Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

If A and B are coefficient of x n in the expansions of (1 + x)²ⁿ and (1 + x)^2n–1 respectively, then `A/B` equals ______.

The largest coefficient in the expansion of (1 + x)³⁰ is ______.

The ratio of the coefficients of x^p and x^q in the expansion of (1 + x)^{p + q} is ______.

If 25¹⁵ is divided by 13, the reminder is ______.

The sum of the series `sum_(r = 0)^10  ""^20C_r` is `2^19 + (""^20C_10)/2`

The expression 7⁹ + 9⁷ is divisible by 64.

If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of a G.P. Then prove that x^{b – c}. y^{c – a} . z^{a – b} = 1

If x, y, z are positive integers then value of expression (x + y)(y + z)(z + x) is ______.

If A is the arithmetic mean and G₁, G₂ be two geometric means between any two numbers, then prove that 2A = `(G_1^2)/(G_2) + (G_2^2)/(G_1)`

The minimum value of 4^x + 4^1–x, x ∈ R, is ______.

If the equation of the parabola is x² = – 8y, find coordinates of the focus, the equation of the directrix and length of latus rectum.

The area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the ends of its latus rectum is ______.

If the latus rectum of an ellipse with axis along x-axis and centre at origin is 10, distance between foci = length of minor axis, then the equation of the ellipse is ______.

If the eccentricity of an ellipse is `5/8` and the distance between its foci is 10, then find latus rectum of the ellipse.

If the parabola y² = 4ax passes through the point (3, 2), then the length of its latus rectum is ______.

The length of the latus rectum of the ellipse 3x² + y² = 12 is ______.

Evaluate: `lim_(h -> 0) (sqrt(x + h) - sqrt(x))/h`

Evaluate: `lim_(x -> 2) (x^2 - 4)/(sqrt(3x - 2) - sqrt(x + 2))`

Which of the following statements are compound statements 

“2 is both an even number and a prime number”

Which of the following statements are compound statements 

“9 is neither an even number nor a prime number”