A· {(B + C) x (A + B + C)} equals
[A B C]
[B A C]
0
1
If equation y + y33 + y55 + ...∞ = 2x + x33 + x55 + ...∞ , then value of y is
x1 - x2
2x1 - x2
1 - x22x
None of these
If xx21 + x3yy21 + y3zz21 + z3 = 0, then
z = xy
z = 1xy
z = - 1xy
If A ≠ 0 and A is of order n, then adj(adj A) is equal to
An
A2
An - 1 . I
An - 2 . A
Which is incorrect ?
(AB)' = B'A'
ABθ = BAAθ
AB = B A
AB-1 = B-1A-1
A square matrix A is called an orthogonal matrix, if
A A = I
AA' = I
AAθ = I
A2 = I
The value of 'c' of Rolle's theorem for f(x) = ex sin(x) in [0, x] is given by
π4
3π4
5π6
π2
∫- aaxa2 - x2dx is equal to
π3
π8
∫0π2xsinx . cosxcos4x + sin4xdx is equal to
π28
π216
B.
Let I = ∫0π2xsinx . cosxcos4x + sin4xdx ...i⇒ I = ∫0π2π2 - xsinx . cosxsin4x + cos4x ...iiOn adding Eqs. (i) and (ii), we get2I = π2∫0π2sinx . cosxcos4x + sin4xdx⇒ I = π2∫0π2sinx . cosx1 + tan4xdx∵ dividing Nr and Dr by cos4xPut, tan2x = t ⇒ 2tanxsec2xdx = dt∴ I = π4∫0∞121 + t2dt = π8tan-1t0∞ = π8 × π2 = π216
Use Simpson's 13 rule to find the value of ∫15fxdx given,
140.88
256.66
160.26