scra 2014 mathematics paper

8/13/2019 SCRA 2014 Mathematics Paper

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SCRA Paper 3

Mathematics

SET C

Mathematics Paper III

1. In four throws of a fair die, what is the

probability of getting a score of more than

4 at least once ?

(a) (b)

(c ) (d) None of the above

For the next 03(three) items that follow:

A die is rolled so that the probability of

face is proportional to where 2. What is the proportionality constant ?

(a) (b) (c ) (d)

3. What is the probability of getting aneven number ?

(a) (b)

(c ) (d)

4. What is the probability of getting a

multiple of 3 ?

(a)

(b)


5. The probability of a shooter hitting a

target is What is the minimum number

of times that the shooter must fire so that

the probability of hitting the target at least

once is more than (a) 4 (b) 5 (c ) 6

(d) None of the above

6. Consider the following statements

about the random variables and onthe same sample space 1. 2. Which of the above statements is/are

correct ?

(a) 1 only (b) 2 only

(c ) Both 2 and 2 (d) Neither 1 nor 2

7. Consider the following statements :

1. Area under a histogram gives total

frequency .

2. Width of the tallest vertical bar of the

histogram gives modal class.

Which of the above statements is/are

correct ?



8. Consider the following statements

related to measure of central tendency of

50 positive numbers :

1. The median is not influenced byextreme values in the set of numbers.

2. The harmonic mean is unreliable if oneor more of the numbers is near zero.


correct ?


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9. A fair coin is tossed 6 times ; call heads

a success. This is a binomial experiment

with and What is theprobability of getting at least 4 heads ?(a)

(b) (c )

(d) 10. If and are two events suchthat

then what is

equal

to ?

(a) (b)

(c ) (d)


1.

2. Where Which of the above statements is/are

correct ?


(c ) Both 1and 2 (d) Neither 1 nor 2


1. If then

2. If then


correct ?



For the next 02 (two)items that follow :

Consider 13. What is if (a) 0 (b) (c )

(d) 14. What is of (a) (b) (c )

(d) For the next 02 (two) items that follow:

Consider 15. What is the value of ?(a) (b) (c ) (d) 16. What is

equal to ?(a) 0 (b) 1

(c ) 2 (d) None of the above


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For the next 02 (two) items that follow

Consider

17. What is equal to ?(a) (b) (c ) (d) 18. what is equal to ?(a)

(b)

(c ) (d) For the next 02 (two) items that follow:

Let Where 19. If

is real, then which one of the

following is correct ?

(a)

(b) (c )


20. If is purely imaginary, then whichone of the following is correct ?

(a)

(b) (c ) (d) None of the above

For the next 02 (two) items that follow:

The th , th , th terms of an are respectively.21. What is equal to ?(a) 0 (b) 1

(c ) (d) 22. What is

Equal to ?

(a)

(b)

(c ) (d) For the next 02 (two) items that follow:

Consider the system of equations

23. What is /are the value (s) of which make(s) the system of equations to

possess the solution ?

(a) 0 (b) 1 or 2

(c ) 3 or 4 (d) None of the above


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1. The system of equations can have

infinite solutions for some value of 2. The system of equations can have

unique solution for some value of Which of the above statements is/are

correct ?


(c ) Both 1 and 2

(d) Neither 1 nor 2

25. For what value (s) of

where is a natural numebr, where is the identity matrixand (a) (b) (c ) For all values of (d) None of the values of 26. Let

and

be two points on

-

axis and -axis respectively, being theorigin. If the equal sides and each equal to are produced to and respectively such that then the line always passesthrough the fixed point

(a) (b) (c )

(d)

27. The new position of the point (1, 2)

under rotation through an angle of about the origin in anticlockwise direction

is

(a) (b)

(c ) (d) 28. What is the area of the triangle with

vertices at and(a) square unit(b) square unit(c ) 2 square units

(d) 4 square units

29. Consider two circles

With lying inside circle lying inside touches internally and externally. Then the locus of thecentre of the circle is(a) a circle of radius (b) a parabola of semilatus rectum (c ) an ellipse of major axis (d) None of the above

30. The shortest distance of a point from

the -axis, -axis and -axisrespectively are 2, 3, 6 . What is the

distance of the point from the origin ?

