Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

If `|(α, 3, 4),(1, 2, 1),(1, 4, 1)|` = 0, then the value of α is ______.

Find: `int x^4/((x - 1)(x^2 + 1))dx`.

The value of the determinant `|(6, 0, -1),(2, 1, 4),(1, 1, 3)|` is ______.

Find : `int (2x^2 + 3)/(x^2(x^2 + 9))dx; x ≠ 0`.

Differentiate the following function with respect to x: `(log x)^x+x^(logx)`

If `y=log[x+sqrt(x^2+a^2)]` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`

Write the number of vectors of unit length perpendicular to both the vectors `veca=2hati+hatj+2hatk and vecb=hatj+hatk`

Write the integrating factor of the following differential equation:

(1+y²) dx−(tan⁻¹ y−x) dy=0

Find λ and μ if

`(hati+3hatj+9k)xx(3hati-lambdahatj+muk)=0`

If `veca=4hati-hatj+hatk` then find a unit vector parallel to the vector `veca+vecb`

Find the differential equation of the family of lines passing through the origin.

if x^x+x^y+y^x=a^b, then find `dy/dx`.

Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`

Find the differential equation representing the family of curves v=A/r+ B, where A and B are arbitrary constants.

Differentiate the function with respect to x. 

cos x . cos 2x . cos 3x

Differentiate the function with respect to x.

`sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`

Differentiate the function with respect to x.

(log x)^{cos x}

Differentiate the function with respect to x.

x^x − 2^{sin x}

Differentiate the function with respect to x.

(x + 3)² . (x + 4)³ . (x + 5)⁴

Differentiate the function with respect to x.

`(x + 1/x)^x + x^((1+1/x))`