Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

If the function f(x) = kx³ − 9x² + 9x + 3 is monotonically increasing in every interval, then

f(x) = 2x − tan⁻¹ x − log \[\left\{ x + \sqrt{x^2 + 1} \right\}\] is monotonically increasing when

Function f(x) = | x | − | x − 1 | is monotonically increasing when

Every invertible function is

In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is

If the function f(x) = cos |x| − 2ax + b increases along the entire number scale, then

The function \[f\left( x \right) = \frac{x}{1 + \left| x \right|}\] is 

The function \[f\left( x \right) = \frac{\lambda \sin x + 2 \cos x}{\sin x + \cos x}\] is increasing, if

Function f(x) = a^x is increasing on R, if

Function f(x) = log_a x is increasing on R, if

Let ϕ(x) = f(x) + f(2a − x) and f"(x) > 0 for all x ∈ [0, a]. Then, ϕ (x)

If the function f(x) = x² − kx + 5 is increasing on [2, 4], then

The function f(x) = −x/2 + sin x defined on [−π/3, π/3] is

If the function f(x) = x³ − 9kx² + 27x + 30 is increasing on R, then

The function f(x) = x⁹ + 3x⁷ + 64 is increasing on

Show that the function f given by f(x) = tan^–1 (sin x + cos x) is decreasing for all \[x \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right) .\]

If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.

The radius r of a right circular cylinder is increasing uniformly at the rate of 0·3 cm/s and its height h is decreasing at the rate of 0·4 cm/s. When r = 3·5 cm and h = 7 cm, find the rate of change of the curved surface area of the cylinder. \[\left[ \text{ Use } \pi = \frac{22}{7} \right]\]

Find the general solution of the differential equation \[x \cos \left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x .\]

Using integration, find the area of the region {(x, y) : x² + y² ≤ 1 ≤ x + y}.