HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the graphical solution for the system of linear inequation 2x + y ≤ 2, x − y ≤ 1

Find the feasible solution of linear inequation 2x + 3y ≤ 12, 2x + y ≤ 8, x ≥ 0, y ≥ 0 by graphically

Find the solution set of inequalities 0 ≤ x ≤ 5, 0 ≤ 2y ≤ 7

If θ is the acute angle between the lines given by ax² + 2hxy + by² = 0 then prove that tan θ = `|(2sqrt("h"^2) - "ab")/("a" + "b")|`. Hence find acute angle between the lines 2x² + 7xy + 3y² = 0 

If the angle between the lines represented by ax² + 2hxy + by² = 0 is equal to the angle between the lines 2x² − 5xy + 3y² = 0, then show that 100(h² − ab) = (a + b)²

Draw the graph of inequalities x ≤ 6, y −2 ≤ 0, x ≥ 0, y ≥ 0 and indicate the feasible region

`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