Science (English Medium) Class 12 - CBSE Question Bank Solutions

If `"y = tan"^-1 [("sin x + cos x")/("cos x - sin x")], "then"  "dy"/"dx"` is equal to ____________.

If f(x) = `"log"_("x"^2) ("log x")`, then f(e) is ____________.

Find: `int x^2/((x^2 + 1)(3x^2 + 4))dx`

Evaluate: `int_-2^1 sqrt(5 - 4x - x^2)dx`

If | A | = | kA |, where A is a square matrix of order 2, then sum of all possible values of k is ______.

If f(α) = `[(cosα, -sinα, 0),(sinα, cosα, 0),(0, 0, 1)]`, prove that f(α) . f(– β) = f(α – β).

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.