If α, β are the roots of ax2 + bx + c = 0 (a 

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

61.

If (2 + i) and 5 - 2i are the roots of the equation (x2 + ax + b )(x2 + ex + d) = 0, where a, b, c and d are real constants, then product of all the roots of the equation is

  • 40

  • 95

  • 45

  • 35


62.

Which of the following is /are always false?

  • A quadratic equation with rational coefficients has zero or two irrational roots

  • A quadratic equation with real coefficients has zero or two non-real roots

  • A quadratic equation with irrational coefficients has zero or two irrational roots

  • A quadratic equation with integer coefficients has zero or two irrational roots


63.

The number of solution(s) of the equation x + 1 - x - 1 = 4x - 1 is/are

  • 2

  • 0

  • 3

  • 1


64.

The value of z2 + z - 32 + z - i2 is minimum when z equals

  • 2 - 23i

  • 45 + 3i

  • 1 + i3

  • 1 - i3


Advertisement
65.

The solution of the equation log101log7x + 7 + x = 0 is

  • 3

  • 7

  • 9

  • 49


66.

In a ABCtanA and tanB are the roots of pq(x2 + 1) = r2x. Then, ABC is

  • a right angled triangle

  • an acute angled triangle

  • an obtuse angled triangle

  • an equilateral triangle


67.

Let f(x) = 2x+ 5x + 1. If we write f(x) as f(x) = a(x + 1)(x - 2) + b(x - 2)(x - 1) + c(x - 1)(x + 1) for real numbers a, b, c then

  • there are infinite number of choices for a, b, c

  • only one choice for a but infinite number of choices for b and c

  • exactly one choice for each of a, b, c

  • more than one but finite number of choices for a, b, c


Advertisement

68.

If α, β are the roots of ax2 + bx + c = 0 (a  0) and α + h, β + h are the roots of px2 + qx + r = 0 (p  0), then the ratio of the squares of their discriminants is

  • a2 : p2

  • a : p2

  • a2 : p

  • a : 2p


A.

a2 : p2

Given, a, p are the roots of ax2 + bx + c = 0 and α + h, β + h are the roots of px2 + qx + r = 0

 α + β = - ba, αβ = caand α + h + β + h = - qp, α + hβ + h = rp

Now, α + h - β + h = α - β α + h - β + h2 = α - β2  α + h - β + h2 - 4α + hβ + h= α - β2 - 4αβ

 q2p2 - 4rp = b2a2 - 4ca q2 - 4prp2 = b2 - 4aca2 b2 - 4acq2 - 4pr = a2p2

Hence, the ratio of the square of their discriminants is a2 : p2.


Advertisement
Advertisement
69.

Suppose that z1, z2, z3 are three vertices of an equilateral triangle in the Argand plane. Let α = 123 + i and β be a non-zero complex number. The points αz1 + β, αz2 + β, αz3 + β will be

  • the vertices of an equilateral triangle

  • the vertices of an isosceles triangle 

  • collinear

  • the vertices of a scalene triangle


70.

In the Argand plane, the distinct roots of 1 + z + z3 + z4 = 0 (z is a complex number) represent vertices of

  • a square

  • an equilateral triangle

  • a rhombus

  • a rectangle


Advertisement