ECAT Pre Engineering MCQ Test With Answer for Chapter 8 Mathematics

The n numbers A₁,A₂,A₃,.....A_nare called an arithmetic means between a and b if a.A₁,A₂,A₃.....A_n, b is ______

• An arithmetic series A
• An arithmetic sequence B
• A geometric sequence C
• A harmonic sequence D

• 2 A
• -3/2 B
• 1 C
• 0 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

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

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

• 1/2 A
• 2 B
• 1/4 C
• 4 D

• 
  A
• 
  B
• 
  C
• 
  D

• 15/23 A
• 7/15 B
• 7/8 C
• 15/7 D

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

• 3.5 A
• 3 B
• 4 C
• None of these D

If x,y are two positive distinct numbers then

• A>G>H A
• A<G<H B
• A=G=H C
• None of these D

The common ration of a geometric sequence cannot be

• 0 A
• 1 B
• 2 C
• 3 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

The nth term of a G.P. is

• a₁rⁿ A
• a₁rⁿ⁺¹ B
• a₁r^n-1 C
• a₁r^-n D

An indicated sum of terms of a sequence is represented by

• Sn A
• an B
• S(n) C
• {Sn} D

A sequence is a functions whose domain is a subset of the set of

• Natural numbers A
• Real numbers B
• Whole numbers C
• Rational numbers D

• 
  A
• 
  B
• 
  C
• 
  D

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

A Geometric Series is divergent only if

• |r|>1 A
• |r|≥1 B
• |r|=1 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

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

• 
  A
• 
  B
• 
  C
• 
  D

Find the geometric mean between 4 and 16

• 
  A
• 
  B
• 
  C
• 
  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

How many term are there in the A.P, in which a₁ = 11 , a_n =68, d=3

• 30 A
• 27 B
• 20 C
• 21 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

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 a₁, r and a_nare the first term, common ratio and the nth term respectively of a G. P. then a_n=

• a₁rⁿ A
• a₁r^n-1 B
• a₁rⁿ⁺¹ C
• a₁r 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

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

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

• 136 A
• -136 B
• 148 C
• -148 D