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

If f and g are real functions defined by f(x) = x² + 7 and g(x) = 3x + 5, find the following:

f(t) – f(– 2)

If f and g are real functions defined by f(x) = x² + 7 and g(x) = 3x + 5, find the following:

`(f(t) - f(5))/(t - 5)`, if t ≠ 5

Let f and g be real functions defined by f(x) = 2x + 1 and g(x) = 4x – 7. For what real numbers x, f(x) = g(x)?

Let f and g be real functions defined by f(x) = 2x + 1 and g(x) = 4x – 7. For what real numbers x, f(x) < g(x)?

If f and g are two real valued functions defined as f(x) = 2x + 1, g(x) = x² + 1, then find fg

If f and g are two real valued functions defined as f(x) = 2x + 1, g(x) = x² + 1, then find `f/g`

Find the values of x for which the functions f(x) = 3x² – 1 and g(x) = 3 + x are equal.

Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? Justify. If this is described by the relation, g(x) = αx + β, then what values should be assigned to α and β?

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 ______.