BASIC OPERATION AND FACTORISATION (CDS)

Total Questions: 77

51. For what value of k is (x + 1) a factor of x³ + kx² - x + 2 ? [2016 (I) Morning Shift]

Correct Answer: (d) -2
Solution:

52. Solve the following equation [2016 (I) Morning Shift]

Correct Answer: (c) 3
Solution:


53. If (s - a) + (s - b) + (s - c) = s then the value of [2016 (I) Morning Shift]

Correct Answer: (b) 1
Solution:Given, (s - a) + (s - b) + (s - c) = s, ⇒ 2s = (a + b + c)

54. Let p and q be non-zero integers. Consider the polynomial A(x) = x² + px + q It is given that (x - m) and (x - km) are simple factors of A (x), where m is a non-zero integer and k is a positive integer, k ≥ 2 Which one of the following is correct? [2016 (I) Morning Shift]

Correct Answer: (b) (k + 1)²q = kp²
Solution:

55. If the linear factors of ax² - (a² + 1) x + a are p and q, then p + q is equal to [2016 (I) Morning Shift]

Correct Answer: (a) (x - 1)(a + 1)
Solution:

56. The value of the expression [2016 (I) Morning Shift]

Correct Answer: (c) 2
Solution:


57. If the polynomial x⁶ + px⁵ + qx⁴ - x² - x - 3 is divisible by (x⁴ - 1) then the value of p² + q² is [2016 (I) Morning Shift]

Correct Answer: (c) 10
Solution:

58. Solve the following equation [2016 (I) Morning Shift]

Correct Answer: (a) Only 1
Solution:


59. Solve the following equation [2016 (I) Morning Shift]

Correct Answer: (a) 0
Solution:


60. If a³ = 117 + b³ and a = 3 + b then the value of a + b is (given that a > 0 and b > 0 ) [2016 (I) Morning Shift]

Correct Answer: (a) 7
Solution:We have,