If the standard deviation of the numbers 2, 3, a and 11 is 3.5,

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let   be three unit vectors such that   then the angle between   is

  • 3π/4

  • π/2

  • 2π/3

  • 5π/6

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2.

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

  • 3a2−26a+55=0

  • 3a2−32a+84=0

  • 3a2−34a+91=0

  • 3a2−34a+91=0


B.

3a2−32a+84=0

We know that, if x1, x2..... xn are n observations, then their standard deviation is given by


square root of 1 over straight n sum straight x subscript straight i superscript 2 space minus open parentheses fraction numerator space stack sum straight x subscript straight i with space below over denominator straight n end fraction close parentheses squared end root

we begin inline style space end style begin inline style have end style begin inline style comma end style begin inline style space end style begin inline style space end style begin inline style left parenthesis end style begin inline style 3 end style begin inline style. end style begin inline style 5 end style begin inline style right parenthesis squared end style begin inline style space end style begin inline style equals end style begin inline style space end style fraction numerator left parenthesis 2 squared space plus 3 squared space plus straight a squared plus 11 squared right parenthesis over denominator 4 end fraction begin inline style space end style begin inline style minus end style begin inline style space end style begin inline style open parentheses begin display style fraction numerator 2 plus 3 plus straight a plus 11 over denominator 4 end fraction end style close parentheses squared end style begin inline style space end style begin inline style space end style begin inline style space end style

space begin inline style rightwards double arrow end style begin inline style space end style 49 over 9 begin inline style space end style begin inline style equals end style begin inline style space end style fraction numerator 4 space plus space 9 space plus straight a squared plus 121 over denominator 4 end fraction begin inline style minus end style begin inline style open parentheses begin display style fraction numerator 16 plus straight a over denominator 4 end fraction end style close parentheses squared end style begin inline style space end style begin inline style space end style begin inline style space end style begin inline style space end style begin inline style space end style
begin inline style rightwards double arrow end style begin inline style space end style 49 over 9 begin inline style space end style begin inline style equals end style begin inline style space end style fraction numerator 134 space plus straight a squared over denominator 4 end fraction begin inline style minus end style fraction numerator 256 space plus straight a squared plus 32 straight a over denominator 16 end fraction begin inline style space end style begin inline style space end style begin inline style space end style begin inline style space end style begin inline style space end style

49 over 9 begin inline style space end style begin inline style equals end style begin inline style space end style fraction numerator 4 straight a squared space plus 536 minus 256 minus straight a squared minus 32 straight a over denominator 16 end fraction

space begin inline style space end style begin inline style 49 end style begin inline style space end style begin inline style straight x end style begin inline style space end style begin inline style 4 end style begin inline style space end style begin inline style equals end style begin inline style space end style begin inline style 3 end style begin inline style straight a squared end style begin inline style minus end style begin inline style 32 end style begin inline style straight a end style begin inline style plus end style begin inline style 280 end style begin inline style space end style begin inline style 3 end style begin inline style straight a squared end style begin inline style minus end style begin inline style 32 end style begin inline style straight a end style begin inline style space end style begin inline style plus end style begin inline style space end style begin inline style 84 end style begin inline style space end style begin inline style equals end style begin inline style 0 end style

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3.

Let y(x) be the solution of the differential equation left parenthesis straight x space log space straight x right parenthesis dy over dx space plus straight y space equals space 2 space straight x space log space straight x comma (x  ≥1). Then, y (e) is equal to 

  • e

  • 0

  • 2

  • 2

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4.

If left parenthesis 2 space sin space straight x right parenthesis space dy over dx space plus space left parenthesis space straight y space plus 1 right parenthesis space cos space straight x space equals space 0 space and space straight y left parenthesis 0 right parenthesis space equals 1 space then space straight y open parentheses straight pi over 2 close parentheses is equal to

  • 4/3

  • 1/3

  • -2/3

  • -2/3

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5.

Let In ∫tan x dx,(n> 1) . I4 + I6 = a tan5x + bx5 + C, where C is a constant of integration, then the ordered pair (a, b) is equal to

  • open parentheses negative 1 fifth comma 0 close parentheses
  • open parentheses negative 1 fifth comma 1 close parentheses
  • open parentheses 1 fifth comma 0 close parentheses
  • open parentheses 1 fifth comma 0 close parentheses
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6.

How many real solutions does the equation x7+ 14x5+ 16x3+ 30x – 560 = 0 have?

  • 7

  • 1

  • 3

  • 3

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7.

Let the orthocentre and centroid of a triangle be A(–3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is

  • 352

  • 10

  • 210

  • 352


8.

Consider the non-constant differentiable function f of one variable which obeys the relation f(x)fy f(x - y ). If f'(0)= p and f(y) . f'(5) = q, then f'(- 5) is

  • p2q

  • qp

  • pq

  • q


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9.

If f(x)=log5(log3(x)), then f'(e) is equal to

  • e loge(5)

  • e loge(3)

  • 1eloge5

  • 1eloge3


10.

Let F(x)=ex, G(x)=e- x and H(x) = G(F(x)), where x is a real variable. Then, dHdx at x= 0 is

  • 1

  • - 1

  • - 1e

  • - e


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