If k > 1 and the determinant of the matrix A2, where A = kkαα0αkα00k, is k2, then α = ?
1k2
k
k2
1k
If x > 0, y > 0, z > 0, xy + yz + zx < 1 and if tan-1x + tan-1y + tan-1z = π, then x + y + z =?
0
xyz
3xyz
sech-112 - cosec-134 = ?
loge32 + 3
loge1 + 33
loge2 + 33
loge2 - 33
If fx = x1 + x and gx = ffx, then g'x =
12x + 32
1x + 12
1x2
12x + 12
If ∫dxsin3xcosx = gx + c, then gx = ?
- 2cotx
- 2tanx
2cotx
2tanx
If ∫dx1 + xx - x2 = Ax1 -x + B1 - x + C, where C is real constant, then A + B = ?
3
1
2
B.
Given,∫dx1 + xx - x2 = Ax1 -x + B1 - x + COn differentiating both sides, we get11 + xx - x = 1 -xA12x - Ax + B122 - x - 11 -x2⇒ 11 + xx - x2 = 1 - xA + Ax + Bx1 - x2x1 -x⇒ 21 - x1 +x = A + Bx⇒ 2 - 2x = A = Bx⇒ A = 2, B = 2∴ A - B = 0
For any integer n ≥ 2, let In = ∫tann(x)dx. If In = 1atann - 1x - bIn - 2 for n≥ 2, then the ordered par (a, b) equals to
n - 1, n - 1n - 2
n - 1, n - 2n - 1
(n, 1)
(n - 1, 1)
If x2 - 1x + 12xx2 + x + 1dx= Atan-1x2 + x + 1x C, in which C is a constant, then A =?
12
By the defination of the definite integral, the value oflimn→∞1415 + n5 + 2425 + n5 + 3435 + n6 + ... + n4n5 + n5 is
log2
15log2
14log2
13log2
∫0π6cos43θ . sin26θdθ = ?
π96
5192
5π256
5π192