**Find the minors and cofactors of all the elements of the following determinant.**

`|(5,20),(0, -1)|`

Concept: Determinants

**Find the minors and cofactors of all the elements of the following determinant.**

`|(1,-3,2),(4,-1,2),(3,5,2)|`

Concept: Determinants

Evaluate `|(3,-2,4),(2,0,1),(1,2,3)|`

Concept: Determinants

Solve: `|(2,x,3),(4,1,6),(1,2,7)|` = 0

Concept: Determinants

Find |AB| if A = `[(3,-1),(2,1)]` and B = `[(3,0),(1,-2)]`

Concept: Determinants

Solve: `|(7,4,11),(-3,5,x),(-x,3,1)|` = 0

Concept: Determinants

Evaluate: `|(1,a,a^2 - bc),(1,b,b^2 - ca),(1,c,c^2 - ab)|`

Concept: Determinants

Prove that `|(1/a,bc,b+c),(1/b,ca,c+a),(1/c,ab,a+b)|` = 0

Concept: Determinants

Prove that `|(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)| = 4a^2b^2c^2`

Concept: Determinants

Find the amount of an ordinary annuity of ₹ 3,200 per annum for 12 years at the rate of interest of 10% per year. [(1.1)^{12} = 3.1384]

Concept: Annuities

If the payment of ₹ 2,000 is made at the end of every quarter for 10 years at the rate of 8% per year, then find the amount of annuity. [(1.02)^{40} = 2.2080]

Concept: Annuities

Find the amount of an ordinary annuity of 12 monthly payments of ₹ 1,500 that earns interest at 12% per annum compounded monthly. [(1.01)^{12} = 1.1262]

Concept: Annuities

The value of x if `|(0,1,0),(x,2,x),(1,3,x)|` = 0 is

Concept: Determinants

The value of `|(2x + y,x,y),(2y+z,y,z),(2z+x,z,x)|` is

Concept: Determinants

The cofactor of –7 in the determinant `|(2,-3,5),(6,0,4),(1,5,-7)|` is

Concept: Determinants

A bank pays 8% per annum interest compounded quarterly. Find the equal deposits to be made at the end of each quarter for 10 years to have ₹ 30,200? [(1.02)^{40} = 2.2080]

Concept: Annuities

If `Delta = |(1,2,3),(3,1,2),(2,3,1)|` then `|(3,1,2),(1,2,3),(2,3,1)|` is

Concept: Determinants

A person deposits ₹ 2,000 at the end of every month from his salary towards his contributory pension scheme. The same amount is credited by his employer also. If 8% rate of compound interest is paid, then find the maturity amount at end of 20 years of service. [(1.0067)^{240} = 4.9661]

Concept: Annuities

Find the present value of ₹ 2,000 per annum for 14 years at the rate of interest of 10% per annum. If the payments are made at the end of each payment period. [(1.1)^{–14} = 0.2632]

Concept: Annuities

Find the present value of an annuity of ₹ 900 payable at the end of 6^{th} month for 6 years. The money compounded at 8% per annum. [(1.04)^{–12} = 0.6252]

Concept: Annuities