ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 8 (Sequences and Series)

p, q, r and s are integers. If the A.M. of the roots of x2- px + q2= 0 and G.M. of the roots of x2- rx + s2= 0 are equal, then

• q is an odd integer A
• r is an even integer B
• p is an even integer C
• s is an odd integer D

The 26th term of the A.P -2,-4,10,.............is

• 136 A
• -136 B
• 148 C
• -148 D

The harmonic mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  D

How many numbers are there between 103 and 750 which are divisible by 6

• 125 A
• 107 B
• 108 C
• 113 D

The third term of a G.P. is 4, The product of first five terms is

• 43 A
• 45 B
• 46 C
• None of these D

The nth term of an A.P is (3n+5) Its 75th term is

• 26 A
• 7 B
• 21 C
• Cannot be determined D

An indicated sum of terms of a sequence is represented by

• Sn A
• an B
• S(n) C
• {Sn} D

The sum of the squares of three distinct real numbers, which are in G.P., is S². if their sum isαS then

• 
  A
• 
  B
• 
  C
• 
  D

H₁, H₂, H₃, .... H_nare called n harmonic means between a and b if a, H₁, H₂, H₃, ... H_nb are in

• H.P. A
• G.P. B
• A.P. C
• None of these D

• 1 A
• 2 B
• 3/2 C
• 5/2 D

An A.P. consists of n(odd terms) and its middle term is m. then the sum of the A.P. is

• 2 mn A
• 1/2 mn B
• mn C
• mn² D

Arithmetic mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

The5thand 13th terms of an A.P are 5 and-3 respectively The first term of the A.P is

• 1 A
• -15 B
• 9 C
• 2 D

For an arithmetic series to be convergent it is necessary that the series has

• Finite terms A
• d<0 B
• Infinite terms C
• None of these D

If a, b, c are in AP., a, b, c are in G.P. then A, m²b, c are in

• A.P. A
• G.P. B
• H.P. C
• None of these D

A number A is called the arithmetic mean between a and b if a, A, b is ______

• Arithmetic sequence A
• Geometric sequence B
• Harmonic sequence C
• Arithmetic sequence D

If three unequal numbers p, q, r are in H.P. and their squares are in A.P., then the ration p : q : r is

• 
  A
• 
  B
• 
  C
• 
  D

A Geometric Series is divergent only if

• |r|>1 A
• |r|≥1 B
• |r|=1 C
• None of these D

• 15/23 A
• 7/15 B
• 7/8 C
• 15/7 D

If S_rdenotes the sum of the first r terms of a G.P., then S_n, S_2n- S_n, S_3n- S_2nare in

• A.P. A
• G.P. B
• H.P. C
• None of these D

G is geometric mean between a and b if a, G, b is

• A.P. A
• G.P. B
• H.P. C
• None of these D

Let a₁, a₂, a₃, a₄and a₅be such that a₁, a₂, and a₃are in A.P., a₂, a₃and a₄are in G.P and a₃, a₄and a₅are in H.P. Then, a₁, a₃and a₅are in

• G.P. A
• A.P. B
• H.P. C
• None of these D

The 7th term of the A.P 7,11,15,is

• 24 A
• 31 B
• 26 C
• 23 D

If the domain of sequence is finite set then the sequence is called

• geometric sequence A
• infinite sequence B
• finite sequence C
• arithmetic sequence D

Let S_ndenote the sum of the first n terms of an A.P. If S_2n= 3 S_n: S_nis equal to

• 4 A
• 6 B
• 8 C
• 10 D

If a_n= 2n -3, write the first four terms

• -3, -1, 1, 3 A
• 1, 3, 5, 7 B
• -1, 1, 3, 5 C
• None of these D

In an A.P,a +(n-a)d is

• 1st term A
• General term B
• Last term C
• None of these D

If a^x= b^y= c^zand a, b, c are in G.P. then x, y, z are in

• A.P. A
• G.P. B
• H.P. C
• None of these D

A function whose domain is a subset of natural numbers is called ______

• Identity function A
• Sequence B
• Onto function C
• Series D