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
A.
Given, fx = 1sinx + cosxOn differentiating w.r.t. x, we getf'x = - 1sinx + cosx2cosx - sinxFor minimum, put f'(x) = 0∴ cosx - sinx = 0⇒ tanx = 1⇒ x = π4∴ x = π4, f'x > 0, minima∴ Minimum value isfπ4 = 1sinπ4 + cosπ4 = 112 + 12 = 122 = 22
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
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