NCERT Solutions for Class 11 Mathematics Chapter 5 Complex Numbers And Quadratic Equations

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

• less than 4ab

The conjugate of a complex number is . Then the complex number is

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

• 2

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 13 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

• 1

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 < 4 

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

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

• 2