#### Term 1 Five Mark Model Questions

11th Standard

Reg.No. :
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Time : 02:00:00 Hrs
Total Marks : 50
10 x 5 = 50
1. If A = $\begin{bmatrix}3 & -1 & 1 \\ -15 & 6 & -5\\5 & -2 & 2 \end{bmatrix}$ then, find the Inverse of A.

2. Solve by matrix inversion method: x - y + 2z = 3; 2x +Z = 1; 3x + 2y + z = 4.

3. Find adjoint of $A=\left[ \begin{matrix} 1 & -2 & -3 \\ 0 & 1 & 0 \\ -4 & 1 & 0 \end{matrix} \right]$

4. Resolve into partial fractions for the following:
$\frac { x+2 }{ (x-1)(x+3)^{ 2 } }$

5. By the principle of mathematical induction, prove the following.
an-bn is divisible by a-b, for all $n\in N$ .

6. The profit Rs.y accumulated in thousand in x months is given by y = -x2  +10x - 15. Find the best time to end the project.

7. If $\sin { A } =\frac { 3 }{ 5 }$ 0 < A < $\frac{\pi}{2}$  and $\cos { B } =\frac { -12 }{ 13 }$ , π < B < $\frac{3\pi}{2}$ find the values of the following $\cos (A+B)$

8. If cosec A + sec A = cosec B + sec B, prove that cot$\left( \frac { A+B }{ 2 } \right)$=tanA tanB

9. Examine the following functions for continuity at indicated points
$f(x)=\begin{cases} \frac { { x }^{ 2 }-4 }{ x-4 } ,\quad if\quad x\neq 2 \\ \quad \quad \quad 0,\quad \quad if\quad x=2 \end{cases}at\quad x=2$

10. Draw the graph of the function f(x) = x2 - 5.