(a) (b)

(c ) (d) For the next 02 (two) items that follow :

Consider a plane parallel to -axis andpassing through the points (0 ,1, 3) and

(2, 4, 5) .


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31. What are the direction ratios of

normal to the plane ?

(a) (b) (c )


32. What is the equation to the plane ?

(a) (b) (c ) (d) None of the above

For the next 03 (three)items that follow :

Consider a unit cube.

33. What is the perpendicular distance of

a corner to the diagonal not passing

through that corner ?

(a) (b)

(c )


34. What is the sum of squares of

direction cosines of all the four diagonals

of the cube ?

(a) 1 (b) 2 (c ) 4

(d) Cannot be determined as the data is

inadequate

35. If

is the acute angle between any

two diagonals of the cube, then what is equal to ?(a) 1 (b) 2 (c ) 4


36. If are two vectors inclined atangle such that is a unitvector, then what is equal to ?(a)

(b)

(c ) (d) 37. If is a non-zero vector ofmagnitude then is a unit vector if(a) (b) (c ) (d) For the next 02 (two) items that follow:

The vectors are of same lengthand equally inclined to each other. Let

and 38. What is the angle between and ?

(a)

(b)

(c ) (d) 39. What can be the direction ratios of

(a) (b) (c ) (d) None of the above40. If

and

are two matrices such

that and then what is equal to ?(a) (b) (c ) zero matrix (d) Identity matrix

41. If


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Then what is equal to ?(a)

(b) (c )

(d) None of the aboveWhere is the constant of integration.42. What is

equal to ?

(a) (b)

(c ) (d)

43 What is Equal to ?

(a) (b) (c ) 0 (d) Limit does not exist

44. If

Then what is

Equal to ?

(a) (b)


45. What is

Equal to ?

(a) 0 (b) 1


46. The differential equation

Where is a constant, represents(a) a set of circles having centre on the -axis

(b) a set of parabolas

(c ) a set of circles having centre on the

-axis(d) a set of straight lines47. What is the degree of the differential

equation

(a) 1 (b) 2

(c ) 3 (d) 48. Consider the following statements :

1.


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2. Which of the above statements is/arecorrect ?



49. The solution of the differentialequation


Where is an arbitrary constant.50. What is

Where [. ] denotes the greatest integer

function ?

(a) (b) (c ) (d) Limit does not exist51. If

Then what is equal to(a)

(b)

(c ) (d)

Where

is the constant of integration.

52. What is the general solution of the

equation

(a) (b) (c ) (d) None of the aboveWhere is an arbitrary constant .53. What is the equation of straight line

parallel to the line andwhich is such that the sum of its intercepts

on the axes is 10 ?

(a)

(b) (c ) (d) 54. A straight line through issuch that its intercept between the axes is

bisected at Its equation is(a)

(b)

(c ) (d) 55. If the line meets the lines and atthe same point, then is equal to(a) 1 (b) 2


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(c ) (d) For the next 02 (two)items that follow:

Consider the function

On the interval 56. The function is continuous at

(a) (b) every point in (c ) every rational point in

(d) every irrational point in 57. Consider the following statements :

1. has its own inverse in 2. is differentiable at Which of the above statements is/are

correct ?


(c) Both 1 and 2 (d) Neither 1 nor 2

58. The function

Is increasing for

(a) (b) (c ) (d) For the next 02 (two) items that follow:

Consider the function


1. The function is neither increasing nordecreasing in the interval [1, 2] .

2. The function has neither relative

maximum nor relative minimum at Which of the above statements is/are

correct ?




1. The function attains relative maximum

at 2. The function attains relative minimum

at Which of the above statements is/arecorrect ?




Consider

Where is a natural number.61. What is equal to ?(a) 0 (b) (c )

(d)


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62. are(a) in AP only (b) in GP only

(c ) both in AP and GP

(d) neither in AP nor in GP


Let be definedfor

63. The function is monotonicallydecreasing in the interval

(a) (b) (c ) (d) 64. The function is monotonicallyincreasing in the interval

(a) (b) (c ) (d) For the next 02 (two)items that follow :

Let where is a nonnegative integer.

65. What is the coefficient of in (a)

(b)

(c ) (d) None of the above66. What is

Equal to ?

