56. HCF of 8, 9 and 25 is
(a) 8
(b) 9
(c) 25
(d) 1
(d) 1
57. Question: The product of a rational and irrational number is.
(a) rational
(b) irrational
(c) both of above
(d) none of above
(b) irrational
Explanation:
The product of a non-zero rational number and an irrational number is always irrational.
(a) 10
(b) -10
(c) 5
(d) -5
(b) -10
Substitute x=2 into the polynomial: (2)2+3(2)+k=0⟹4+6+k=0⟹k=−10.
59. Question: If one of the zeroes of the cubic polynomial x3+ax2+bx+c is -1, then the product of the other two zeroes is.
(a) b-a+1
(b) b-a-1
(c) a-b+1
(d) a-b-1
(a) b−a+1
Let zeroes be α,β,γ with α=−1. Using Vieta’s formulas, αβ+βγ+γα=b and α+β+γ=−a. Solving these gives the product of the other two zeroes, βγ=b−a+1.
60. Question: Half the perimeter of a rectangular room is 46 m, and its length is 6 m more than its breadth. What is the length and breadth of the room?
(a) 2m, 20m
(b) 2m, 3m
(c) 56m, 40m
(d) 26m, 20m
(d) 26m, 20m
Let length be ‘l’ and breadth be ‘b’. We have l+b=46 and
l=b+6. Substituting gives (b+6)+b=46⟹2b=40⟹b=20m.
Then l=26m.
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