PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

The interval of increase of the function f(x) = x − e^x + tan (2π/7) is

The function f(x) = cot⁻¹ x + x increases in the interval

The function f(x) = x^x decreases on the interval

The function f(x) = 2 log (x − 2) − x² + 4x + 1 increases on the interval

If the function f(x) = 2x² − kx + 5 is increasing on [1, 2], then k lies in the interval

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