12th Public Exam March 2019 Important Creative One Mark Test

12th Standard

    Reg.No. :
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Business Maths

Time : 00:45:00 Hrs
Total Marks : 80
    80 x 1 = 80
  1. The vertex of the parabola (y+a)2 = 8a(x-a) is

    (a)

    (-a, -a)

    (b)

    (a, -a)

    (c)

    (-a, a)

    (d)

    none of these

  2. The equation 16x2+y2+8xy-74x-78y+212 = 0 represents a

    (a)

    circle

    (b)

    parabola

    (c)

    ellipse

    (d)

    hyperbola

  3. The focus of the parabola y = 2x+ x is

    (a)

    (0, 0)

    (b)

    \(\left( \frac { 1 }{ 2 } ,\frac { 1 }{ 4 } \right) \)

    (c)

    \(\left( -\frac { 1 }{ 4 } ,0 \right) \)

    (d)

    \(\left( -\frac { 1 }{ 4 } ,\frac { 1 }{ 8 } \right) \)

  4. For the ellipse x2 + 4y2 = 9.

    (a)

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

    (b)

    LR is \(\frac { 3 }{ 2 } \)

    (c)

    focus is \(\left( 3\sqrt { 3 } ,0 \right) \)

    (d)

    x = -2\(\sqrt { 3 } \)

  5. The eccentricity of the conic 9x2+25y2 = 225 is

    (a)

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

    (b)

    \(\frac { 4 }{ 5 } \)

    (c)

    \(\frac { 1 }{ 3 } \)

    (d)

    \(\frac { 1 }{ 5 } \)

  6. The sum of the focal distances of any point on the ellipse 9x2+16y2 = 144 is

    (a)

    32

    (b)

    18

    (c)

    16

    (d)

    8

  7. The equation of the conic with focus at (1, -1) directrix along x - y + 1 = 0 and e = \(\sqrt { 2 } \) is

    (a)

    xy = 1

    (b)

    2xy + 4x - 4y - 1 = 0

    (c)

    x2 - y2 = 1

    (d)

    2xy - 4x + 4y + 1 = 0

  8. The distance between the foci of a hyperbola is 16 and its eccentricity is \(\sqrt { 2 } \), then equation of the hyperbola

    (a)

    x2 + y2 = 32

    (b)

    x2-y2 = 16

    (c)

    x2 + y2 = 16

    (d)

    x2 - y2 = 32

  9. The latusrectum of the hyperbola 16x2-9y2 = 144 is

    (a)

    \(\frac { 16 }{ 3 } \)

    (b)

    \(\frac { 32 }{ 3 } \)

    (c)

    \(\frac { 8 }{ 3 } \)

    (d)

    \(\frac { 4 }{ 3 } \)

  10. The combined equation of the asymptotes to the hyperbola 36x2-25y2 = 900 is

    (a)

    25x2 + 36y2 = 0

    (b)

    36x2-25y2 = 0

    (c)

    36x2+25y2 = 0

    (d)

    25x2-36y2 = 0

  11. The average fixed cost of the function C = 10x3 - 7x + 5 is

    (a)

    10x - 7

    (b)

    10x2 - 7x

    (c)

    5/x

    (d)

    5x

  12. The demand for .some commodity is given by q = 8p + 7 where p is the unit price. The elasticity of demand is

    (a)

    \(8p\over 8p+7\)

    (b)

    \(-8p\over 8p+7\)

    (c)

    \(p\over 8p+7\)

    (d)

    \(-p\over 8p+7\)

  13. For the cost function C = e-0.5x, the marginal cost is

    (a)

    e-0.5x

    (b)

    -0.5e0.5x

    (c)

    -0.5 e-0.5x

    (d)

    \(e^{-0.5x}\over-0.5\)

  14. If the rate of change of area of a circle is equal to. the rate of change of its diameter then its radius is ____ unit

    (a)

    1

    (b)

    \(\sqrt{2\pi}\)

    (c)

    \(1\over\sqrt{2\pi}\)

    (d)

