Science (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

If the sum of n terms of an A.P. is given by S_n = 3n + 2n², then the common difference of the A.P. is ______.

If 9 times the 9^th term of an A.P. is equal to 13 times the 13^th term, then the 22^nd term of the A.P. is ______.

If in an A.P., S_n = qn² and S_m = qm², where S_r denotes the sum of r terms of the A.P., then Sq equals ______.

Let S_n denote the sum of the first n terms of an A.P. If S_2n = 3S_n then S_3n: S_n is equal to ______.

The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.

Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.

If the sum of n terms of a sequence is quadratic expression then it always represents an A.P

Find the distance of the point whose position vector is `(2hati + hatj - hatk)` from the plane `vecr * (hati - 2hatj + 4hatk)` = 9

Find the distance of the point (– 2, 4, – 5) from the line `(x + 3)/3 = (y - 4)/5 = (z + 8)/6`

Find the distance of the point (–1, –5, – 10) from the point of intersection of the line `vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk)` and the plane `vecr * (hati - hatj + hatk)` = 5.

The distance of a point P(a, b, c) from x-axis is ______.

Find the angle between the lines `vecr = 3hati - 2hatj + 6hatk + lambda(2hati + hatj + 2hatk)` and `vecr = (2hatj - 5hatk) + mu(6hati + 3hatj + 2hatk)`

Prove that the line through A(0, –1, –1) and B(4, 5, 1) intersects the line through C(3, 9, 4) and D(– 4, 4, 4).

Find the equation of a plane which is at a distance `3sqrt(3)` units from origin and the normal to which is equally inclined to coordinate axis

Find the distance of a point (2, 4, –1) from the line `(x + 5)/1 = (y + 3)/4 = (z - 6)/(-9)`

Find the shortest distance between the lines given by `vecr = (8 + 3lambdahati - (9 + 16lambda)hatj + (10 + 7lambda)hatk` and `vecr = 15hati + 29hatj + 5hatk + mu(3hati + 8hatj - 5hatk)`

Find the equation of the plane through the intersection of the planes `vecr * (hati + 3hatj) - 6` = 0 and `vecr * (3hati + hatj + 4hatk)` = 0, whose perpendicular distance from origin is unity.

Distance of the point (α, β, γ) from y-axis is ______.

The distance of the plane `vecr * (2/4 hati + 3/7 hatj - 6/7hatk)` = 1 from the origin is ______.

Find the mean deviation about the mean of the following data: