If `A=[a_(ij)]_(mxxn)` and `a_(ij)=(i^(2)+j^(2)-ij)(j-i)`, `n` odd, then which of the following is not the value of `Tr(A)`

`V_(rms)=220V` `Z=sqrt(R^(2)+(X_(L)-X_(C))^(2)) rArr Z=8Omega`

`V_(rms)=220 V` `Z=sqrt(R^(2)+(X_(L)-X_(C))^(2)) rArr Z=8Omega`

Correct Answer - D If A is nth root of `I_(2)`, then `A^(n)=I_(2)`. Now, `A^(2)=[(a,b),(0,a)][(a,b),(0,a)]=[(a^(2),2ab),(0,a^(2))]` `A^(3)=A^(2) A=[(a^(2),2ab),(0,a^(2))][(a,b),(0,a)]=[(a^(3),3a^(2)b),(0,a^(3))]` Thus, `A^(n)=[(n^(n),na^(n-1)b),(0,a^(n))]` Now, `A^(n)=I implies [(a^(n),na^(n-1)b),(0,a^(n))]=[(1,0),(0,1)]` `implies a^(n)=1, b=0`

Correct Answer - C As second row of all the options is same, we have to look at the elements of the first row. Let the left inverse be `[(a,b,c),(d,e,f)]`. Then...

Correct Answer - A::C Given equation is `x^(2) + 2x sin(cos^(-1) y) + 1 =0` Since x is real, `D ge 0`. Therefore, `4(sin(cos^(-1)y))^(2) -4 ge 0` or `(sin(cos^(-1)y))^(2) ge 1`...

Correct option is: A. Highest value

Correct option is: B. Lowest value

(a) , ( c) , (d) `f(theta) = 4 sin theta cos^(2) theta = 4 sin theta + 1 - sin^(2) theta` `= 5 -(4-4sin theta + sin^(2) theta) =...

`sin^2theta_1+sin^2theta_2+sin^2theta_3=0` `rArr sin^2theta_1=sin^2theta_2=sin^2theta_3=0` `rArr cos^2theta_1,cos^2theta_2,cos^2theta_3=1` `rArr costheta_1,costheta_2,costheta_3=pm1` `cos^2theta_1+cos^2theta_2+cos^2theta_3"can be-3 (when all are -I)"` or 3 (when all are +I) or -1 (when any two are -1 and one is +1)...

Correct Answer - B `(b)` We have `S_(n)-S_(n-2)=T_(n)+T_(n-1)` (Taking `n` to be odd) `:.T_(n-1)(1+(T_(n))/(T_(n-1)))=((n+1)/(2))-((n-1))/(2)=1` (As `S_(n)=(n+1)/(2)`, if `n` is odd) `:.T_(n-1)(1+(n^(2))/(1-n^(2)))=1` `:.T_(n-1)=-(n^(2)-1)` when `n` is odd Also, `S_(m)=S_(m-1)+T_(m)` If `m` is...