HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Evaluate :`intxlogxdx`

The probability that a certain kind of component will survive a check test is 0.6. Find the probability that exactly two of the next four components tested will survive.

Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`

Write down the following statements in symbolic form :

(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls

The surface area of a spherical balloon is increasing at the rate of 2cm²/sec. At what rate the volume of the balloon is increasing when radius of the balloon is 6 cm?

Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p

In any ΔABC, with usual notations, prove that b² = c² + a² – 2ca cos B.

Find : `int((2x-5)e^(2x))/(2x-3)^3dx`

Find: `int(x+3)sqrt(3-4x-x^2dx)`

If y = e^ax. cos bx, then prove that

`(d^2y)/(dx^2) - 2ady/dx + (a^2 + b^2)y` = 0

Find `intsqrtx/sqrt(a^3-x^3)dx`

In Δ ABC, if a = 13, b = 14 and c = 15, then sin (A/2)= _______.

(A) `1/5`

(B) `sqrt(1/5)`

(C) `4/5`

(D) `2/5`

The angles of the ΔABC are in A.P. and b:c=`sqrt3:sqrt2` then find`angleA,angleB,angleC`

Evaluate: `int sqrt(tanx)/(sinxcosx) dx`

If in ∆ABC with usual notations a = 18, b = 24, c = 30 then sin A/2 is equal to

(A) `1/sqrt5`

(B) `1/sqrt10`

(C) `1/sqrt15`

(D) `1/(2sqrt5)`

Evaluate : `∫1/(3+2sinx+cosx)dx`

With usual notations, in ΔABC, prove that a(b cos C − c cos B) = b² − c²

Find the co-ordinates of the point, which divides the line segment joining the points A(2, − 6, 8) and B(− 1, 3, − 4) externally in the ratio 1 : 3.

Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p

Evaluate: `int 1/(x(x-1)) dx`