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

Find the coefficient of x¹⁵ in the expansion of (x – x²)¹⁰.

Find the sixth term of the expansion `(y^(1/2) + x^(1/3))^"n"`, if the binomial coefficient of the third term from the end is 45.

If the coefficient of second, third and fourth terms in the expansion of (1 + x)²ⁿ are in A.P. Show that 2n² – 9n + 7 = 0.

Find the coefficient of x⁴ in the expansion of (1 + x + x² + x³)¹¹.

In the expansion of (x + a)ⁿ if the sum of odd terms is denoted by O and the sum of even term by E. Then prove that O² – E² = (x² – a²)ⁿ 

In the expansion of (x + a)ⁿ if the sum of odd terms is denoted by O and the sum of even term by E. Then prove that 4OE = (x + a)²ⁿ – (x – a)²ⁿ 

The total number of terms in the expansion of (x + a)¹⁰⁰ + (x – a)¹⁰⁰ after simplification is ______.

Given the integers r > 1, n > 2, and coefficients of (3r)^th and (r + 2)^nd terms in the binomial expansion of (1 + x)²ⁿ are equal, then ______.

The two successive terms in the expansion of (1 + x)²⁴ whose coefficients are in the ratio 1:4 are ______.

The number of terms in the expansion of (x + y + z)ⁿ ______.

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.