{1}+\:{cos}\mathrm{2}{A}}\:=\:{TanA} \\ $$

Question Number 38006    Answers: 1   Comments: 5

Question Number 37972    Answers: 1   Comments: 0

The distance S metres is given as a funtion f(t) where is time taken... if S = t^3 + t^2 + 4 find the velocity and acceleration

$$\:{The}\:{distance}\:{S}\:{metres}\:{is}\: \\ $$$${given}\:{as}\:{a}\:{funtion}\: \\ $$$${f}\left({t}\right)\:{where}\:{is}\:{time}\:{taken}... \\ $$$${if}\:{S}\:=\:{t}^{\mathrm{3}} \:+\:{t}^{\mathrm{2}} \:+\:\mathrm{4} \\ $$$${find}\:{the}\:{velocity}\:{and}\:{acceleration} \\ $$

Question Number 37991    Answers: 1   Comments: 4

1. Find the sum s_n =1+2x+3x^2 +4x^3 +...+nx^(n−1) Hence,or otherwise, find the sum Σ_(k=1) ^n k.2^k 2. Simplify the following i. Σ_(r=0) ^n (_(2r−1) ^(2n) ) ii.Σ_(r=0) ^n (−1)^r r(_r ^n ) iii.Σ_(r=0) ^n (−1)^r (1/(r+1))(_r ^n ) iv.Σ_(r=0) ^n (_(2r) ^(2n) ) v.Σ_(r=0) ^n (−1)^r (_(n−r) ^(n+1) ) 3.Find the sum Σ_(r=0) ^(n−k) (_k ^(n−r) ), where k=0,1,2,3,...,n

$$\mathrm{1}.\:{Find}\:{the}\:{sum} \\ $$$$\:\:\:\:{s}_{{n}} =\mathrm{1}+\mathrm{2}{x}+\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}^{\mathrm{3}} +...+{nx}^{{n}−\mathrm{1}} \\ $$$${Hence},{or}\:{otherwise},\:{find}\:{the}\:{sum} \\ $$$$\:\:\:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}.\mathrm{2}^{{k}} \\ $$$$\mathrm{2}.\:{Simplify}\:{the}\:{following} \\ $$$${i}.\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(_{\mathrm{2}{r}−\mathrm{1}} ^{\mathrm{2}{n}} \right) \\ $$$${ii}.\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{r}} {r}\left(_{{r}} ^{{n}} \right) \\ $$$${iii}.\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{r}} \frac{\mathrm{1}}{{r}+\mathrm{1}}\left(_{{r}} ^{{n}} \right) \\ $$$${iv}.\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(_{\mathrm{2}{r}} ^{\mathrm{2}{n}} \right) \\ $$$${v}.\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{r}} \left(_{{n}−{r}} ^{{n}+\mathrm{1}} \right) \\ $$$$\mathrm{3}.{Find}\:{the}\:{sum} \\ $$$$\:\:\:\:\:\:\:\:\:\underset{{r}=\mathrm{0}} {\overset{{n}−{k}} {\sum}}\left(_{{k}} ^{{n}−{r}} \right),\:\:\:{where}\:{k}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},...,{n} \\ $$

Question Number 37989    Answers: 2   Comments: 7

Question Number 37964    Answers: 1   Comments: 0

Question Number 37961    Answers: 1   Comments: 0

calculate ∫_0 ^∞ (dx/(x^(2 ) +(√(1+x^2 )))) .

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}\:} \:+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:. \\ $$

Question Number 37957    Answers: 0   Comments: 0

Question Number 37953    Answers: 0   Comments: 1

Question Number 37948    Answers: 0   Comments: 1

If x ∈R show that (2+i)e^((1+3i)) +(2−i)e^((1−3i)) is also real.

$${If}\:{x}\:\in\mathbb{R} \\ $$$${show}\:{that}\:\left(\mathrm{2}+{i}\right){e}^{\left(\mathrm{1}+\mathrm{3}{i}\right)} +\left(\mathrm{2}−{i}\right){e}^{\left(\mathrm{1}−\mathrm{3}{i}\right)} \:{is}\:{also}\:{real}. \\ $$

Question Number 37940    Answers: 1   Comments: 0

Which of the following expressions are positive for all real values of x? a) x^2 − 2x + 5 b) x^2 −2x−1 c) x^2 +4x+2 d) 2x^2 −6x + 5

$${Which}\:{of}\:{the}\:{following}\: \\ $$$${expressions}\:{are}\:{positive}\:{for} \\ $$$${all}\:{real}\:{values}\:{of}\:\:{x}? \\ $$$$\left.{a}\left.\right)\:{x}^{\mathrm{2}} −\:\mathrm{2}{x}\:+\:\mathrm{5}\:\:\:{b}\right)\:{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1}\: \\ $$$$\left.{c}\left.\right)\:{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}\:\:\:\:\:\:{d}\right)\:\mathrm{2}{x}^{\mathrm{2}} −\mathrm{6}{x}\:+\:\mathrm{5} \\ $$

