JEE Maths - Sequence and Series

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Question - 1

The value of x satisfying
\({ log }_{ a }x+{ log }_{ \sqrt { a } }x+{ log }_{ 3\sqrt { a } }x+...{ log }_{ a\sqrt { a } }x=\cfrac { a+1 }{ 2 } \) is mn. Find m x n.

  • A 1
  • B 5
  • C 2
  • D 3

Question - 2

Jairam purchased a house in Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual installment of Rs. 1000 with 10% per annum interest. Money is to be paid by Jairam is A. Find A/100.

  • A 205
  • B 400
  • C 320
  • D 185

Question - 3

If the roots of the equation x2-12x2-39x-28 are in A.P., then sum of all possible values of common difference will be

  • A 0
  • B 1
  • C 2
  • D 3

Question - 4

Let n(>1) be a positive integer, then the largest integer m such that(nm+1) divides (1+n+n2+...+n127),is 

  • A 64
  • B 35
  • C 52
  • D 70

Question - 5

If f(x) is a function satisfying f(x+y)=f(x)f(y) for all x,y,∈ N such that f(1)=3 and \(\sum _{ x=1 }^{ n }{ f(x) } =120\).Then the value of n is

  • A 3
  • B 2
  • C 4
  • D 1

Question - 6

α,β are the roots of the equation x2-3x+a=0 and γ,ઠ are the roots of the equation x2-12x+b=0 If α,β,γ,δ form an increasing G.P., then a + b is

  • A 14
  • B 25
  • C 32
  • D 34

Question - 7

If a, b, c are the positive integers, then (a + b)(b + c)(c + a) is greater than equal to Aabc. Find minimum possible value of A.

  • A 2
  • B 6
  • C 8
  • D 4

Question - 8

In a G.P. the sum of three numbers is 14, if 1 is added to first two numbers and subtracted from third number, the series becomes A.P., then the greatest number is

  • A 1
  • B 2
  • C 8
  • D 9

Question - 9

2sinθ+2cosθ is greater than 21-1/A.Find A2.

  • A 1
  • B 2
  • C 4
  • D 4

Question - 10

The sum of the series \(\cfrac { 1 }{ 1+1^{ 2 }+{ 1 }^{ 4 } } +\cfrac { 2 }{ 1+{ 2 }^{ 2 }+{ 2 }^{ 4 } } +\cfrac { 3 }{ 1+{ 3 }^{ 2 }+{ 3 }^{ 4 } } +...\) to 4 terms is M. Find 21M.

  • A 9
  • B 10
  • C 8
  • D 8
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