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

Show that the function `f(x)=|x-3|,x in R` is continuous but not differentiable at x = 3.

Using the method of integration, find the area of the triangular region whose vertices are (2, -2), (4, 3) and (1, 2).

Find the values of p and q for which

f(x) = `{((1-sin^3x)/(3cos^2x),`

is continuous at x = π/2.

`sin^-1  1/2-2sin^-1  1/sqrt2`

`sin^-1{cos(sin^-1  sqrt3/2)}`

Find the domain of the following function:

`f(x)=sin^-1x^2`

Find the domain of the following function:

`f(x) = sin^-1x + sinx`

Find the domain of the following function:

`f(x)sin^-1sqrt(x^2-1)`

Find the domain of the following function:

`f(x)=sin^-1x+sin^-1 2x`

If `sin^-1 x + sin^-1 y+sin^-1 z+sin^-1 t=2pi` , then find the value of x² + y² + z² + t² 

Evaluate the following:

`tan^-1 1+cos^-1 (-1/2)+sin^-1(-1/2)`

Evaluate the following:

`tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(sin(-pi/2))`

Evaluate the following:

`tan^-1(tan  (5pi)/6)+cos^-1{cos((13pi)/6)}`

Find the set of values of `cosec^-1(sqrt3/2)`

Find the domain of `f(x)=cotx+cot^-1x`

Evaluate the following:

`cot^-1  1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`

Evaluate the following:

`cot^-1{2cos(sin^-1  sqrt3/2)}`

Evaluate the following:

`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`

Evaluate the following:

`tan^-1(-1/sqrt3)+cot^-1(1/sqrt3)+tan^-1(sin(-pi/2))`

Test the continuity of the function on f(x) at the origin: 

\[f\left( x \right) = \begin{cases}\frac{x}{\left| x \right|}, & x \neq 0 \\ 1 , & x = 0\end{cases}\]