If both the roots of the quadratic equation x² – 2kx + k² + k – 5 = 0 are less than 5, then k lies in the interval

• (5, 6]

• (6, ∞)

• (-∞, 4)

• (-∞, 4)

If the equation a_nxⁿ +a_n-1x^n-1 +....... +a₁x =0, a₁ ≠ 0, n≥2, has a positive root x =  α, then the equation na_nx^n-1 + (n-1)a_n-1x_n-2 +......+a₁ = 0 has a positive root, which is

• greater than α

• smaller than α

• greater than or equal to α

• greater than or equal to α

Let z, w be complex numbers such that z iw + = 0 and arg zw = π. Then arg z equals

• π/4

• 5π/4

• 3π/4

• 3π/4

If z = x – i y and z^1/3 = p+ iq , then  is equal to 

• 1

• -2

• 2

• 2

If (1 – p) is a root of quadratic equation x² +px + (1-p)=0 , then its roots are

• 0, 1

• -1, 2

• 0, -1

• 0, -1

If one root of the equation x²+px+12 =0 is 4, while the equation x² +px +q = 0 has equal roots, then the value of 'q' is

• 49/3

• 4

• 3

• 3

The coefficient of xⁿ in expansion of (1+x)(1-x)ⁿ is

• (n-1)

• (-1)ⁿ(1-n)

• (-1)^n-1(n-1)²

• (-1)^n-1(n-1)²

118.

If 2a + 3b + 6c =0, then at least one root of the equation ax² + bx+ c = 0  lies in the interval

• (0,1)

• (1,2)

• (2,3)

• (2,3)

If x = ω – ω² – 2. Then the value of (x⁴ + 3x³ + 2x² – 11x – 6) is

• 0

• -1

• 1

• 1

If α, β ∈ C are the distinct roots, of the equation x² -x + 1 = 0, then α¹⁰¹ + β¹⁰⁷ is equal to

• 2

• -1

• 0

• 1