If, for a positive integer n, the quadratic equation,x(x + 1) +

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

11.

If z is a complex number of unit modulus and argument θ, then arg open parentheses fraction numerator 1 plus straight z over denominator 1 plus straight z with bar on top end fraction close parentheses is equal to

  • π/2-θ

  • θ

  • θ

223 Views

12.

The equation esinx-e-sinx -4 = 0 has

  • infinite number of real roots

  • No real root

  • exactly one real root

  • exactly one real root

312 Views

13.

Let α,  β be real and z be a complex number. If z2 + αz + β = 0 has two distinct roots on the line Re z = 1, then it is necessary that

  • β ∈(0, 1)

  • β ∈(-1, 0)

  • |β| = 1

  • |β| = 1

286 Views

14.

If ω(≠1) is a cube root of unity, and (1 + ω)7 = A + Bω.Then (A, B) equals

  • (0,1)

  • (1,1)

  • (1,0)

  • (1,0)

159 Views

Advertisement
15.

The Number of complex numbers z such that |z– 1| = |z + 1| = |z – i| equals 

  • 0

  • 1

  • 2

  • 2

149 Views

16.

If α and β are the roots of the equation x2 – x +1 =0, then α2009 + β2009 =

  • -2

  • -1

  • 1

  • 1

157 Views

Advertisement

17.

If, for a positive integer n, the quadratic equation,
x(x + 1) + (x + 1) (x + 2) + .....
+ (x + n -1 ) (x + n) = 10n
has two consecutive integral solutions, then n is equal to :

  • 11

  • 12

  • 9

  • 9


A.

11

nx squared space plus space straight x left parenthesis 1 space plus space 3 plus 5 plus..... space plus space left parenthesis 2 straight n minus 1 right parenthesis right parenthesis space plus
space left parenthesis 1.2 space plus space 2.3 space plus space..... space plus space left parenthesis straight n minus 1 right parenthesis. straight n right parenthesis minus 10 straight n space equals space 0
rightwards double arrow space nx squared space plus space straight x space left parenthesis straight n squared right parenthesis space plus space fraction numerator straight n left parenthesis straight n squared minus 1 right parenthesis over denominator 3 end fraction space minus space 10 straight n space equals space 0
rightwards double arrow space straight x squared space plus space straight x space left parenthesis straight n right parenthesis space plus space fraction numerator left parenthesis straight n squared minus 1 right parenthesis over denominator 3 end fraction minus 10 space equals space 0 space less than subscript straight beta superscript straight alpha
left parenthesis straight alpha space minus space straight beta right parenthesis squared space equals space 1
rightwards double arrow space left parenthesis straight alpha space plus space straight beta right parenthesis squared space minus space 4 αβ space equals space 1
rightwards double arrow space straight n squared space minus space 4 space open parentheses fraction numerator straight n squared minus 1 over denominator 3 end fraction minus 10 close parentheses space equals space 1
rightwards double arrow space straight n space equals space 11
2171 Views

Advertisement
18.

If the roots of the equation bx2+ cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c2 is

  • greater than 4ab

  • less than 4ab

  • greater than -4ab

  • greater than -4ab

134 Views

Advertisement
19.

The conjugate of a complex number is fraction numerator 1 over denominator straight i minus 1 end fraction. Then the complex number is

  • fraction numerator negative 1 over denominator straight i minus 1 end fraction
  • fraction numerator 1 over denominator straight i plus 1 end fraction
  • fraction numerator negative 1 over denominator 1 plus straight i end fraction
  • fraction numerator negative 1 over denominator 1 plus straight i end fraction
118 Views

20.

The quadratic equations x2 – 6x + a = 0 and x2 – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

  • 1

  • 4

  • 3

  • 3

135 Views

Advertisement