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

If 2sin²θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.

Find the general solution of the equation 5cos²θ + 7sin²θ – 6 = 0

Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x

The minimum value of 3cosx + 4sinx + 8 is ______.

Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.

In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.

The coefficient of xⁿ in the expansion of (1 + x)²ⁿ and (1 + x)^2n–1 are in the ratio ______.

If the coefficients of 2^nd, 3^rd and the 4^th terms in the expansion of (1 + x)ⁿ are in A.P., then value of n is ______.

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 ______.