21)The following Venn-diagram design represented by C equals
22)The shaded area in the figure is
23)The remainder of 3x3 -2x2 + x + 2 when divided by 3x + 1 is
D) None
Explanation:p(x) = 3 x3 -2 x2 + 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
View Answer
D) None
Explanation:p(x) = 3 x3 -2 x2 + 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) =
25)If the difference of two numbers is 5 and their product is 84, then the numbers are
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
C) 12,5
Explanation:perimeter of a rectangle = 34
2(l + b) = 34 ⇒ l + b = 17
length of the diagonal = = 13
l2 + b2 = 169
(l + b)2 = l2 + b2 + 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
View Answer
C) 12,5
Explanation:perimeter of a rectangle = 34
2(l + b) = 34 ⇒ l + b = 17
length of the diagonal =
= 13l2 + b2 = 169
(l + b)2 = l2 + b2 + 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 a1x + b1y + c1= 0 and a2x + b2y + c2 = 0 has unique solution, then
29)The graph of y + x2 = 0 lies in the quadrants
30)The line x = 2017 is
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