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

The coefficient of a^–6b⁴ in the expansion of `(1/a - (2b)/3)^10` is ______.

Number of terms in the expansion of (a + b)ⁿ where n ∈ N is one less than the power n.

P is a point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5, then its y co-ordinate is ______.

The equations of x-axis in space are ______.

The points (1, 2, 3), (–2, 3, 4) and (7, 0, 1) are collinear.

The vector equation of the line passing through the points (3, 5, 4) and (5, 8, 11) is.

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.