If \(\begin{vmatrix} x & 3 \\ 2 & 7 \end{vmatrix} = 15\), find the value of x
3
4
5
2
Correct answer is A
\(\begin{vmatrix} x & 3 \\ 2 & 7 \end{vmatrix} = 15\)
x x 7 - 2 x 3 = 15
7x - 6 = 15
7x = 15+6
7x = 21
x = 21/7
x = 3
If p and q are two non zero numbers and 18(p+q) = (18+p)q, which of the following must be true?
q = 18
p <1
p = 18
q < 1
Correct answer is A
If 18(p + q) = (18 + p)q
then 18p + 18q = 18q + pq
18p = pq ⟹⟹ q = 18.
If x * y = x + y2, find then value of (2*3)*5
36
25
11
55
Correct answer is A
x * y = x + y2
2 * 3 = 2 + 32
= 2 + 9
= 11
(2 * 3) * 5 = 11 + 52
= 11 + 25
= 36
If y varies directly as the square root of x and y = 3 when x = 16. Calculate y when x = 64
12
6
3
5
Correct answer is B
y ∝ √x
y = K√x
K = y/√x = 3/√16
= 3/4
y = 3/4√x
= 3/4√64 when x = 64
= 3/4 x 8/1
= 6
Factorize completely \(\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8}\)
| x(x-5) |
| 2(x+2) |
| x(x-5) |
| 2(x-2) |
| x(x+5) |
| 2(x+2) |
| x2+5 |
| 2x+4 |
Correct answer is C
\(\frac{x^{3} + 3x^{2} - 10x}{2x^{2} - 8} = \frac{x(x^{2} + 3x - 10)}{2(x^{2} - 4)}\)
= \(\frac{x(x^{2} - 2x + 5x - 10)}{2(x - 2)(x + 2)}\)
= \(\frac{x(x - 2)(x + 5)}{2(x - 2)(x + 2)}\)
= \(\frac{x(x + 5)}{2(x + 2)}\)