    \({1\over2}\sqrt{\pi}\)

  15. A cylindrical vessel of radius 0.5m is filled with oil at the rate of 0.25πm3/min. The rate at which the surface of the oil is rising is

    (a)

    1 m/min

    (b)

    2m/min

    (c)

    5m/min

    (d)

    1.25m/min

  16. The equation of the normal to the curve y = sinx at (0, 0) is

    (a)

    x = 0

    (b)

    y = 0

    (c)

    x+y=0

    (d)

    x - y = 0

  17. The point on the curve y = 12x - r where the slope of the tangent is zero will be

    (a)

    (0,0)

    (b)

    (2, 16)

    (c)

    (3,9)

    (d)

    (6,36)

  18. The slope of the tangent to the curve x = 3t2 + 1, y = t2 - 1 at x = 1 is

    (a)

    1/2

    (b)

    0

    (c)

    -2

    (d)

  19. The normal at the point (1, 1) on the curve 2y + x= 3 is

    (a)

    x + y = 0

    (b)

    x - y = 0

    (c)

    x + y + 1 = 0

    (d)

    x - y = 1

  20. The normal to the curve x2 = 4y passing through (I, 2) is

    (a)

    x +y = 3

    (b)

    x - y = 3

    (c)

    x.+ y = 1

    (d)

    x - y = 1

  21. f(x) = x2 - 27x + 5 is an increasing function when

    (a)

    x < -3

    (b)

    |x|>3

    (c)

    x\(\le \)-3

    (d)

    |x|\(\ge \)3

  22. The function f(x) = \(\frac { x }{ 1+|x| } \)is

    (a)

    strictly increasing

    (b)

    strictly decreasing

    (c)

    neither increasing nor decreasing 

    (d)

    none of these

  23. The function f(x) x9+3x7+64 is increasing on

    (a)

    R

    (b)

    (-\(\infty \), 0)

    (c)

    (0, \(\infty \))

    (d)

    R+

  24. f(x) = x3 + 3x2-9x+2 has a

    (a)

    maximum at x = 1

    (b)

    minimum at x = 1

    (c)

    neither maximum nor minimum at x = -3

    (d)

    none of these

  25. The least value of function f(x) = x3 - 18x2 + 96 x in [0, 9] is 

    (a)

    126

    (b)

    135

    (c)

    160

    (d)

    0

  26. The point on the curve y2 = 4x which is nearest to the point (2, 1) is

    (a)

    (1,2\(\sqrt { 2 } \))

    (b)

    (1,2)

    (c)

    (1, -2)

    (d)

    (-2, 1)

  27. If x+y = 8, then the maximum value of xy

    (a)

    6

    (b)

    16

    (c)

    20

    (d)

    24

  28. If u = 5xy + 7x + 8y then \(\frac { \partial u }{ \partial x } \) is

    (a)

    5x + 8

    (b)

    5y + 7

    (c)

    7x + 8

    (d)

    5xy

  29. If q1 = 7000 - 5p1 + 8\({ p }_{ 2 }^{ 2 }\) then \(\frac { \partial { q }_{ 1 } }{ \partial { p }_{ 2 } } \)is

    (a)

    -5

    (b)

    16p2

    (c)

    7000-5p1+16p2

    (d)

    -5p1 + 16p2

  30. f(x,y) = cos-1\(\left( \frac { { x }^{ 3 }+{ y }^{ 3 } }{ x+y } \right) \) is a homogeneous function of degree

    (a)

    3

    (b)

    1

    (c)

    2

    (d)

    4

  31. \(\overset { 1 }{ \underset { 0 }{ \int } } \sqrt { x\left( 1-x \right) } dx\) equals

    (a)

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

    (b)

    \(\frac{\pi}{4}\)

    (c)

    \(\frac{\pi}{6}\)

    (d)

    \(\frac{\pi}{8}\)

  32. The value of \(\overset { \frac { \pi }{ 2 } }{ \underset { 0 }{ \int } } \frac { \sqrt { \cos { x } } }{ \sqrt { \cos x+\sqrt { \sin { x } } } } dx\) is