Question Number 37938    Answers: 5   Comments: 5

Question Number 37945    Answers: 0   Comments: 10

Two plane mirrors are inclined at an angle of 30°.A ray of light which makes an angle of incidence of 50° with one of the mirrors,undergoes two successive reflections at the mirrors.Calculate the angle of deviation. please help....its urgent

$${Two}\:{plane}\:{mirrors}\:{are}\:{inclined}\:{at} \\ $$$${an}\:{angle}\:{of}\:\mathrm{30}°.{A}\:{ray}\:{of}\:{light}\:{which} \\ $$$${makes}\:{an}\:{angle}\:{of}\:{incidence}\:{of}\:\mathrm{50}° \\ $$$${with}\:{one}\:{of}\:{the}\:{mirrors},{undergoes} \\ $$$${two}\:{successive}\:{reflections}\:{at}\:{the} \\ $$$${mirrors}.{Calculate}\:{the}\:{angle}\:{of} \\ $$$${deviation}. \\ $$$$ \\ $$$$ \\ $$$${please}\:{help}....{its}\:{urgent} \\ $$

Question Number 37930    Answers: 1   Comments: 1

n∈N U_(n+1) =((1/2))^(n+1) +U_n U_n =?

$${n}\in\mathbb{N} \\ $$$${U}_{{n}+\mathrm{1}} =\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{{n}+\mathrm{1}} +{U}_{{n}} \\ $$$${U}_{{n}} =? \\ $$

Question Number 37922    Answers: 1   Comments: 2

f : N → R g : N → R f(n)=∫_0 ^(2π) x^n sin x dx g(n)=∫_0 ^(2π) x^n cos x dx ((f(n+1)−f(n))/(g(n+1)−g(n)))=?

$${f}\::\:\mathbb{N}\:\rightarrow\:\mathbb{R} \\ $$$${g}\::\:\mathbb{N}\:\rightarrow\:\mathbb{R} \\ $$$${f}\left({n}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} {x}^{{n}} \mathrm{sin}\:{x}\:{dx} \\ $$$${g}\left({n}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} {x}^{{n}} \mathrm{cos}\:{x}\:{dx} \\ $$$$\frac{{f}\left({n}+\mathrm{1}\right)−{f}\left({n}\right)}{{g}\left({n}+\mathrm{1}\right)−{g}\left({n}\right)}=? \\ $$

Question Number 37915    Answers: 1   Comments: 0

If y=4x^2 −1 , then find ((85)/(169))+Σ_(i=1) ^(84) (1/(y(i)))

$$\mathrm{If}\:{y}=\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}\:,\:\mathrm{then}\:\mathrm{find} \\ $$$$\frac{\mathrm{85}}{\mathrm{169}}+\underset{{i}=\mathrm{1}} {\overset{\mathrm{84}} {\Sigma}}\:\frac{\mathrm{1}}{{y}\left({i}\right)}\: \\ $$

Question Number 37914    Answers: 1   Comments: 0

In △ABC, if sin A=sin^2 B then prove 4 cos 2A−4 cos 2B=1−cos 4B

$$\mathrm{In}\:\bigtriangleup{ABC},\:\mathrm{if}\:\mathrm{sin}\:\mathrm{A}=\mathrm{sin}^{\mathrm{2}} {B}\: \\ $$$$\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{4}\:\mathrm{cos}\:\mathrm{2}{A}−\mathrm{4}\:\mathrm{cos}\:\mathrm{2}{B}=\mathrm{1}−\mathrm{cos}\:\mathrm{4}{B} \\ $$

Question Number 37913    Answers: 1   Comments: 0

Solve the diferential equatuion (dy/dx)=((2x+y+1)/(x−2y+3))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{diferential}\:\mathrm{equatuion} \\ $$$$\frac{{dy}}{{dx}}=\frac{\mathrm{2}{x}+{y}+\mathrm{1}}{{x}−\mathrm{2}{y}+\mathrm{3}}\: \\ $$

Question Number 37912    Answers: 1   Comments: 1

Evaluate : the Integral ∫_(-(π/2)) ^(π/2) ∫_0 ^(3 cos θ) r^2 sin^2 θ. dr dθ

$$\mathrm{Evaluate}\::\:\mathrm{the}\:\mathrm{Integral} \\ $$$$\int_{-\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\mathrm{3}\:\mathrm{cos}\:\theta} {r}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \theta.\:{dr}\:{d}\theta\: \\ $$

Question Number 37911    Answers: 0   Comments: 1

the function f(x) is defined by f(x) = { ((−x + 1 , for x≤3)),((kx − 8 , for x ≥ 3)) :} find the value of k .

$$\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by} \\ $$$${f}\left({x}\right)\:=\begin{cases}{−{x}\:+\:\mathrm{1}\:,\:{for}\:{x}\leqslant\mathrm{3}}\\{{kx}\:−\:\mathrm{8}\:,\:{for}\:{x}\:\geqslant\:\mathrm{3}}\end{cases} \\ $$$${find}\:{the}\:{value}\:{of}\:{k}\:. \\ $$

  Pg 1692      Pg 1693      Pg 1694      Pg 1695      Pg 1696      Pg 1697      Pg 1698      Pg 1699      Pg 1700      Pg 1701   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com