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All Chapter 1 mark Impatant Question

11th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    50 x 1 = 50
  1. If A is a square matrix of order 3, then |kA| is

    (a)

    k|A|

    (b)

    -k|A|

    (c)

    k3|A|

    (d)

    -k3|A|

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

    (a)

    1

    (b)

    3

    (c)

    4

    (d)

    2

  3. The value of \(\begin{vmatrix} x & x^2 & -yz & 1 \\ y & y^2 & -zx & 1 \\ z & z^2 & -xy &1 \end{vmatrix}\) is

    (a)

    1

    (b)

    0

    (c)

    -1

    (d)

    -xyz

  4. If \(\begin{vmatrix} x & 2 \\ 8 &5 \end{vmatrix}=0\) then the value of x is

    (a)

    \({{-5}\over{6}}\)

    (b)

    \({{5}\over{6}}\)

    (c)

    \({{-16}\over{5}}\)

    (d)

    \({{16}\over{5}}\)

  5. If any three-rows or columns of a determinant are identical, then the value of the determinant is

    (a)

    0

    (b)

    2

    (c)

    1

    (d)

    3

  6. If nC3 = nC2, then the value of nC4 is

    (a)

    2

    (b)

    3

    (c)

    4

    (d)

    5

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

    (a)

    4

    (b)

    5

    (c)

    6

    (d)

    7

  8. The last term in the expansion of (3 +\(\sqrt{2}\) )8 is

    (a)

    81

    (b)

    16

    (c)

    8\(\sqrt{2}\)

    (d)

    27\(\sqrt{3}\)

  9. If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to 

    (a)

    9

    (b)

    11

    (c)

    5

    (d)

    7

  10. 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!

  11. If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is

    (a)

    (-1, 1)

    (b)

    (1,1)

    (c)

    (1, -1 )

    (d)

    (-1, -1)

  12. The x - intercept of the straight line 3x + 2y - 1 = 0 is

    (a)

    3

    (b)

    2

    (c)

    1/3

    (d)

    1/2

  13. The length of the tangent from (4,5) to the  circle x2 +y2 = 16 is

    (a)

    4

    (b)

    5

    (c)

    16

    (d)

    25

  14. The centre of the circle x2 + y - 2x + 2y - 9 = 0 is

    (a)

    (1,1)

    (b)

    (-1,-1)

    (c)

    (-1,1)

    (d)

    (1, -1)

  15. The double ordinate passing through the focus is

    (a)

    focal chord

    (b)

    latus rectum

    (c)

    directrix

    (d)

    axis

  16. 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)

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

  17. The value of \(\sin(-420^o)\) is

    (a)

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

    (b)

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

    (c)

    \(\frac{1}{2}\)

    (d)

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

  18. The value of sin 15o cos 15o is

    (a)

    1

    (b)

    \(\frac{1}{2}\)

    (c)

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

    (d)

    \(\frac{1}{4}\)

  19. If sin A+ cos A=1, then sin 2A is equal to

    (a)

    1

    (b)

    2

    (c)

    0

    (d)

    \(\frac{1}{2}\)

  20. \(\sec^{-1}\frac{2}{3}+cosec^{-1}\frac{2}{3}=\)

    (a)

    \(\frac{-\pi}{2}\)

    (b)

    \(\frac{\pi}{2}\)

    (c)

    \(\pi\)

    (d)

    \(-\pi\)

  21. If f(x) = \(\frac{1-x}{1+x}\) then f(-x) is equal to

    (a)

    -f(x)

    (b)

    \(\frac{1}{f(x)}\)

    (c)

    \(\frac{-1}{f(x)}\)

    (d)

    f(x)

  22. The graph of f(x) = ex is identical to that of

    (a)

    f(x) = ax, a > 1

    (b)

    f(x) = ax, a < 1

    (c)

    f(x) = ax, 0 < a < 1

    (d)

    y = ax +b, a \(\ne\) 0

  23. If f(x) = x2 and g(x) = 2x + 1 then (fg)(0) is

    (a)

    0

    (b)

    2

    (c)

    1

    (d)

    4

  24. For what value of x, f(x) = \(\frac{x+2}{x-1}\) is not continuous?

    (a)

    -2

    (b)

    1

    (c)

    2

    (d)

    -1

  25. A function f(x) is continuous at x = a if \(\lim _{ x\rightarrow a }{ f\left( x \right) } \) is equal to

    (a)

    f(-a)

    (b)

    f\((\frac{1}{a})\)

    (c)

    2f(a)

    (d)

    f(a)

  26. If the demand function is said to be inelastic, then

    (a)

    |nd|>1

    (b)

    |nd|=1

    (c)

    |nd|<1

    (d)

    |nd| = 0

  27. Relationship among MR, AR and ηd is

    (a)

    \({ n }_{ d }=\frac { AR }{ AR-MR } \)

    (b)

    n4 =  AR - MR

    (c)

    MR = AR = n4

    (d)

    \(AR=\frac { MR }{ { n }_{ 4 } } \)

  28. Profit P(x) is maximum when 

    (a)

    MR = MC

    (b)

    MR = 0

    (c)

