Quarterly Model Question Paper

11th Standard

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Business Maths

Time : 02:45:00 Hrs
Total Marks : 90
    20 x 1 = 20
  1. The value of x if \(\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0\) is

    (a)

    0, -1

    (b)

    0, 1

    (c)

    -1, 1

    (d)

    -1, -1

  2. The value of the determinant \({\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}\)is

    (a)

    abc

    (b)

    0

    (c)

    a2b2c2

    (d)

    -abc

  3. The number of Hawkins-Simon conditions for the viability of an input - output analysis is

    (a)

    1

    (b)

    3

    (c)

    4

    (d)

    2

  4. If A and B are non-singular matrices then, which of the following is incorrect?

    (a)

    A2 = Iimplies A-1 = A

    (b)

    I-1 = I

    (c)

    If AX = B, then X = B-1 A

    (d)

    If A is square matrix of order 3 then |adj A|= |A|2

  5. If A = \(\begin{vmatrix}cos \theta & sin \theta \\ -sin \theta&cons\theta \end{vmatrix}\) then |2A| is equal to

    (a)

    4 cos 2 \(\theta\)

    (b)

    4

    (c)

    2

    (d)

    1

  6. If nPr = 720 (nCr), then r is equal to

    (a)

    4

    (b)

    5

    (c)

    6

    (d)

    7

  7. The number of parallelograms that can be formed from the set of four parallel lines intersecting another set of three parallel lines is

    (a)

    18

    (b)

    12

    (c)

    9

    (d)

    6

  8. The total number of 9 digit number which have all different digit is

    (a)

    10!

    (b)

    9!

    (c)

    9\(\times\)9!

    (d)

    10\(\times\)10!

  9. Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is

    (a)

    7!

    (b)

    3!

    (c)

    8!

    (d)

    5!

  10. The angle between the pair of straight lines x2 - 7xy + 4y2 = 0

    (a)

    \(tan^{-1}\left(1\over 3\right)\)

    (b)

    \(tan^{-1}\left(1\over 2\right)\)

    (c)

    \(tan^{-1}\left(\sqrt{33}\over 5\right)\)

    (d)

    \(tan^{-1}\left(5\over\sqrt{33}\right)\)

  11. The locus of the point P which moves such that P is always at equidistance from the line x + 2y+ 7 = 0 is

    (a)

    x+2y+2=0

    (b)

    x - 2y + 1 = 0

    (c)

    2x - y + 2 = 0

    (d)

    3x + y + 1=0

  12. ax2 + 4xy + 2y2 = 0 represents a pair of parallel lines then 'a' is

    (a)

    2

    (b)

    -2

    (c)

    4

    (d)

    -4

  13. The double ordinate passing through the focus is

    (a)

    focal chord

    (b)

    latus rectum

    (c)

    directrix

    (d)

    axis

  14. The value of \(\sin15^o\) is

    (a)

    \(\frac{\sqrt{3}+1}{2\sqrt{2}}\)

    (b)

    \(\frac{\sqrt{3}-1}{2\sqrt{2}}\)

    (c)

    \(\frac{\sqrt3}{\sqrt2}\)

    (d)

    \(\frac{\sqrt3}{2\sqrt2}\)

  15. If p sec 50o=tan 50o then p is

    (a)

    cos 50o

    (b)

    sin 50o

    (c)

    tan 50o

    (d)

    sec 50o

  16. If f(x) = x2 - x + 1, then f (x + 1) is

    (a)

    x2

    (b)

    x

    (c)

    1

    (d)

    x2 + x + 1

  17. The graph of the line y = 3 is

    (a)

    Parallel to x-axis

    (b)

    Parallel to y-axis

    (c)

    Passing through the origin

    (d)

    Perpendicular to x-axis

  18. The graph of y = ex intersect the y-axis at

    (a)

    (0,0)

    (b)

    (1,0)

    (c)

    (0,1)

    (d)

    (1,1)

  19. \(\lim _{ x\rightarrow \infty }{ \frac { \tan { \theta } }{ \theta } } =\)

    (a)

    1

    (b)

    \(\infty\)

    (c)

    \(-\infty\)

    (d)

    \(\theta\)

  20. If y = x and z = \(\frac{1}{x}\) then \(\frac{dy}{dz}=\)

    (a)

    x2

    (b)

    1

    (c)

    -x2

    (d)

    \(-\frac{1}{x^2}\)

  21. 7 x 2 = 14
  22. The technology matrix of an economic system of two industries is \(\begin{bmatrix} 0.50 & 0.25 \\ 0.40 & 0.67 \end{bmatrix}\). Test whether the system is viable as per Hawkins-Simon conditions.

  23. Using the property of determinant, evaluate \(\begin{vmatrix} 6 &5 &12 \\ 2 & 4 &4 \\2 & 1 & 4 \end{vmatrix}.\)

  24. Expand the following by using binomial theorem.\(\left( x+\frac { 1 }{ y } \right) ^{ 7 }\)

  25. Find the angle between the pair of lines represented by the equation 3x2+10xy+8y2+14x+22y+15=0.

  26. Find the value of \(\cos\left(\frac{5\pi}{12}\right)\)

  27. Show that the functions f(x) = 5x - \(\left| x \right| \) is continuous at x = 0

  28. Differentiate \({ x }^{ \frac { 2 }{ 3 } }\) from first principles

  29. 7 x 3 = 21
  30. Solve: 2x+ 5y = 1 and 3x + 2y = 7 using matrix method.

  31. Find the equation of the circle which touches the line x=0, y=0 and x=a.

  32. Differentiate the following with respect to x
    (ax2+bx+c)n

  33. Differentiate the following with respect to x.  \(\frac { { e }^{ x } }{ 1+x } \)

  34. Differentiate the following with respect to x. cos3x

  35. If ey (x + 1) = 1, show that \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } ={ \left( \frac { dy }{ dx } \right) }^{ 2 }\)

  36. Differentiate: \(\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}\)

  37. 7 x 5 = 35
  38. Evaluate:\(\begin{vmatrix} 1&a&a^2-bc\\1&b&b^2-ca\\1&c&c^2-ab \end{vmatrix}\)

  39. If \(A=\left[ \begin{matrix} 1 & tan\quad x \\ -tan\quad x & \quad \quad \quad 1 \end{matrix} \right] \), then show that ATA-1=\(\left[ \begin{matrix} cos\quad 2x & -sin2x \\ sin\quad 2x & cos2x \end{matrix} \right] .\)

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

  41. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

  42. Show that the given lines 3x-4y-13=0, 8x-11y=33 and2x-3y-7=0 are concurrent and find the concurrent point.

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

  44. Differentiate: \(\frac { sinx+cosx }{ sinx-cosx } \)with respect to 'x'

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