Mathematics – Class 12 Practice Test 1

1. What is the value of 2 tan^-1⁡x in terms of sin^-1⁡?

2. The function f:R→R defined by f(x)=5x+9 is invertible.

3. What is the principle value of \(sec^{-1}⁡(\frac{2}{\sqrt{3}})\).

4. What will be the value of x + y + z if cos^-1 x + cos^-1 y + cos^-1 z = 3π?

5. Find the value of a,b,c,d if \(\begin{bmatrix}a+b&c\\a-b&2c+d\end{bmatrix}\)=\(\begin{bmatrix}3&2\\1&6\end{bmatrix}\).

6. What is sec^-1⁡x in terms of tan^-1⁡?

7. \(sin^{-1}⁡x\) is same as \((sin⁡x)^{-1}\).

8. Find a,b,c,d if \(\begin{bmatrix}a&b+c\\c+d&b\end{bmatrix}\)=\(\begin{bmatrix}3&2\\3&-1\end{bmatrix}\) are equal matrices.

9. If the order of the matrix is m×n, then how many elements will there be in the matrix?

10. Let f:R₊→[9,∞) given by f(x)=x²+9. Find the inverse of f.