If the angle between the curves y = 2x and y = 3x is α, then the value of tan(α) is equal to
log321 + log2log3
67
17
log61 + log2log3
The function f(x) = 3x3 - 36x + 99 is increasing for
- ∞ < x < 2
- 2 < x < ∞
- 2 < x < 2
x < - 2 or x > 2
Let f(x) = x3 - x + p (0 ≤ x ≤ 2) where p is a constant. The value c of mean value theorem is
32
63
33
233
The minimum value of the function fx = 1sinx + cosx in the interval 0, π2 is
22
- 22
23 + 1
-23 + 1
If n(A) = 5 and n(B) = 7, then the number of relations on A x B is
235
249
225
235 × 35
Let ϕx = bx - ab - a + ax - ba - b, where x ∈ R and a and b are fixed real numbers with a ≠ b. Then, ϕa + b is equal to
ϕab
ϕ- ab
ϕa + ϕb
ϕa - b
The range of the function f(x) = x2 + 8x2 + 4, x ∈ R is
- 1, 32
(1, 2]
(1, 2)
[1, 2]
If n(A) = 1000, n(B) = 500 and if n(A ∩ B) ≥1 and nA ∪ B = p, then
500 ≤ p ≤ 1000
1001 ≤ p ≤ 1498
1000 ≤ p ≤ 1498
1000 ≤ p ≤ 1499
D.
Given, nA = 1000, nB = 500and nA ∩ B ≥ 1 and nA ∪ B = p∵ nA ∩ B = nA + nB - nA ∪ B = 1000 + 500 - p = 1500 - p
∵ nA ∩ B ≥ 1⇒ 1500 - p ≥ 1⇒ p ≤ 1500 ...iAlso, nA ∪ B ≥ nA⇒ p ≥ 1000 ...ii∴ From Eqs. (i) and (ii), we get 1000 ≤ p ≤ 1500
The domain of the function fx = sin-1x + 52 is
[- 1, 1]
[2, 3]
[3, 7]
[- 7, - 3]
If f(x) = x + 1 and g(x) = 2x, then f{g(x)} is equal to
2(x + 1)
2x(x + 1)
x
2x + 1