(i^(0))[(15^(1/4))/(3^(1/2))]^(-2)

Simplify. (i) ((15^(1//3))/(9^(1//4)))^(-6) (ii) ((12^(1//5))/(27^(1//5)))^(5//2) (iii) ((15^(1//4))/(3^(1//2)))^(-2)

Prove that: (i) (1-i)^(2)=-2i (ii) (1+i)^(4)xx(1+(1)/(i))^(4)=16 (iii) {i^(19)+((1)/(i))^(25)}^(2)=-4 (iv) i^(4n)+i^(4n+1)+i^(4n+2)+i^(4n+3)=0 (v) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25)=1+4i .

IfI_(1)=int_(0)^(1)2^(x^(2)),I_(2)=int_(0)^(1)2^(x^(3))dx,I_(3)=int_(1)^(2)2^(x^(2))dx,I_(4)=int_(1)^(2)2^(x^(3))dx then which of the following is/are true? I_(1)>I_(2)(b)I_(2)>I_(1)I_(3)>I_(4)(d)I_(3)

l_(1)=int_(0)^(1)3^(x^(2))dx,l_(2)=int_(0)^(1)3^(x^(3))dx,l_(3)=int_(1)^(2)3^(x^(2))dx,l_(4)=int_(1)^(2)3^(x^(3))dx then (i)I_(1)>I_(2)(ii)I_(2)>I_(1)(iii)I_(3)>I_(4)(iv)I_(4)>I_(3)

If a>0, then minimum value of a+2a^(2)+a^(3)+15+a^(-1)+a^(-3)+a^(-4) is

4sin^(3)75^(0)-3cos15^(0)= (1)/(2) (1)/(sqrt(2)) (1)/(sqrt(3)) sqrt(3)

The value of (1+i)(1+i^(2))(1+i^(3))(1+i^(4)) is a.2 b.0 c.1 d.i

I_(1)=int_(0)^((pi)/(2))(sin x-cos x)/(1+sin x cos x)dx,I_(2)=int_(0)^(2 pi)cos^(6)xdx,I_(3)=int_((pi)/(2))^((pi)/(2))sin^(3)xdx,I_(4)=int_(0)^(1)1n((1)/(x)-1)dx. Then I_(1)=I_(3)=I_(4)=0,I_(1)!=0I_(1)=I_(3)=0,I_(4)!=0I_(1)=I_(2)=0,I_(4)!=0I_(1)=I_(2)=I_(3)=0,I_(4)!=0

For 2 times 2 matrices A,B and I, if A+B=I and 2A-2B=I , then A equals 1) [[(1)/(4),0],[0,(1)/(4)]] 2) [[(1)/(2),0],[0,(1)/(2)]] 3) [[(3)/(4),0],[0,(3)/(4)]], 4) [[1,0],[0,1]]

I: If A=[(-2,1,0),(3,4,-5)],B=[(1,2),(4,3),(-1,5)] then A+B^(T)=[(-1,5,-1),(5,7,0)] II: If A=[(2,-1,2),(1,3,-1)],B=[(3,-2,1),(2,0,-1)] then (AB^(T))^(T)=[(10,2),(-4,3)]