ECAT Pre Engineering MCQ Test With Answer for Chapter 8 Mathematics

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

if a₁ =3, d=7 and a_n =59 , then the number of terms in A.P is

• 7 A
• 9 B
• 11 C
• 13 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

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

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

• 136 A
• -136 B
• 148 C
• -148 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

• 1, 1/2, 0 A
• 1, 2, 1 B
• 1, 2, 3 C
• 1, 2, 0 D

Write the first four terms of the sequence if a_n= (-1)ⁿn²

• -1, 4, -9, 16 A
• 1, -4, 9, 16 B
• 1, 4, 9, 16 C
• None of these D

The third term of the sequence a_n= (-1)^n-1(n-7) is ______

• 8 A
• 4 B
• -4 C
• 8 D

Arithmetic mean between a and b is

• 
  A
• 
  B
• 
  C
• 
  D

Three consecutive terms of a progression are 30, 24, 20. The next terms of the progression is

• 
  A
• 
  B
• 
  C
• 
  D

• 15/23 A
• 7/15 B
• 7/8 C
• 15/7 D

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

• Convergent A
• Divergent B
• Oscillatroy C
• None of these D

An infinite arithmetic series is always

• Convergent A
• Oscillatory B
• Divergent C
• None of these D

• 12 A
• 13 B
• 14 C
• 15 D

The sum of n terms of a series is denoted by

• d A
• n B
• S_n C
• a_n D

An infinite sequence has no

• nth term A
• Last term B
• Sum 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 x, y, z are the pth, qth, rth terms of an A.P. and also of G.P., then x^y-z. y^z-x. z^x-yeqals

• xyz A
• 0 B
• 1 C
• None of these D

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

The nth term of an A.P., is 12-4n. Its common difference is

• 8 A
• 4 B
• 4 C
• 16 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

3, 6, 12,.... is

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

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

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

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

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

• 3 A
• -4 B
• 7 C
• 1 D

The sum of first 60 natural numbers is

• 1830 A
• 3660 B
• 1640 C
• 1770 D

The fifth term of the sequence a_n= 2n + 3 is ______

• 13 A
• -13 B
• 8 C
• 3 D