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

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

A vector makes an angle of \[\frac{\pi}{4}\] with each of x-axis and y-axis. Find the angle made by it with the z-axis.

A vector \[\vec{r}\] is inclined at equal acute angles to x-axis, y-axis and z-axis.
If |\[\vec{r}\]| = 6 units, find \[\vec{r}\].

A vector \[\vec{r}\] is inclined to -axis at 45° and y-axis at 60°.  If \[|\vec{r}|\] = 8 units, find \[\vec{r}\].

Find the direction cosines of the following vector:

`2hati + 2hatj - hatk`

Find the direction cosines of the following vectors:
\[6 \hat{i} - 2 \hat{j} - 3 \hat{k}\]