Prove that: `|[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1`

Without expanding the following determinant, show that : |[[3p+q, 2p, p],[4p+3q, 3p, 3p],[5p+6q,4p,6p]]|=p^3

Prove that |[1,p,p^2-qr],[1,q,q^2-rp],[1,r,r^2-pq]|= 0

Show that: |[p-q-r,2p,2p],[2q,q-r-p,2q],[2r,2r,r-p-q]|=(p+q+r)^3

Using the properties of determinant, show that : |[1,p+q,p^2+q^2],[1,q+r,q^2+r^2],[1,r+p,r^2+p^2]| = (p-q)(q-r)(r-p)

The value of |[[1,p,q+r],[1,q,r+p],[1,r,p+q]]| is

Subtract 3pq (p – q) from 2pq (p + q).

Subtract: 4pq – 5q^2 – 3p^2 from 5p^2 + 3q^2 – pq

Write the name & symbol of the element with electronic configuration 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6

If tan alpha= p/q , where alpha=6 beta, alpha being an acute angle, prove that : 1/2 {p cosec 2 beta- qsec 2 beta} = sqrt(p^2 +q^2) .

Find the product: p xx q^2 xx p^3 xx p ^4