Let ` A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]]` .` If |A^2| = 25,` then `alpha` equals to:

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

Given A=[[2,0,-alpha],[5,alpha,0],[0,alpha,3]] For a in R-{a, b} , A^(-1) exists and A^(-1)=A^2-5bA + cI , when alpha = 1 . The value of a +5b +c is:

If 0 < alpha < pi/ 6 then alpha(cosec alpha) is

if (1+tan alpha )(1+tan4 alpha ) =2 where alpha in (0 , pi/16 ) then alpha equal to

If 0 < alpha < pi/6 and sin alpha + cos alpha =sqrt(7 )/2, then tan alpha/2 is equal to

If B = [{:(5, 2alpha, 1),(0, 2, 1),(alpha, 3, -1):}] is the inverse of a 3 xx 3 matrix A, then the sum of all values of alpha for which det (A) + 1 =0, is

Let A(alpha)=[(cos alpha, 0,sin alpha),(0,1,0),(sin alpha, 0, cos alpha)] and [(x,y,z)]=[(0,1,0)] . If the system of equations has infinite solutions and sum of all the possible value of alpha in [0, 2pi] is kpi , then the value of k is equal to

If cos( alpha+beta) + sin(alpha-beta) = 0 and 2010tan beta - 1 = 0 then tan alpha is equal to

If cot (alpha + beta) = 0 , then sin (alpha + 2 beta) is equal to

Let A(alpha)=[cosalpha0sinalpha0 1 0sinalpha0cosalpha] and X is a set of all matrices A(alpha) for different values of alpha . Which of the following is true (a)A^(-1)(alpha)=A(-alpha) (b) A^(-1)(alpha)=A(alpha) (c)det(a d j(A^(-1)(alpha)))=sec^2 2alpha (d)det(A^(-1)(alpha))=1/(cos2alpha)