(a) (b) (c ) (d) For the next 02 (two) items that follow:

Consider the ellipses and 67. What is the area common to both theellipses ?

(a) square units(b)

square units

(c ) square units(d) None of the above

68. What is the bounded area not common

to both the ellipses ?

(a) square units(b) square units(c ) square units(d) None of the aboveFor the next 02 (two)items that follow :

Consider the functions and on the interval 69. Consider the following statements :

1. The function is alwaysincreasing on 2. The function is alwaysincreasing on Which of the statements given above is/are

correct ?


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1. The function is alwaysincreasing on 2. The function is alwaysincreasing on Which of the above statements is/are

correct ?



71. Addition is not a binary operation on

the set

(a) of natural numbers(b) is a real number and (c ) of rational numbers(d)

of real numbers

72. The locus of the point of intersection

of the straight lines

Where is a variable, is(a) a circle (b) a parabola

(c ) an ellipse (d) a hyperbola

73. If the product of positive numbersis unity, then their sum is

(a) a positive integer

(b) divisible by

(c ) equal to (d) never less than 74. The number of numbers between 1

and

which contain the digit 1, is


75. If are any three consecutiveterms in an then the line (a) has a fixed direction

(b) passes through the origin (c ) always passes through a fixed point


76. A five digit number divisible by 3 is

to be formed using the numbers 0, 1, 2, 3,

4, 5 without repetition. The total number

of ways in which this can be done is

(a) 216 (b) 240

(c ) 600 (d) 3125

77. If are the roots of the equation

Then is greater than

(a) 1 (b) 2


78. The number of terms in the expansion

of which is apositive integer, is


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(a) (b) (c ) (d) 79. If and are in

then

is

equal to

(a) (b) (c ) (d) 80. If Then what is equal to ?(a)

(b)

(c ) (d) 81. If an angle is divided into twoparts and such that

Then what is equal to ?(a) (b)

(c )

(d)

82. What is the sum of the first 30 terms

of the series

(a) 21010 (b) (c ) 22100 (d) 9920

83. The total number of ways of

selecting tow numbers from the set {1, 2,

3, , 30} , so that their sum is divisible

by 3, is

(a) 95 (b) 145


84. The sum of terms of the series Where is(a)

(b) (c ) (d)

85. The 5

th term from the end in the

expansion of in increasingpower of is is a positive integer ](a)

(b)

(c ) (d) None of the above86. The function defined by

Where is(a) not one one but onto

(b) one one but not onto

(c ) both one one and onto

(d) neither one one nor onto

87. If then which of thefollowing is/are the function(s) from toitself ?


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I. II. Select the correct answer using the code

given below.

(a) I only (b) II only

(c ) Both I and II (d) Neither I nor II

88. If be given by

Then is invertible if(a)

(b)

(c ) (d) None of the above89. The complex numbers satisfying are(a) (b) (c ) (d) 90. If

are complex numbers

such that

Then what is equal to ?(a) Less than 1

(b) Lies between 1 and 3

(c ) 1 (d) 3

91. IF the lines and areconcurrent, then are in(a) (b) (c ) (d) None of the above

92. Let and be theroots of the equations respectively. Then the product of their

common roots is equal to(a) (d) (c ) (d) 93. The roots of the equation

When where are realnumbers, are always

(a) irrational (b) real

(c ) complex (d) rational

94. If is a complex number, then thecommon roots of the equations

are(a)

(b)

(c ) (d) 95. The range of in the interval such that the points (3, 5) and lie on the same side of theline is(a) (b) (c ) (d) 96. A line passing through the point (2, 2)encloses an area with the axes. Theintercepts on the axes made by the line are

given by the two roots of

(a) (b)


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(c ) (d) 97. The area bounded by the curve

the

-axis and the two

ordinates corresponding to minimal of thefunction is

(a) square unit

(b) square unit

(c )


98. If Holds good for all then and arerespectively

(a) (b) (c ) (d) 99. In a triangle

Then what is the value of (a)

(b) (c ) (d) 100. The graph of the function

is a(a) straight line passing through the point and parallel to -axis(b) straight line passing through the origin

(c ) parabola with vertex (d) None of the above

scra 2014 mathematics paper

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