A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are 

• 12 kg and 13 kg

• 5 kg and 5 kg

• 5 kg and 12 kg

• 5 kg and 12 kg

If the difference between the roots of the equation x² + ax + 1 = 0 is less than 5 , then the set of possible values of a is

•  (−3, 3)

• (−3, ∞)

• (3, ∞)

• (3, ∞)

If the roots of the quadratic equation x² + px + q = 0 are tan30° and tan15°, respectively then the value of 2 + q − p is

• 2

• 3

• 0

• 0

All the values of m for which both roots of the equations x² − 2mx + m² − 1 = 0 are greater than −2 but less than 4, lie in the interval

• −2 < m < 0

• m > 3

• −1 < m < 3 

• −1 < m < 3 

If z² + z + 1 = 0, where z is a complex number, then the value of

• 18

• 54

• 6

If the cube roots of unity are 1, ω, ω² then the roots of the equation (x – 1)³ + 8 = 0, are

• -1 , - 1 + 2ω, - 1 - 2ω²

• -1 , -1, - 1

• -1 , 1 - 2ω, 1 - 2ω²

• -1 , 1 - 2ω, 1 - 2ω²

27.

The value of α for which the sum of the squares of the roots of the equation x² – (a – 2)x – a – 1 = 0 assume the least value is

• 1

• 0

• 3

• 3

If roots of the equation x² – bx + c = 0 be two consectutive integers, then b² – 4c equals

• – 2

• 3

• 2

• 2

If the coefficient of x⁷  in equals the coefficient of x^-7 inthen a and b satisfy the relation

• a – b = 1

• a + b = 1

• a/b =1

• a/b =1

If z₁ and z₂ are two non-zero complex numbers such that |z₁ + z₂| = |z₁| + |z2| then argz₁ – argz₂ is equal to

• π/2

• -π

• 0

• 0