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

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.

Probability that A speaks truth is `4/5` . A coin is tossed. A reports that a head appears. The probability that actually there was head is ______.

If A and B are two events such that A ⊂ B and P (B) ≠ 0, then which of the following is correct?

Find the shortest distance between the lines: 

`vecr = (hati+2hatj+hatk) + lambda(hati-hatj+hatk)` and `vecr = 2hati - hatj - hatk + mu(2hati + hatj + 2hatk)`

Find the shortest distance between the lines.

`(x + 1)/7 = (y + 1)/(- 6) = (z + 1)/1` and `(x - 3)/1 = (y - 5)/(- 2) = (z - 7)/1`.

Find the shortest distance between the lines whose vector equations are `vecr = (hati + 2hatj + 3hatk) + lambda(hati - 3hatj + 2hatk)` and `vecr = 4hati + 5hatj + 6hatk + mu(2hati + 3hatj + hatk)`.

Find the shortest distance between the lines whose vector equations are `vecr = (1-t)hati + (t - 2)hatj + (3 -2t)hatk` and `vecr = (s+1)hati + (2s + 1)hatk`.

Find the shortest distance between lines `vecr = 6hati + 2hatj + 2hatk + lambda(hati - 2hatj + 2hatk)` and `vecr =-4hati - hatk + mu(3hati - 2hatj - 2hatk)`.

Find the unit vector in the direction of the vector `veca = hati + hatj + 2hatk`.

Find the unit vector in the direction of vector `vec(PQ)`, where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle α is one-third that of the cone and the greatest volume of cylinder is `4/27 pih^3` tan²α.

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of ______.

Integrate the functions:

`(2x)/(1 + x^2)`

Integrate the functions:

`(log x)^2/x`

Integrate the functions:

`1/(x + x log x)`

Integrate the functions:

sin x ⋅ sin (cos x)

Integrate the functions:

sin (ax + b) cos (ax + b)

Integrate the functions:

`sqrt(ax + b)`

Integrate the functions:

`xsqrt(x + 2)`

Integrate the functions:

`xsqrt(1+ 2x^2)`