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

Two events, A and B, will be independent if ______.

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability `1/2`).

Find the angle between the following pair of lines:

`vecr = 2hati - 5hatj + hatk + lambda(3hati - 2hatj + 6hatk) and vecr = 7hati - 6hatk + mu(hati + 2hatj + 2hatk)`

Find the angle between the following pair of lines:

`vecr = 3hati + hatj - 2hatk + lambda(hati - hatj - 2hatk) and vecr = 2hati - hatj -56hatk + mu(3hati - 5hatj - 4hatk)`

Find the angle between the following pairs of lines: 

`(x-2)/2 = (y-1)/5 = (z+3)/(-3)` and `(x+2)/(-1) = (y-4)/8 = (z -5)/4`

Find the angle between the following pairs of lines:

`x/y = y/2 = z/1` and `(x-5)/4 = (y-2)/1 = (z - 3)/8`

Find the values of p so the line `(1-x)/3 = (7y-14)/2p = (z-3)/2` and `(7-7x)/(3p) = (y -5)/1 = (6-z)/5` are at right angles.

Find the angle between the lines whose direction ratios are a, b, c and b − c, c − a, a − b.

Differentiate the function with respect to x.

sin (x² + 5)

Differentiate the function with respect to x.

cos (sin x)

Differentiate the function with respect to x.

sin (ax + b)

Differentiate the function with respect to x.

`sec(tan (sqrtx))`

Differentiate the function with respect to x.

`(sin (ax + b))/cos (cx + d)`

Differentiate the function with respect to x. 

cos x³ . sin² (x⁵)

Differentiate the function with respect to x. 

`2sqrt(cot(x^2))`

Differentiate the function with respect to x.

`cos (sqrtx)`

Prove that the function f given by f(x) = |x − 1|, x ∈ R is not differentiable at x = 1.

Differentiate the function with respect to x:

(3x² – 9x + 5)⁹

Differentiate the function with respect to x:

sin³ x + cos⁶ x

Differentiate the function with respect to x:

`(5x)^(3cos 2x)`