Term 1 Model Question Paper

11th Standard

    Reg.No. :
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Business Maths

Time : 02:00:00 Hrs
Total Marks : 60
    5 x 1 = 5
  1. The inventor of input-output analysis is

    (a)

    Sir Francis Galton

    (b)

    Fisher

    (c)

    Prof. Wassily W. Leontief

    (d)

    Arthur Caylay

  2. The possible out comes when a coin is tossed five times

    (a)

    25

    (b)

    52

    (c)

    10

    (d)

    \(\frac { 5 }{ 2 } \)

  3. The slope of the line 7x + 5y - 8 = 0 is

    (a)

    7/5

    (b)

    -7/5

    (c)

    5/7

    (d)

    -9/7

  4. The degree measure of \(\frac{\pi}{8}\) is

    (a)

    20o60'

    (b)

    22o30'

    (c)

    20o60'

    (d)

    20o30'

  5. The graph of y = 2x2 is passing through

    (a)

    (0,0)

    (b)

    (2,1)

    (c)

    (2,0)

    (d)

    (0,2)

  6. 7 x 2 = 14
  7. Find the minors and cofactors of all the elements of the following determinants
    \(\begin{vmatrix}5&20\\ 0&-1 \end{vmatrix}\)

  8. Expand the following by using binomial theorem. (2a - 3b)4

  9. Find the rank of the word 'CHAT' in dictionary.

  10. Find the center and radius of the circle 5x2 + 5y2 +4x - 8y - 16 = 0

  11. Prove that \(2\tan^{-1}(x)=\sin^{-1}\left(\frac{2x}{1+x^2}\right)\)

  12. If \(f(x)={ x }^{ 3 }-\frac { 1 }{ { x }^{ 3 } } \) then show that \(f(x)+f\left( \frac { 1 }{ x } \right) =0\)

  13. Evaluate: \(\underset { x\rightarrow 2 }{ lim } \frac { { x }^{ 2 }-4x+6 }{ x+2 } \)

  14. 7 x 3 = 21
  15. Solve: \(\begin{vmatrix} x & 2 & -1 \\ 2 & 5 & x \\ -1 & 2 & x \end{vmatrix}=0.\)

  16. Find the 5th term in the expansion of (x - 2y)13.

  17. Find the value of 'a' for which the straight lines 3x +4y = 13; 2x -7y = -1  and ax - y -14 = 0 are concurrent

  18. Prove that \(2\sin^2\frac{3\pi}{4}+2\cos^2\frac{\pi}{4}+2\sec^2\frac{\pi}{4}=10\)

  19. Prove that: \((cos\alpha -cos\beta )^{ 2 }+(sin\alpha -sin\beta )^{ 2 }=4sin^{ 2 }\left( \frac { \alpha -\beta }{ 2 } \right) \)

  20. Evaluate the following \(\lim _{ x\rightarrow 2 }{ \frac { { x }^{ 3 }+2 }{ x+1 } } \)

  21. Differentiate \(\frac{x^2}{1+x^2}\) with respect to x2

  22. 4 x 5 = 20
  23. If A = \(\begin{bmatrix}3 & -1 & 1 \\ -15 & 6 & -5\\5 & -2 & 2 \end{bmatrix}\) then, find the Inverse of A.

  24. By the principle of mathematical induction, prove the following.
    13+23+33+.......+n3=\(\frac { { n }^{ 2 }(n+1)^{ 2 } }{ 4 } \) for all \(n\in N\).

  25. How many numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3?

  26. Prove that \(\tan { \left( \pi +x \right) } \cot { \left( x-\pi \right) } -\left( \cos { \left( 2\pi -x \right) } \cos { \left( 2\pi +x \right) } \right) =\sin ^{ 2 }{ x } \)

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