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

If (1 – x + x²)ⁿ = a₀ + a₁ x + a₂ x² + ... + a_2n x²ⁿ , then a₀ + a₂ + a₄ + ... + a_2n equals ______.

The coefficient of x^p and x^q (p and q are positive integers) in the expansion of (1 + x)^{p + q} are ______.

The number of terms in the expansion of (a + b + c)ⁿ, where n ∈ N is ______.

If z = `sqrt(3)/2 + i^5/2 + sqrt(3)/2 - i^5/2`, then ______.

Find the coefficient of x in the expansion of (1 – 3x + 7x²)(1 – x)¹⁶.

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.