    (a)

    0

    (b)

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

    (c)

    \(\frac{\pi}{4}\)

    (d)

    none of these

  33. \(\overset { \frac { { \pi }^{ 2 } }{ 4 } }{ \underset { 0 }{ \int } } \frac { \sin { \sqrt { x } } }{ \sqrt { x } } dx\) equals

    (a)

    2

    (b)

    1

    (c)

    \(\frac{\pi}{4}\)

    (d)

    \(\frac{\pi^2}{8}\)

  34. The value of \(\overset { \pi }{ \underset { -\pi }{ \int } } \sin ^{ 3 }{ x } \cos ^{ 2 }{ x } dx\) is

    (a)

    \(\frac{\pi^2}{4}\)

    (b)

    \(\frac{\pi^4}{4}\)

    (c)

    0

    (d)

    none of these

  35. The area bounded by x = 4 - y2 and y-axis is square units is

    (a)

    \(\frac{3}{32}\)

    (b)

    \(\frac{32}{3}\)

    (c)

    \(\frac{33}{2}\)

    (d)

    \(\frac{16}{3}\)

  36. The area bounded by the curve y = sin x, between the ordinates x = 0, x = \(\pi\) and the x-axis is ______ sq.units.

    (a)

    2

    (b)

    4

    (c)

    3

    (d)

    1

  37. Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is

    (a)

    2

    (b)

    \(\frac{9}{4}\)

    (c)

    \(\frac{9}{3}\)

    (d)

    \(\frac{9}{2}\)

  38. If the marginal cost function MC = 8 + 7x - x2 then the cost function is

    (a)

    7 - 2x

    (b)

    \(8x+\frac{7x^2}{2}-\frac{x^3}{3}\)

    (c)

    \(8x+\frac{7x^2}{2}-\frac{x^3}{3}+k\)

    (d)

    8 + 7x + x2

  39. The marginal revenue of a firm is MR. = 3 - 2x. Then the revenue function is

    (a)

    -2

    (b)

    3

    (c)

    3x - x2

    (d)

    3x - x2 + k

  40. The marginal revenue R'(x) = \(\frac{1}{x}\) then the revenue function is

    (a)

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

    (b)

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

    (c)

    log x

    (d)

    log |x| + k

  41. The degree of the differential equation \(\left(d^2y\over dx^2\right)-\left(dy\over dx\right)=y^3\) is

    (a)

    1/2

    (b)

    2

    (c)

    3

    (d)

    4

  42. The general solution of the differential equation \({dy\over dx}={y\over x}\) is

    (a)

    logy = kx

    (b)

    y=kx

    (c)

    y=k

    (d)

    y = k log x

  43. Integrating factor of the differential equation \(cos\ x\left(dy\over dx\right)+ysin\ x=1\)is

    (a)

    sin x

    (b)

    see x

    (c)

    tan x

    (d)

    cos x

  44. The solution of the differential equation \({dy\over dx}+{2y\over x}=0\)with y'(l) = 1 is given by

    (a)

    \(y={1\over x^2}\)

    (b)

    \(x={1\over y^2}\)

    (c)

    \(y={1\over y}\)

    (d)

    \(y={1\over x}\)

  45. The differential equation for ax2 + by2 = 1 is

    (a)

    xyy2+ y1 +yy1 =

    (b)

    xyy2+xy12 +yy1 = 0

    (c)

    xyy2 - xy12 +yy1 = 0

    (d)

    none of these

  46. The solution of \(x^2+y^2{dy\over dx}=4\) is

    (a)

    x2 + y2 = 12x + c

    (b)

    x+ y2 = 3x + c

    (c)

    x3 + y3 = 3x + c

    (d)

    x3 + y2 = 12x + c

  47. The degree of the differential equation \([5+\left(dy^2\over dx\right)^{5/3}=x^5\left(d^2y\over dx^2\right)\)

    (a)

    4

    (b)

    2

    (c)

    5

    (d)

