Mathematics - Sequences & Series

Buy AP EAMCET Engineering Practice test pack

Question - 1

If the sum of the first 2n terms of the A.P. 2, 5, 8, .... is equal to the sum of the first n terms of the A.P. 57, 59, 61, ..... then n equal equals

  • A 10
  • B 12
  • C 11
  • D 13

Question - 2

If x, y, z (x>1, y>1, z>1) are three positive numbers in G.P. then \({1\over {1+1n\ x}}\), \({1\over {1+1n\ y}}\), \({1\over {1+1n\ z}}\) are in

  • A A.P.
  • B G.P.
  • C H.P.
  • D NONE OF THESE

Question - 3

Let an be the nth terms of a G.P. of positive integers. Let \(\overset { 100 }{ \underset { n=1 }{ \sum { { a }_{ 2n } } } } \quad =\quad \alpha \quad and\quad \overset { 100 }{ \underset { n=1 }{ \sum { { a }_{ 2n } } } } +1\quad =\quad \beta \) such that \(\alpha \quad \neq \quad \beta \).  Thus common ratio of the G.P. is

  • A \(\frac { \alpha }{ \beta } \)
  • B \(\frac { \beta }{ \alpha } \)
  • C \({ \left( \frac { \alpha }{ \beta } \right) }^{ 1/2 }\)
  • D \({ \left( \frac { \beta }{ \alpha } \right) }^{ 1/2 }\)

Question - 4

Let T be the rth term of an A.P. for r = 1, 2, 3 .... If for some positive integers m, n \({ T }_{ m }\quad =\quad \frac { 1 }{ n } ,\quad { T }_{ n }\quad =\quad \frac { 1 }{ m } \), then Tmn equals

  • A \(1\over mn\)
  • B \({1\over m}+{1\over n}\)
  • C 1
  • D 0

Question - 5

Let the positive numbers a, b, c, d be in A.P. Then abc, abd, bcd are

  • A not in A.P./G.P./H.P.
  • B in A.P.
  • C in G.P.
  • D in H.P.

Question - 6

Consider an infinite series with first term a and common ratio r. If its sum is 4 and the second term is \(3\over 4\), then

  • A \(a\quad =\quad \frac { 7 }{ 4 } ,\quad r\quad =\quad \frac { 3 }{ 7 } \)
  • B \(a\quad =\quad 2,\quad r\quad =\quad \frac { 3 }{ 8 } \)
  • C \(a\quad =\quad \frac { 3 }{ 2 } ,\quad r\quad =\quad \frac { 1 }{ 2 } \)
  • D \(a\quad =\quad 3,\quad r\quad =\quad \frac { 1 }{ 4 } \)

Question - 7

If a, b , c are positive numbers, the least value of \(\frac { a+b }{ c } +\frac { b+c }{ a } +\frac { c+a }{ b } \), is

  • A 6
  • B 4
  • C 3
  • D NONE OF THESE

Question - 8

If a, b, c are positive numbers then value of \((a+b+c)\left( \frac { 1 }{ a } +\frac { 1 }{ b } +\frac { 1 }{ c } \right) \), is

  • A \(\ge 10\)
  • B \(\ge 9\)
  • C \(\ge 12\)
  • D NONE OF THESE

Question - 9

If the 9th term of A.P. is zero, then ratio of 29th term to 19th term is

  • A 2 : 1
  • B 3 : 1
  • C 9 : 1
  • D NONE OF THESE

Question - 10

The sum of the first m terms of an A.P. is the same as the sum of the n terms, where \(m\quad \neq \quad n\). Then the sum of the first (m+n) terms is

  • A m
  • B n
  • C 0
  • D NONE OF THESE
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next