`alpha^m/alpha^n` is equal to

int(cosalpha)/(a^2+sin^2alpha)d alpha is equal to

If 0ltalpha,betaltpi and cos alpha+cos beta -cos(alpha+beta)=(3)/(2) , then the value of sqrt3 sin alpha+cos alpha is equal to

lim_(x->alpha)(tanxcotalpha)^(1/(x-alpha)) is equal to

If tan alpha + cot alpha=a , then the value of tan^(4)alpha + cot^(4)alpha is equal to

("lim")_(n vec oo)"{"(n/(n+1))^(alpha)+sin (1/n)]^n (when alpha in Q ) is equal to (a) e^(-alpha) (b) -alpha (c) e^(1-alpha) (d) e^(1+alpha)

If (log)_(10)(1025)/(1024)=alphaa n d(log)_(10)2=beta , then the value of (log)_(10)4100 in terms of alphaa n dbeta is equal to alpha+9beta (b) alpha+12beta 12alpha+beta (d) 9alpha+beta

If (log)_(10)(1025)/(1024)=alphaa n d(log)_(10)=beta, then the value of (log)_(10)4100 in terms of alpha and beta is equal to a. alpha+9beta b. alpha+12beta c. 12alpha+beta d. 9alpha+beta

If alpha=^m C_2,t h e n^(alpha)C_2 is equal to a. ^m+1C_4 b. ^m-1C_4 c. 3^(m+2)C_4 d. 3^(m+1)C_4

The determinant Delta = |(b,c,b alpha +c),(c,d,c alpha + d),(b alpha + c,c alpha + d,a a^(3) - c alpha)| is equal to zero, if

If A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))] , then A(alpha, beta)^(-1) is equal to