21) The following Venn-diagram design represented by C equals
A) {1,2,5, 6}
B) {6,5,4}
C) {4,5,6,7}
D) {2,5,6}
22) The shaded area in the figure is
A) A⋂(B⋃C)
B) A⋂(B⋃C)
C) A⋃(B⋂C)
D) A⋃(B⋃C)
23) The remainder of 3x3 -2x2 + x + 2 when divided by 3x + 1 is
A) 4/3
B) 3/4
C) -4/3
D) None
D) None
Explanation:p(x) = 3 x
3 -2 x
2 + x + 2
3x + 1 = 0 ⇒ x = -1/3
P(-1/3) = 3(-1/3)
3 – 2(-1/3)
2 +(-1/3)+2
= -3 x 1/27 -2 x1/9-1/3+2/1
=1/9-2/9-1/3+2/1
=
=
= 14/9
24) If α, β are the roots of 5×2 + 5x + 6 = 0, then (1 + α) (1 + β) =
A) 4/5
B) 3/5
C) 6/5
D) -6/5
25) If the difference of two numbers is 5 and their product is 84, then the numbers are
A) 14,6
B) 12,7
C) 21,4
D) 14,9
2 = (α – β)2 + 4 x β2 + 4 x 84
26) If the perimeter of a rectangular room is 34 and the length of the diagonal is 13, then the dimensions of the room are
A) 7,6
B) 11,6
C) 12,5
D) 12,6
C) 12,5
Explanation:perimeter of a rectangle = 34
2(l + b) = 34 ⇒ l + b = 17
length of the diagonal =
= 13
l
2 + b
2 = 169
(l + b)
2 = l
2 + b
2 + 2/b
(17)
2 = 169 + 2lb
⇒ 289- 169 = 2lb
2lb = 120 ⇒ lb = 60
(l – b)
2 = (l + b)
2 -4lb
= (17)
2 -4x 60 = 289-240 = 49
L – b=-749 = 7
l + b= 17
l – b =27
________
2l = 24 ⇒ l = 12, b = 17 – 12 = 5
∴ The dimensions of the room are 12 and 5
27) If 9x + 11y = 51 and 11x + 9y = 49, then x =
28) If the pair of equations a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0 has unique solution, then
A) a1 / a2 = b1 / b2
B) a1 / a2 ≠ b1 / b2
C) b1 / b2 ≠ c1 / c2
D) b1 / b2 = c1 / c2
1 / a2 ≠ b1 / b2
29) The graph of y + x2 = 0 lies in the quadrants
A) Q1 ,Q2
B) Q2 ,Q3
C) Q3 ,Q4
D) Q4 ,Q1
3 ,Q4 2 ⇒ y = mx2 (m < 0)3 and Q4
30) The line x = 2017 is
A) Slope not defined
B) Parallel to y-axis
C) Slope not defined and Parallel to y-axis
D) None
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