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 |z²-1|=|z|²+1, then z lies on

• the real axis

• an ellipse

• a circle

• a circle

If a₁, a₂, a₃ , ....,a_n , .... are in G.P., then the value of the determinant  is

• 0

• -2

• 1

• 1

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

• x² + 18x +16 = 0

• x²-18x-16 = 0

• x²+18x-16 =0

• x²+18x-16 =0

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

7.

Let S(K) = 1 +3+5+..... (2K-1) = 3+K². Then which of the following is true?

• S(1) is correct

• Principle of mathematical induction can be used to prove the formula

• S(K) ≠S(K+1)

• S(K) ≠S(K+1)

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

• 120

• 480

• 360

• 360

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

• 5

• ⁸C₃

• 3⁸

• 3⁸

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