ECAT Pre Engineering MCQ Test With Answer for Chapter 8 Mathematics

Given two numbers a and b. Let A denote the single A.M. between these and S denote the sum of n A.M.'s between them. Then S/A depends upon

• n, a, b A
• n, a B
• n, b C
• n D

No term of a geometric sequence can be

• 0 A
• 1 B
• 2 C
• 3 D

• 
  A
• 
  B
• 
  C
• 
  D

Write the first four terms of the arithmetic sequence 5, 2, -1, ... is

• 3 A
• -4 B
• 7 C
• 1 D

For an A.P common difference d

• Can be zero A
• May or may not zero B
• Cannot be zero C
• None of these D

Find the sum of the infinite geometric series 2 + 1 + 0.5 + ....

• 3.5 A
• 3 B
• 4 C
• None of these D

An indicated sum of terms of a sequence is represented by

• Sn A
• an B
• S(n) C
• {Sn} D

What is the 26th term of the sequence, if its general term is a_{n = (-1)}ⁿ⁺¹

• 2 A
• 26 B
• 27 C
• 1 D

The difference of two consecutive terms of an A.P is called the

• Common difference A
• Common ratio B
• Geometric series C
• Geometric mean D

The series obtained by adding the terms of a geometric sequence is called

• Infinite series A
• Arithmetic series B
• Geometric series C
• Harmonic series D

The sum of first twenty odd integers in A.P is

• 400 A
• 397 B
• 404 C
• 408 D

-2, 1, 4, 7,.... is ______

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

A Series which does not coverage to a Unique sum is called

• Harmonic Series A
• Oscillatroy Series B
• Arithmetic Series C
• None of these 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

• 
  A
• 
  B
• 
  C
• 
  D

The fifth term of an A.P. Whose first term is 5 and common difference is 3,is

• 20 A
• 17 B
• 25 C
• 30 D

• 2²- n - 1 A
• 1 - 2^-n B
• n + 2^-n-1 C
• 2ⁿ- 1 D

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

• 24 A
• 31 B
• 26 C
• 23 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

If a₁, r are first term and the common ratio respectively then the sum of an infinite geometric series is

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

Arithmetic mean between x - 3 and x + 5 is

• x + 1 A
• x + 2 B
• x + 3 C
• x + 4 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 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

The formula an = arn-1represents

• nth term of G.P A
• Sum of the first n terms B
• G.M between a and b C
• None of these D

If 5,7 and 9 are A.Ms between a and b, then a and b is equal to

• 2 and 12 A
• 1 and 10 B
• 3 and 11 C
• -7 and 2 D

A,G,H are in

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

The numbers of G₁, G₂, G₃...... G_nare called n geometric means between a and b is a, G₁, G_2,G₃, ... G_n, b are in

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

5th term of a G.P. is 2, then the product of first 9 terms is

• 256 A
• 128 B
• 512 C
• None of these 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