HSC Arts (English Medium) इयत्ता १२ वी - Maharashtra State Board Important Questions

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

`int_0^(pi/2) log(tanx)  "d"x` =

Evaluate: `int_(pi/6)^(pi/3) cosx  "d"x`

Evaluate: `int_0^1 "e"^x/sqrt("e"^x - 1)  "d"x`

Evaluate: `int_1^3 (cos(logx))/x  "d"x`

Evaluate: `int_0^1 (1/(1 + x^2)) sin^-1 ((2x)/(1 + x^2))  "d"x`

Evaluate: `int_0^pi 1/(3 + 2sinx + cosx)  "d"x`

Evaluate: `int_0^(π/4) sec^4 x  dx`

If `int_2^e [1/logx - 1/(logx)^2].dx = a + b/log2`, then ______.

A body is heated at 110°C and placed in air at 10°C. After 1 hour its temperature is 60°C. How much additional time is required for it to cool to 35°C?

Solve the differential equation (x² + y²)dx- 2xydy = 0

Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`

If the population of a country doubles in 60 years, in how many years will it be triple under
the assumption that the rate of increase in proportional to the number of inhabitants?
[Given : log 2 = 0.6912 and log 3 = 1.0986.]

Find the area of the region bounded by the curves y² = 4x and 4x² + 4y² = 9 with x > = 0.

Determine the order and degree of the following differential equation:

`(dy)/(dx) = (2sin x + 3)/(dy/dx)`

Determine the order and degree of the following differential equation:

`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^2`

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = A cos (log x) + B sin (log x)

Solve the following differential equation:

cos x . cos y dy − sin x . sin y dx = 0

Solve the following differential equation:

`(cos^2y)/x dy + (cos^2x)/y dx` = 0

Solve the following differential equation:

(x² + y²)dx - 2xy dy = 0