Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Let f(x) = x³ + ax² + bx + 5 sin²x be an increasing function on the set R. Then, a and b satisfy.

The function \[f\left( x \right) = \log_e \left( x^3 + \sqrt{x^6 + 1} \right)\] is of the following types:

If the function f(x) = 2 tan x + (2a + 1) log_e | sec x | + (a − 2) x is increasing on R, then

Let \[f\left( x \right) = \tan^{- 1} \left( g\left( x \right) \right),\],where g (x) is monotonically increasing for 0 < x < \[\frac{\pi}{2} .\] Then, f(x) is

Let f(x) = x³ − 6x² + 15x + 3. Then,

The function f(x) = x² e^−x is monotonic increasing when

Function f(x) = cos x − 2 λ x is monotonic decreasing when

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

Function f(x) = x³ − 27x + 5 is monotonically increasing when ______.

Function f(x) = 2x³ − 9x² + 12x + 29 is monotonically decreasing when

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