Let `P=[(2alpha),(5),(-3alpha^(2))] and Q=[(2l,-m,5n)]` are two matrices, where `l, m, n, alpha in R`, then the value of determinant PQ is equal to

Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[q_(ij)] is a matrix such that PQ=kl, where k in RR, k != 0 and l is the identity matrix of order 3. If q_23=-k/8 and det(Q)=k^2/2, then

Let log_(3)N=alpha_(1)+beta_(1) log_(5)N=alpha_(2)+beta_(2) log_(7)N=alpha_(3)+beta_(3) where alpha_(1), alpha_(2) and alpha_(3) are integers and beta_(1), beta_(2), beta_(3) in [0,1) . Q. Largest integral value of N if alpha_(1)=5, alpha_(2)=3 and alpha_(3)=2 .

Let log_(3)N=alpha_(1)+beta_(1) log_(5)N=alpha_(2)+beta_(2) log_(7)N=alpha_(3)+beta_(3) where alpha_(1), alpha_(2) and alpha_(3) are integers and beta_(1), beta_(2), beta_(3) in [0,1) . Q. Number of integral values of N if alpha_(1)=4 and alpha_(2)=2 :

If 8l^2+35 m^2+36 l m+6l+12 m+1=0 and the line l x+m y+1=0 touches a fixed circle whose centre is (alpha,beta) and radius is ' r^(prime), then the value of (alpha+beta-r) is equal to

If |(a,b,c),(l,m,n),(p,q,r)|=2 , then what is the value of the determinant |(6a,3b,15c),(2l,m,5n),(2p,q,5r)| = ?

Let A=[(5,5alpha,alpha),(0,alpha,5alpha),(0,0,5)] . If |A|^2=25 , then |alpha| is equal to :

If 4 n alpha = pi , then the numerical value of tan alpha tan 2 alpha tan 3 alpha….tan (2n - 1) alpha is equal to