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

Find `"dy"/"dx"`, if y = `2^("x"^"x")`.

Evaluate the following.

`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx

Evaluate the following.

`int "x"^3/(16"x"^8 - 25)` dx

Evaluate the following.

`int 1/(sqrt(3"x"^2 - 5))` dx

Solve the following matrix equation for x: `[x 1] [[1,0],[−2,0]]=0`

If `|[2x,5],[8,x]|=|[6,-2],[7,3]|`, write the value of x.

Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`

Find the value of a if `[[a-b,2a+c],[2a-b,3c+d]]=[[-1,5],[0,13]]`

If A =  `([cos alpha, sin alpha],[-sinalpha, cos alpha])` , find α satisfying 0 < α < `pi/r`when `A+A^T=sqrt2I_2` where A^T is transpose of A.

If `A=([2,0,1],[2,1,3],[1,-1,0])` find A² - 5A + 4I and hence find a matrix X such that  A² - 5A + 4I + X = 0

Find the principal value of the following:

`sin^-1(-sqrt3/2)`

Find the principal value of the following:

`sin^-1(cos  (2pi)/3)`

Find the principal value of the following:

`sin^-1((sqrt3-1)/(2sqrt2))`

Find the principal value of the following:

`sin^-1((sqrt3+1)/(2sqrt2))`

Find the principal value of the following:

`sin^-1(cos  (3pi)/4)`

Find the principal value of the following:

`sin^-1(tan  (5pi)/4)`

For the principal value, evaluate of the following:

`cos^-1  1/2 + 2 sin^-1 (1/2)`

For the principal value, evaluate of the following:

`sin^-1(-1/2)+2cos^-1(-sqrt3/2)`

For the principal value, evaluate of the following:

`sin^-1(-sqrt3/2)+cos^-1(sqrt3/2)`

Find the principal value of the following:

`tan^-1(1/sqrt3)`