If x2+y2+−2x−6y+5=0, evaluate dy/dx when x=3 and y=2.
2
-2
-4
4
Correct answer is A
x2+y2+−2x−6y+5=0
When differentiated:
x2+y2+−2x−6y+5=0 → 2x + 2y - 2 - 6 = 0
where x=3 and y=2
2[3] + 2[2] - 8 = 0
6 + 4 - 8 = 2
Given that 8x+mx2−3x−4≡5x+1+3x−4
23
17
-17
18
Correct answer is C
8x+mx2−3x−4≡5x+1+3x−4
8x+mx2−3x−4 ≡ 5(x−1)+3(x+4)x2−3x−4
multiplying both sides by x2-3x-4
8x+m ≡ 5(x-4)+3(x+1)
8x + m ≡ 5x - 20 + 3x + 3
8x - 5x - 3x + m = -20 + 3
m = -17
Differentiate 5x3+x2x, x ≠ 0 with respect to x.
10x + 1
10x + 2
x(15x + 1)
x(15x + 2)
Correct answer is A
5x3+x2x → 5x3x+x2x
5x2 + x
Then dy/dx = 10x + 1
If 36, p,94 and q are consecutive terms of an exponential sequence (G.P), find the sum of p and q.
9/16
81/16
9
9 916
Correct answer is D
GP : 36, P, q4, q, ... p + q = ?
| Recall, | common | ratio, | r | = | Tn
Tn-1 |
= | T2
T1 |
= | T3
T2 |
= | T4
T3 |
| ∴ | P
36 |
= | 9
4 |
÷ | p | ; | p2 | = | 9
4 |
x | 36 | ; | p2 | = | 81 |
| p | = | 9 | ∴ | r | = | T2
T1 |
= | 9
36 |
= | 1
4 |
| Also | r | = | T4
T3 |
= | q | ÷ | 9
4 |
∴ 14 = q ÷ 94 ;
94 = 4q
| 16q | = | 9 | , | q | = | 9
16 |
∴ | p | + | q | = | 9 | + | 9
16 |
= | 9 | 9
16 |
Evaluate ∫0−1 (x + 1)(x - 2) dx
7/6
5/6
-5/6
-7/6
Correct answer is D
∫0−1 (x + 1)(x - 2) dx
= ∫0−1 x2−x−2 dx
Integrated x2−x−2 = x33−x22−2