Mathematics – Class 12 Practice Test 3

1. If Δ=\(\begin{vmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33} \end{vmatrix}\), then the determinant in terms of cofactors A_ij can be expressed as a₁₁ A₁₁+a₂₁ A₂₁+a₃₁ A₃₁.

2. What is the area of the triangle whose vertices are (0,1), (0,2), (1,5)?

3. Which one among the following is correct if x, y, z are eliminated from, (\(\frac{bx}{y+z}\) = a, \(\frac{cy}{z+x}\) = b, \(\frac{az}{x+y}\) = c)?

4. What is derivative of cotx?

5. What is derivative of xⁿ?

6. Differentiate 8e^-x+2e^x w.r.t x.

7. The given system of equation is inconsistent.

4x+2y=7
6x+3y=9

8. Find the derivative of f(x) = sin(x²).

9. Find the value of k for which (1,2), (3,0), (2,k) are collinear.

10. What is the value of _{r = 1}Σⁿ f(x) if f(r) = \(\begin{vmatrix}2r & x & n(n + 1) \\(6r^2 - 1) & y & n^2 (2n + 3) \\(4r^3 - 2nr) & z & n^3(n + 1) \end {vmatrix}\) where n € N?