    MC = AC

    (d)

    TR = AC

  29. if u = 4x2 + 4xy + y2 + 32 + 16 , then \(\frac { \partial ^{ 2 }u }{ \partial y\partial x } \) is equal to

    (a)

    8x + 4y + 4

    (b)

    4

    (c)

    2y + 32

    (d)

    0

  30. The demand function is always

    (a)

    Increasing function

    (b)

    Decreasing function

    (c)

    Non-decreasing function

    (d)

    Undefined function

  31. The dividend received on 200 shares of face value Rs.100 at 8% dividend value is

    (a)

    1600

    (b)

    1000

    (c)

    1500

    (d)

    800

  32. A man received a total dividend of Rs 25,000 at 10% dividend rate on a stock of face value Rs.100, then the number of shares purchased.

    (a)

    3500

    (b)

    4500

    (c)

    2500

    (d)

    300

  33. If ‘a’ is the annual payment, ‘n’ is the number of periods and ‘i’ is compound interest for Rs 1 then future amount of the annuity is

    (a)

    A = \(\frac{a}{i}(1+i)(1+i)^n-1]\)

    (b)

    A = \(\frac{a}{i}[(1+i)^n-1]\)

    (c)

    P = \(\frac{a}{i}\)

    (d)

    P = \(\frac{a}{i}(1+i)[1-(1+i)^{-n}]\)

  34. An annuity in which payments are made at the beginning of each payment period is called

    (a)

    Annuity due

    (b)

    An immediate annuity

    (c)

    perpetual annuity

    (d)

    none of these

  35. The present value of the perpetual annuity of Rs 2000 paid monthly at 10 % compound interest is

    (a)

    Rs 2,40,000

    (b)

    Rs 6,00,000

    (c)

    20,40,000

    (d)

    Rs 2,00,400

  36. The geometric mean of two numbers 8 and 18 shall be

    (a)

    12

    (b)

    13

    (c)

    15

    (d)

    11.08

  37. Harmonic mean is the reciprocal of

    (a)

    Median of the values.

    (b)

    Geometric mean of the values.

    (c)

    Arithmetic mean of the reciprocal of the values.

    (d)

    Quartiles of the values.

  38. Harmonic mean is better than other means if the data are for

    (a)

    Speed or rates.

    (b)

    Heights or lengths.

    (c)

    Binary values like 0 and 1.

    (d)

    Ratios or proportions.

  39. If median = 45 and its coefficient is 0.25, then the mean deviation about median is

    (a)

    11.25

    (b)

    180

    (c)

    0.0056

    (d)

    45

  40. Probability of an impossible event is

    (a)

    1

    (b)

    0

    (c)

    0.2

    (d)

    0.5

  41. The variable which influences the values or is used for prediction is called

    (a)

    Dependent variable

    (b)

    Independent variable

    (c)

    Explained variable

    (d)

    Regressed

  42. The regression coefficient of Y on X

    (a)

    bxy=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

    (b)

    byx=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

    (c)

    byx=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dx^{ 2 }-(\Sigma dx)^{ 2 } } \)

    (d)

    bxy=\(\frac { N\Sigma xy-(\Sigma x)(\Sigma y) }{ \sqrt { N\Sigma { x }^{ 2 }-(\Sigma x)^{ 2 }\times \sqrt { N\Sigma { y }^{ 2 }-(\Sigma y)^{ 2 } } } } \)

  43. The lines of regression of X on Y estimates

    (a)

    X for a given value of Y

    (b)

    Y for a given value of X

    (c)

    X from Y and Y from X

    (d)

    none of these

  44. The person suggested a mathematical method for measuring the magnitude of linear relationship between two variables say X and Y is

    (a)

    Karl Pearson

    (b)

    Spearman

    (c)

    Croxton and Cowden

    (d)

    Ya Lun Chou

  45. The lines of regression intersect at the point

    (a)

    (X,Y)

    (b)

    \(\left( \bar { X } ,\bar { Y } \right) \)

    (c)

    (0,0)

    (d)

    x, σy)

  46. A solution which maximizes or minimizes the given LPP is called

    (a)

    a solution

    (b)

    a feasible solution

    (c)

    an optimal solution

    (d)

    none of these

  47. The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤20, x + 2y ≤ 20,x > 0 and y > 0 is

    (a)

    10

    (b)

    20

    (c)

    0

    (d)

    5

  48. Which of the following is not correct?

    (a)

    Objective that we aim to maximize or minimize

    (b)

    Constraints that we need to specify

    (c)

    Decision variables that we need to determine

    (d)

    Decision variables are to be unrestricted

  49. The objective of network analysis is to

    (a)

    Minimize total project cost

    (b)

    Minimize total project duration

    (c)

    Minimize production delays, interruption and conflicts

    (d)

    All the above

  50. Given an L.P.P maximize Z=2x1+3x2 subject to the constrains x1+x2≤1, 5x1+5x2≥0 and x1≥0, x2≥0 using graphical method, we observe

    (a)

    No feasible solution

    (b)

    unique optimum solution

    (c)

    multiple optimum solution

    (d)

    none of these

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