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

Let f and g be two real functions given by
f = {(0, 1), (2, 0), (3, – 4), (4, 2), (5, 1)}
g = {(1, 0), (2, 2), (3, – 1), (4, 4), (5, 3)}
then the domain of f . g is given by ______.

Let f = {(2, 4), (5, 6), (8, – 1), (10, – 3)}
g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, 5)}
be two real functions. Then Match the following :

Solve the equation sin θ + sin 3θ + sin 5θ = 0

Solve 2 tan²x + sec²x = 2 for 0 ≤ x ≤ 2π.

Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`

If sin θ and cos θ are the roots of the equation ax² – bx + c = 0, then a, b and c satisfy the relation ______.

If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a² + b² = m² + n² 

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`