    10

  48. The order of the differential equation \(\sqrt{1-x^4}+\sqrt{1-y^2}=a(x^2-y^2)\)is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  49. A homogeneous differential equation of the form \({dy\over dx}=h\left(y\over x\right)\) can be solved by making the substitution

    (a)

    y=vx

    (b)

    x=vy

    (c)

    v=yx

    (d)

    x=v

  50. Solution of (D2 - 5D + 6) y = 0 is

    (a)

    (Ax + B) e2x

    (b)

    (Ax + B) e3x

    (c)

    Ae3x + Be2x

    (d)

    Ae-3x + Be-2x

  51. If a random variable X has the following probability distribution

     X   0   1   2   3   4   5   6   7   8 
      p(X)     a     3a     5a     7a     9a     11a     13a     15a     17a  

    then the value of a is

    (a)

    \(\frac{7}{18}\)

    (b)

    \(\frac{5}{81}\)

    (c)

    \(\frac{2}{81}\)

    (d)

    \(\frac{1}{81}\)

  52. Let x be a discrete random variable then the variance of x is

    (a)

    E(x)2

    (b)

    E(x)2 + [E(x)]2

    (c)

    E(x2) + [E(x)]2

    (d)

    \(\sqrt{E(x^2)-E(x)^2}\)

  53. For the following distribution:

     X   1   2   3   4 
      p(X)     \(\frac{1}{10}\)     \(\frac{1}{5}\)     \(\frac{3}{10}\)     \(\frac{2}{5}\)  

    Then value of E(X2) is

    (a)

    3

    (b)

    5

    (c)

    7

    (d)

    10

  54. A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If p(X = 3) = 2. p(X = 1) and p(X = 2) = 0.3 then p(X = 0) is

    (a)

    0.1

    (b)

    0.2

    (c)

    0.3

    (d)

    0.4

  55. If a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?

    (a)

    \(\frac{1}{16}\)

    (b)

    \(\frac{1}{81}\)

    (c)

    \(\frac{1}{27}\)

    (d)

    \(\frac{1}{8}\)

  56. In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?

    (a)

    \((\frac{9}{10})^5\)

    (b)

    \(\frac{9}{10}\)

    (c)

    10-5

    (d)

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

  57. In a binomial distribution, the probability of getting success is \(\frac{1}{4}\) and S.D. is 3. Then its mean is

    (a)

    6

    (b)

    8

    (c)

    12

    (d)

    10

  58. A coin is tossed 4 times. The probability that at least one head turns up is

    (a)

    \(\frac{1}{16}\)

    (b)

    \(\frac{2}{16}\)

    (c)

    \(\frac{14}{16}\)

    (d)

    \(\frac{15}{16}\)

  59. Which of the following is not line regarding the normal distribution?

    (a)

    Skewers is Lew

    (b)

    Mean = median = moele

    (c)

    The points of inflection are at X = \(\mu\pm\sigma\)

    (d)

    Maximum height of the curve is \(\frac{1}{\sqrt{2\pi}}\)

  60. If X is a continuous random variable, then p(a < X < b) =

    (a)

    \(p(a\le X\le b)\)

    (b)

    \(p(a < X \le b)\)

    (c)

    \(p(a\le X <b)\)

    (d)

    all the above

  61. The range or set of values which have chances to contain value, of population parameter with particular confidence level is considered as

    (a)

    Secondary interval estimation

    (b)

    Confidence interval estimate

    (c)

    Population interval estimate

    (d)

    Sample interval estimate

  62. In confidence interval estimation, formula of calculating confidence interval is

    (a)

    Point estimate -:-margin of error

    (b)

    Point estimate ± margin of error

    (c)

    Point estimate - margin of error

    (d)

    Point estimate + margin of error

  63. Criteria of selecting point estimator must include information of

    (a)

    Consistency

    (b)

    Unbiasedness

    (c)

    Efficiency

    (d)

    All of above

  64. Considering sample statistic, if sample statistic mean ≠ population parameter then sample statistic is considered as

    (a)

    Unbiased estimator

    (b)

