Science (English Medium) Class 11 - CBSE Question Bank Solutions

Find the position vector of a point A in space such that `vec(OA)` is inclined at 60º to OX and at 45° to OY and `|vec(OA)|` = 10 units

Find the vector equation of the line which is parallel to the vector `3hati - 2hatj + 6hatk` and which passes through the point (1 ,–2, 3).

Show that the lines `(x - 1)/2 = (y - 2)/3 = (z - 3)/4` and `(x - 4)/5 = (y - 1)/2` = z intersect.. Also, find their point of intersection.

`vec(AB) = 3hati - hatj + hatk` and `vec(CD) = - 3hati + 2hatj + 4hatk` are two vectors. The position vectors of the points A and C are `6hati + 7hatj + 4hatk` and `-9hatj + 2hatk`, respectively. Find the position vector of a point P on the line AB and a point Q on the line CD such that `vec(PQ)` is perpendicular to `vec(AB)` and `vec(CD)` both.

The reflection of the point (α, β, γ) in the xy-plane is ______.

A plane passes through the points (2, 0, 0) (0, 3, 0) and (0, 0, 4). The equation of plane is ______.

The equation of a line, which is parallel to `2hati + hatj + 3hatk` and which passes through the point (5, –2, 4), is `(x - 5)/2 = (y + 2)/(-1) = (z - 4)/3`.

Prove by direct method that for any integer ‘n’, n³ – n is always even.

Prove by direct method that for any real numbers x, y if x = y, then x² = y².

Identify whether the following set is finite or infinite.

The set of months of a year

Identify whether the following set is finite or infinite.

{1, 2, 3, ...}

Identify whether the following set is finite or infinite.

{1, 2, 3, ... 99, 100}

Identify whether the following set is finite or infinite.

The set of positive integers greater than 100.

Identify whether the following set is finite or infinite.

The set of prime numbers less than 99.

State whether the following set is finite or infinite:

The set of lines which are parallel to the x-axis.

State whether the following set is finite or infinite:

The set of letters in the English alphabet.

State whether the following set is finite or infinite:

The set of numbers which are multiple of 5.

State whether the following set is finite or infinite:

The set of animals living on the earth.

State whether the following set is finite or infinite:

The set of circles passing through the origin (0, 0).

Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = Φ.