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

Integrate the following w.r.t. x : `(2log x + 3)/(x(3 log x + 2)[(logx)^2 + 1]`

Choose the correct options from the given alternatives :

If `int tan^3x*sec^3x*dx = (1/m)sec^mx - (1/n)sec^n x + c, "then" (m, n)` =

Integrate the following with respect to the respective variable : `(6x + 5)^(3/2)`

Integrate the following w.r.t. x: `(2x^2 - 1)/(x^4 + 9x^2 + 20)`

Integrate the following w.r.t. x: `(x^2 + 3)/((x^2 - 1)(x^2 - 2)`

Integrate the following with respect to the respective variable : `(cos 7x - cos8x)/(1 + 2 cos 5x)`

Integrate the following with respect to the respective variable : `cot^-1 ((1 + sinx)/cosx)`

Integrate the following w.r.t.x : `x^2/sqrt(1 - x^6)`

Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`

Integrate the following w.r.t.x : `(1)/(2cosx + 3sinx)`

Integrate the following w.r.t.x:

`x^2/((x - 1)(3x - 1)(3x - 2)`

Integrate the following w.r.t.x : `(1)/(sinx + sin2x)`

Integrate the following w.r.t.x :  `sec^2x sqrt(7 + 2 tan x - tan^2 x)`

Integrate the following w.r.t.x: `(x + 5)/(x^3 + 3x^2 - x - 3)`

Integrate the following w.r.t.x : `sqrt(tanx)/(sinx*cosx)`

Prepare truth tables for the following statement pattern.

p → (~ p ∨ q)

Prepare truth tables for the following statement pattern.

(~ p ∨ q) ∧ (~ p ∨ ~ q)

Prepare truth tables for the following statement pattern.

(p ∧ r) → (p ∨ ~ q)

Prepare truth table for (p ˄ q) ˅ ~ r

(p ∧ q) ∨ ~ r

Examine whether the following statement pattern is a tautology, a contradiction or a contingency.

q ∨ [~ (p ∧ q)]