Solve the equation (x - 2) (x - 3) = 12
2, 3
3, 6
-1, 6
1, -6
Correct answer is C
(x - 2) (x - 3) = 12
x2 - 3x - 2x + 6 = 12
x2 - 5x - 6 = 0
(x +1)(x - 6) = 0
x = -1 or 6
What is the nth term of the progression 27, 9, 3,......?
2713 n - 1
3n + 2
27 + 18(n - 1)
27 + 6(n - 1)
Correct answer is A
Given 27, 9, 3,......this is a G.P
r = 927
= 13
T = arn - 1
= 2713 n - 1
Find the positive number n, such that thrice its square is equal to twelve times the number
1
2
3
4
Correct answer is D
3n2 = 12n
= 3n2 - 12n = 0
= 3n(n - 4) = 0
∴ n = 4
Find the range of values of x which satisfy the inequality x2 + x3 + x4 < 1
x < 1213
x < 13
x < 9
1312
Correct answer is A
x2 + x3 + x4< 1
= 6x+4x+3x<1212
i.e. 13 x < 12 = x < 1213
Find the two values of y which satisfy the simultaneous equation 3x + y = 8, x2 + xy = 6.
-1 and 5
-5 and 1
1 and 5
1 and 1
Correct answer is A
3x+y=8...(i)
x2+xy=6...(ii)
From (i), y=8−3x
From (ii), xy=6−x2⟹y=6−x2x
Equating the two values of y, we have
8−3x=6−x2x⟹x(8−3x)=6−x2
8x−3x2=6−x2⟹6−x2−8x+3x2=0
2x2−8x+6=0
x2−4x+3=0
x2−3x−x+3=0⟹x(x−3)−1(x−3)=0
(x−1)(x−3)=0∴
y = 8 - 3x
When x = 1, y = 8 - 3(1) = 5
When x = 3, y = 8 - 3(3) = -1
\therefore \text{y = -1 or 5}