Term 1 Five Mark Model Questions

11th Standard

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Business Maths

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 \(\sin A=\frac35\) where \(0<A<\frac { \pi }{ 2 } \) and cos \(B=\frac { -12 }{ 13 } ,\pi <A<\frac { 3\pi }{ 2 } \)find the value of  
    \(\cos (A+B)\)

  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.

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