Doubts
Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents
Sign in to save progress →
Doubts
Sign in

Quadratic Equation and Inequalities question

2019 · Shift 1 · Q26
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Advanced
  3. /Mathematics
  4. /Quadratic Equation and Inequalities
  5. /2019 · Shift 1 · Q26

Quadratic Equation and Inequalities question

2019 · Shift 1 · Q26

JEE AdvancedMathematicsQuadratic Equation and InequalitiesMultiple correct+4 / −1
Let α\alphaα and β\betaβ be the roots of x2−x−1=0{x^2} - x - 1 = 0x2−x−1=0, with α\alphaα>β\betaβ. For all positive integers n, define an=αn−βnα−β, n≥1b1=1 and bn=an−1+an+1, n≥2{a_n} = {{{\alpha ^n} - {\beta ^n}} \over {\alpha - \beta }},\,n \ge 1{b_1} = 1\,and\,{b_n} = {a_{n - 1}} + {a_{n + 1}},\,n \ge 2an​=α−βαn−βn​,n≥1b1​=1andbn​=an−1​+an+1​,n≥2 Then which of the following options is/are correct?
  1. A
    ∑n=1∞bn10n=889\sum\limits_{n = 1}^\infty {{{{b_n}} \over {{{10}^n}}}} = {8 \over {89}}n=1∑∞​10nbn​​=898​
  2. B
    bn = α\alphaα n + β\betaβ n for all n ≥\ge≥ 1
  3. C
    a1 + a2 + a3 + ... + an = an+2 −-− 1 for all n ≥\ge≥ 1
  4. D
    ∑n=1∞an10n=1089\sum\limits_{n = 1}^\infty {{{{a_n}} \over {{{10}^n}}}} = {10 \over {89}}n=1∑∞​10nan​​=8910​
PreviousNext

More from Quadratic Equation and Inequalities

  • Let a, b, c three non-zero real numbers such that the equation 3​acosx+2bsinx=c,x∈[−2π​,2π​], has two distinct real roots α and β with $\alpha + \beta = {\pi \over…2018 · Numerical
  • Let p, q be integers and let α, β be the roots of the equation, x2 − x − 1 = 0 where αeβ. For n = 0, 1, 2, ........, let an = p α n + q β n. FACT : If a and b are rational numbers and a + b 5​…2017 · MCQ
  • Let p, q be integers and let α, β be the roots of the equation, x2 − x − 1 = 0 where αeβ. For n = 0, 1, 2, ........, let an = p α n + q β n. FACT : If a and b are rational numbers and a + b 5​…2017 · MCQ
  • Let −6π​<θ<−12π​. Suppose α1​ and β1​ are the roots of the equation x2−2xsecθ+1=0 and α2​ and β2​ are the roots of the equation x2+2xtanθ−1=0.Ifα1​>β1​…2016 · MCQ
  • Let S be the set of all non-zero real numbers α such that the quadratic equation αx2−x+α=0 has two distinct real roots x1​ and x2​ satisfying the inequality ∣x1​−x2​∣<1.…2015 · Multiple correct
  • The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has2014 · MCQ
  • If 3x=4x−1, then x=2013 · Multiple correct
  • The value of 6+log3/2​(32​1​4−32​1​4−32​1​4−32​1​...​​​) is ​.2012 · Numerical