ECAT Pre Engineering MCQ Test With Answer for Chapter 8 Mathematics

A series consisting of an unlimited number of terms is termed as an

• Finite sequence A
• Infinite sequence B
• ^{Infinite series} C
• geometric sequence D

Which term of the A.P 5,8,11,24.............is 320

• 104th A
• 106th B
• 105th C
• 64th D

The three consecutive numbers a,√ab,b are in

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

Sum of first n terms of an arithmetic series is

• 
  A
• 
  B
• 
  C
• 
  D

If a₁and r are the first term and the common ratio respectively then (n + 1)th term of the G.P. is

• 0 A
• a₁r^n-1 B
• a₁rⁿ⁺¹ C
• a₁rⁿ D

The general term of a sequence is denoted by

• a₁ A
• a_n B
• n C
• s_n D

The general term of the A.P. is

• a₁+ (n - 1) d A
• n + (a₁- 1) d B
• d + (n - 1) a₁ C
• None of these D

An infinite sequence has no

• nth term A
• Last term B
• Sum C
• None of these D

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

• 400 A
• 397 B
• 404 C
• 408 D

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

If a, b, c, d, e, f are in A.P.,then e-c is equal to

• 2(c - a) A
• 2(f - d) B
• 2(d - c) C
• d - c D

If the pth, qth, and rth terms of an A.P. are in G.P:., then the common ratio of the G.P. is

• 
  A
• 
  B
• 
  C
• 
  D

A,G,H are in

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

Every term of a G.P. is positive and also every term is the sum of two preceding terms. Then the common ratio of the G.P. is

• 
  A
• 
  B
• 
  C
• 
  D

If G is a G.M between a and b then a,G,b are in

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

H.M. between 3 and 7 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

The number of divisors of 1029, 1547 and 122 are in

• A.P. A
• G.P. B
• H.P. 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

An A.P., a G.P. and a H.P. have the same first and last terms and the same odd numbers of terms, the middle terms of the three series are in

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

The A.M. of two numbers is 34 and G.M. is 16, the numbers are

• 2 and 64 A
• 64 and 3 B
• 64 and 4 C
• None of these D

The third term of a G.P. is the square of first term. If the second term is 8, then the 6th term is

• 120 A
• 124 B
• 128 C
• 132 D

• 0 A
• 1 B
• 2 C
• 3 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

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 all members of a sequence are real numbers then it is called a

• Series A
• Function B
• Real sequence C
• Range 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 sum of first 60 natural numbers is

• 1830 A
• 3660 B
• 1640 C
• 1770 D

The 10th common term between the series 3+7+11+....... and 1 + 6 +11 + ....... is

• 191 A
• 193 B
• 211 C
• None of these D