ECAT Pre Engineering MCQ Test With Answer for Chapter 8 Mathematics

A sequence of number whose reciprocals form an arithmetic sequence is called

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

A number A is said to be the A.M between the two numbers a and b if a, A, b are in

• A.M A
• A.P B
• G.P C
• G.M D

99th term of the series 2 + 7 + 14 + 23 + 34 + ..... is

• 9998 A
• 9999 B
• 10000 C
• None of these D

an - an-1 will be common difference in an A.P if

• n = 1∀n∈ N A
• n>1∧n∈N B
• n∈Z C
• None of the above D

If Sn is a definite number as n → ∞,then the geometric series is

• Convergent A
• Divergent B
• Oscillatroy 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

• 
  A
• 
  B
• 
  C
• 
  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

No term of a harmonic sequence can be

• 0 A
• 1 B
• 2 C
• 3 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 sides of a right angled triangle are in A.P The ratio of sides is

• 1:2:3 A
• 3:4:5 B
• 2:3:4 C
• 5:8:3 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

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

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

A Geometric Series is divergent only if

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

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

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

If P, Q, R be the A.M., G.M., H.M. respectively between any two rational numbers a and b, then P - Q is

• 
  A
• 
  B
• 
  C
• 
  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 a₁= 3, r = 2, then the nth term of the G.P. is

• 2.3^n-1 A
• 3.2ⁿ B
• 3.2ⁿ⁺¹ C
• 3.2^n-1 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

• 2 A
• -3/2 B
• 1 C
• 0 D

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

The sum of all 2 digit number is

• 4750 A
• 3776 B
• 4895 C
• 4905 D

No term of a geometric sequence can be

• 0 A
• 1 B
• 2 C
• 3 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

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

If A, G, H are the arithmetic, geometric and harmonic means between a and b respectively then A, G, H are in

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

If p, q, r and in A.P., a is G.M. between p and q and b is G.M. between q and r, then a², q², b²are in

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

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

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