For any three positive real numbers a, b and c, (25a2 + b2) + 25

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 Multiple Choice QuestionsMultiple Choice Questions

11.

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

  • 18 Months

  • 19 Months

  • 20 Months

  • 20 Months

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12.

A person is to count 4500 currency notes. Let a denote the number of notes he counts in the nth minute. If a1 = a2 = ... = a10 = 150 and a10, a11, ...are in an AP with common difference -2, then the time taken by him to count all notes is

  • 24 min

  • 34 min

  • 125 min

  • 125 min

349 Views

13. Let space straight S subscript 1 space equals space sum from straight j space equals 1 to 10 of space straight j space left parenthesis negative 1 right parenthesis space to the power of 10 straight C subscript straight j space comma space straight S subscript 2 space equals space sum from straight j space equals 1 to 10 of space straight j to the power of 10 straight C subscript straight j space and space straight S subscript 3 space equals sum from straight j space equals 1 to 10 of space straight j squared space to the power of 10 straight C subscript straight j

Statement-1: S3 = 55 × 29.
Statement-2: S1 = 90 × 28 and S2 = 10 × 28.

  • Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

  • Statement-1 is true, Statement-2 is true; statement-2 is not a correct explanation for Statement-1. 

  • Statement-1 is true, Statement-2 is false.

  • Statement-1 is true, Statement-2 is false.

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14.

For any three positive real numbers a, b and c, (25a2 + b2) + 25(c2 – 3ac) = 15b(3a + c), Then

  • b , c and a are in G.P

  • b, c and a are in A.P

  • a, b and c are in A.P

  • a, b and c are in A.P


B.

b, c and a are in A.P

225a2 + 9b2 + 25c2 – 75ac – 45ab – 15bc = 0
(15a)2 + (3b)2 + (5c)2 – (15a)(3b) – (3b)(5c) – (15a) (5c) = 0
1/2[(15a – 3b)2 + (3b – 5c)2 + (5c – 15a)2] = 0
15a = 3b , 3b = 5c , 5c = 15a
5a = b , 3b = 5c , c = 3a
a/1 = b/5 = c/3
a = λ, b = 5λ, c = 3λ
a, c, b are in AP

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15.

Let a, b, c ∈ R. If f(x) = ax2 + bx + c is such
that a + b + c = 3 and f(x + y) = f(x) + f(y) + xy, ∀x,y ∈ R,then sum from straight n space equals 1 to 10 of space straight f space left parenthesis straight n right parenthesis is equal to

  • 225

  • 330

  • 165

  • 165

330 Views

16.

The sum to infinity of the series 1 space plus space 2 over 3 space plus space 6 over 3 squared space plus space 10 over 3 cubed space plus space 14 over 3 to the power of 4 space plus.... space is

  • 2

  • 3

  • 4

  • 4

147 Views

17.

Statement 1: The variance of first n even natural numbers is fraction numerator straight n squared minus 1 over denominator 4 end fraction
Statement 2: The sum of first n natural numbers is fraction numerator straight n space left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction and the sum of squares of first n natural numbers is fraction numerator straight n left parenthesis straight n plus 1 right parenthesis left parenthesis 2 straight n plus 2 right parenthesis over denominator 6 end fraction

  • Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1

  • Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.

  • Statement–1 is true, statement–2 is false.

  • Statement–1 is true, statement–2 is false.

265 Views

18.

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

  • 1 half left parenthesis 1 minus square root of 5 right parenthesis
  • 1 half square root of 5
  • square root of 5
  • square root of 5
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19.

If p and q are positive real numbers such that p2 + q2 = 1, then the maximum value of (p + q) is

  • 2

  • 1/2

  • fraction numerator 1 over denominator square root of 2 end fraction
  • fraction numerator 1 over denominator square root of 2 end fraction
123 Views

20.

The sum of the series fraction numerator 1 over denominator 2 space factorial space end fraction minus fraction numerator 1 over denominator 3 factorial end fraction space plus space fraction numerator 1 over denominator 4 factorial end fraction space..... space upto space infinity

  • e-2

  • e–1

  • e-1/2

  • e-1/2

131 Views

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