    Biased estimator

    (c)

    Interval estimator

    (d)

    Hypothesis estimator

  65. If critical value of normal standard variable is 0.95 and standard error of specific statistic is 3.5 then margin of error is

    (a)

    2.325

    (b)

    3.325

    (c)

    4.325

    (d)

    5.325

  66. Difference between value of parameter of population and value of unbiased estimator point is classified as

    (a)

    sampling error

    (b)

    marginal error

    (c)

    confidence error

    (d)

    population error

  67. An estimator is said to be consistent of the estimate tends to approach the parameter as the sample size.

    (a)

    Increase

    (b)

    decreases

    (c)

    Increases or decreases

    (d)

    Neither increases nor decreases

  68. The interval within which the unknown value of parameter is expected to lie is called

    (a)

    Confidence limits

    (b)

    Confidence interval

    (c)

    Finite range

    (d)

    Infinite range

  69. A hypothesis is complementary to the null hypothesis is

    (a)

    null hypothesis

    (b)

    Type I error

    (c)

    Type II error

    (d)

    Alternate hypothesis

  70. For the test statistic Z, the critical region at 5% level is

    (a)

    |z| > 2.58

    (b)

    |z| < 2.58

    (c)

    > 1.96

    (d)

    |z| > 1.96

  71. Objective function of a LPP is a

    (a)

    Constraint

    (b)

    function to be optimized

    (c)

    relation between the variables

    (d)

    none of these

  72. If the Constraints is a LPP are changed

    (a)

    the problem is to be re-evaluated

    (b)

    solution is no defined

    (c)

    the objective function has to be modified

    (d)

    the change in constraints is ignored

  73. Which of the following statements is correct?

    (a)

    Every LPP admits an optimal solution

    (b)

    A LPP admits unique optimal solution

    (c)

    It a LPP admits two optimal solutions it has an infinite number of optimal solutions

    (d)

    The set of all feasible solutions of a LPP is not a Convex set

  74. If the values of two variables deviate in the same direction, then the Correlation between them is

    (a)

    positive

    (b)

    negative

    (c)

    0

    (d)

    none of these

  75. If the values of the two variables constantly deviate in the opposite directions then the correlation between them is

    (a)

    positive

    (b)

    negative

    (c)

    0

    (d)

    none of these

  76. Correlation Co-efficient lies between

    (a)

    -∞ to ∞

    (b)

    0 to ∞

    (c)

    -∞ to 0

    (d)

    -1 to 1

  77. Season Variation can be measured by the method of

    (a)

    additive model

    (b)

    multiplicative model

    (c)

    simple average

    (d)

    index numbers

  78. The geometric mean of Laspeyres and Paasches index number is

    (a)

    \(\sqrt { { P }_{ 01 }^{ L } } \).

    (b)

    \(\sqrt { { P }_{ 01 }^{ P } } \)

    (c)

    \({ P }_{ 01 }^{ L }\times { P }_{ 01 }^{ P }\).

    (d)

    \(\sqrt { { P }_{ 01 }^{ L }\times { P }_{ 01 }^{ P } } \).

  79. In time reversal test, P01 x P10 =

    (a)

    0

    (b)

    2

    (c)

    Fisher's index number

    (d)

    1

  80. In factor reversal test, P01 x Q01 =

    (a)

    \(\\ \frac { \Sigma { p }_{ 1 }{ q }_{ 1 } }{ \Sigma { p }_{ 1 }{ q }_{ 0 } } \).

    (b)

    \(\\ \frac { \Sigma { p }_{ 1 }{ q }_{ 1 } }{ \Sigma { p }_{ 0}{ q }_{ 0 } } \).

    (c)

    \(\\ \frac { \Sigma { p }_{ 0 }{ q }_{ 0 } }{ \Sigma { p }_{ 1 }{ q }_{ 1 } } \)

    (d)

    \(\\ \frac { \Sigma { p }_{ 1 }{ q }_{ 0 } }{ \Sigma { p }_{ 1 }{ q }_{ 1 } } \).

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