51)If n is a natural number, then 6 n – 5n always ends with
n – 5n , n∈N 2 – 52 = 36 – 25 = 11 3 – 53 = 216 – 125 = 91
52)If n(A) = 5, n(B) = 5 and n(A ∪ B) = 8, then n(A ∩ B) =
53)If A = {x/x ∈ N, I < x < 10}, then n(A) =
54)Identify the disjoint sets among the following:
A) A-B, B-A
B) A-B, A
C) B-A, B
D) None
55)If two zeroes of the polynomial x3 + 3 x2 – 5x – 15 are √5 and – √5, then its third zero is
1 = α+β + γ= -b/a
56)If α and β are the zeroes of the polynomial f(x) = a x2 + bx +c, then 1/α + 1/β =
A) b/c
B) –b/c
C) c/b
D) –c/b
B) –b/c
Explanation:α+β = -b/a , αβ = c/a
1/α + 1/β = α+β/αβ =
= -b/c
57)If the diagram shows the graph of the polynomial f(x) = a x2 + bx + c, then
A) a > 0, b < 0 and c > 0
B) a < 0, b < 0 and c < 0
C) a < 0, b > 0 and c > 0
D) a < 0, b > 0 and c < 0
58)If x = 2 + 22/3 + 21/3 , then the value of x3 – 6 x2 + 6x =
2/3 + 21/3 2/3 + 21/3 2 = (22/3 + 22/3) 3. x3 – 8 – 6 x2 + 12 x 3 + (21/3) 3 + 3 . 22/3 . 21/3 (22/3 + 21/3 )3 – 8 – 6 x2 + 12 x = 6 + 6x – 123 – 6 x2 + 6 x = 2
59)If am ≠ bl, then the system of equations ax + by = c, lx + my = n
A) has a unique solution
B) has no solution
C) has infinitely many solutions
D) has two solutions
1 /a2 ≠b1 /b2
60)The area of the triangle formed by the lines y = x, x = 6 and y = 0 is
A) 36 sq. units
B) 72 sq. units
C) 9 sq. units
D) 18 sq. units
D) 18 sq. units
Explanation:y = x …. (1), x = 6………..(2) , y = 0…………..(3)
(1), (3) ⇒ A(0,0)
(1), (2) ⇒B(6, 6)
(2) ,(3) ⇒C(6,0)
Area =
=
=
=
= 36/2 = 18
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= -b/c
= 36/2 = 18