HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

If A = `[(1, -1, 2),(3, 0, -2),(1, 0, 3)]`, verify that A(adj A) = (adj A)A

Solve the following system of equations by using inversion method

x + y = 1, y + z = `5/3`, z + x = `4/3`

The cost of 4 dozen pencils, 3 dozen pens and 2 dozen erasers is ₹ 60. The cost of 2 dozen pencils, 4 dozen pens and 6 dozen erasers is ₹ 90. Whereas the cost of 6 dozen pencils, 2 dozen pens and 3 dozen erasers is ₹ 70. Find the cost of each item per dozen by using matrices

Find the distance between the parallel lines `x/2 = y/(-1) = z/2` and `(x - 1)/2 = (y - 1)/(-1) = (z - 1)/2`

`int (sinx)/(1 + sin x)  "d"x`

`int 1/(4x + 5x^(-11))  "d"x`

`int (sin(x - "a"))/(cos (x + "b"))  "d"x`

`int 1/sqrt(2x^2 - 5)  "d"x`

`int ["cosec"(logx)][1 - cot(logx)]  "d"x`

`int (cos2x)/(sin^2x cos^2x)  "d"x`

`int sin4x cos3x  "d"x`

`int ("e"^xlog(sin"e"^x))/(tan"e"^x)  "d"x`

`int sqrt(tanx) + sqrt(cotx)  "d"x`

`int_0^(x/4) sqrt(1 + sin 2x)  "d"x` =

If `int_0^1 ("d"x)/(sqrt(1 + x) - sqrt(x)) = "k"/3`, then k is equal to ______.

`int_(pi/5)^((3pi)/10)  sinx/(sinx + cosx)  "d"x` =

`int_0^1 (x^2 - 2)/(x^2 + 1)  "d"x` =

Let I₁ = `int_"e"^("e"^2)  1/logx  "d"x` and I₂ = `int_1^2 ("e"^x)/x  "d"x` then 

`int_0^4 1/sqrt(4x - x^2)  "d"x` =

`int_0^(pi/2) log(tanx)  "d"x` =