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11th Standard English Medium Business Maths Subject Book Back 5 Mark Questions with Solution Part - I

11th Standard

    Reg.No. :
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Business Maths

Time : 00:30:00 Hrs
Total Marks : 50
    10 x 5 = 50
  1. Prove that \(\begin{vmatrix} {1\over a}&bc&b+c\\{1\over b}&ca&c+a\\{1\over c}&ab&a+b \end{vmatrix}=0\)

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

  3. Show that the equation 12x2 - 10xy + 2y2 + 14x - 5y + 2 = 0 represents a pair of straight lines and also find the separate equations of the straight lines.

  4. Prove that:  \(\sin { \theta } \cos { \theta } \left\{ \sin { \left( \frac { \pi }{ 2 } -\theta \right) } \csc { \theta } +\cos { \left( \frac { \pi }{ 2 } -\theta \right) \sec { \theta } } \right\} =1\)

  5. Examine the following functions for continuity at indicated points
    \(f(x)=\left\{\begin{array}{cl} \frac{x^2-4}{x-2}, & \text { if } x \neq 2 \\ 0, & \text { if } x=2 \end{array} \right.\) at x = 2

  6. The cost function of a firm is \(C={1\over3}x^3-3x^2+9x\)Find the level of output (x > 0) when average cost is minimum.

  7. Let u = log\(\frac { { x }^{ 4 }+{ y }^{ 4 } }{ x+y } \). By using Euler’s theorem show that \(x.\frac { \partial u }{ \partial x } +y.\frac { \partial u }{ \partial y } =3\) .

  8. A person buy 20 shares of par value of Rs. 10 of a company which pays 9% dividend at such a price that he gets 12% on his money. Find the market value of a share.

  9. Compute Quartile deviation from the following data

    CI 10-20 20-30 30-40 40-50 50-60 60-70 70-80
    f 12 19 5 10 9 6 6
  10. An examination of 11 applicants for a accountant post was taken by a finance company. The marks obtained by the applicants in the reasoning and aptitude tests are given below.

    Applicant A B C D E F G H I J K
    Reasoning test 20 50 28 25 70 90 76 45 30 19 26
    Aptitude test 30 60 50 40 85 90 56 82 42 31 49

    Calculate Spearman’s rank correlation coefficient from the data given above.

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