Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

Evaluate: `int_(-1)^3 |x^3 - x|dx`

Evaluate: `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`

Find the coordinates of points on line `x/1 = (y - 1)/2 = (z + 1)/2` which are at a distance of `sqrt(11)` units from origin.

Evaluate `int_0^(π//4) log (1 + tanx)dx`.

Evaluate `int_-1^1 |x^4 - x|dx`.

If the angle between `veca` and `vecb` is `π/3` and `|veca xx vecb| = 3sqrt(3)`, then the value of `veca.vecb` is ______.

If `int_0^(2π) cos^2 x  dx = k int_0^(π/2) cos^2 x  dx`, then the value of k is ______.

If `|veca xx vecb| = sqrt(3)` and `veca.vecb` = – 3, then angle between `veca` and `vecb` is ______.

`int_-1^1 |x - 2|/(x - 2) dx`, x ≠ 2 is equal to ______.

Assertion (A): `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x))dx` = 3.

Reason (R): `int_a^b f(x) dx = int_a^b f(a + b - x) dx`.

Find the area of a parallelogram whose adjacent sides are determined by the vectors `veca = hati - hatj + 3hatk` and `vecb = 2hati - 7hatj + hatk`.

The value of `int_0^(π/4) (sin 2x)dx` is ______.

Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.

Evaluate: `int_0^π x/(1 + sinx)dx`.

If `veca = hati + hatj + hatk` and `vecb = hati + 2hatj + 3hatk` then find a unit vector perpendicular to both `veca + vecb` and `veca - vecb`.

For any integer n, the value of `int_-π^π e^(cos^2x) sin^3 (2n + 1)x  dx` is ______.

Evaluate : `int_-1^1 log ((2 - x)/(2 + x))dx`.

Evaluate: `int_0^(π/4) log(1 + tanx)dx`.

Find the projection of the vector `hati+3hatj+7hatk`  on the vector `2hati-3hatj+6hatk`

If `veca ` and `vecb` are two unit vectors such that `veca+vecb` is also a  unit vector, then find the angle between `veca` and `vecb`