The value of α for which the sum of the squares of the roots of

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21.

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

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22.

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, ∞)

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23.

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

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24.

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 

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25.

If z2 + z + 1 = 0, where z is a complex number, then the value ofopen parentheses straight z plus 1 over straight z close parentheses squared space plus open parentheses straight z squared space plus 1 over straight z squared close parentheses squared space plus open parentheses straight z cubed space plus 1 over straight z cubed close parentheses squared space plus..... open parentheses straight z to the power of 6 plus 1 over straight z to the power of 6 close parentheses squared space is

  • 18

  • 54

  • 6

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26.

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

  • -1 , - 1 + 2ω, - 1 - 2ω2

  • -1 , -1, - 1

  • -1 , 1 - 2ω, 1 - 2ω2

  • -1 , 1 - 2ω, 1 - 2ω2

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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


A.

1

x2 – (a – 2)x – a – 1 = 0
⇒ α + β = a – 2
α β = –(a + 1)
α2 + β2 = (α + β)2 - 2αβ
= a2 – 2a + 6 = (a – 1)2 + 5
⇒ a = 1

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28.

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

  • – 2

  • 3

  • 2

  • 2

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29.

If the coefficient of x7  open square brackets ax squared space plus open parentheses 1 over bx close parentheses close square brackets to the power of 11in equals the coefficient of x-7 inopen square brackets ax squared space minus open parentheses 1 over bx close parentheses close square brackets to the power of 11then a and b satisfy the relation

  • a – b = 1

  • a + b = 1

  • a/b =1

  • a/b =1

113 Views

30.

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

  • π/2

  • 0

  • 0

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