ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 10 (Mathematical Inductions)

(2.02)4 s equal to

• 16 A
• 16.6496 B
• 17 C
• 18 D

If n∈Z+ then(a+x)n is a/an

• Finite series A
• Convergent series B
• Infinite series C
• Divergent series D

• 2 and 9 A
• 3 and 2 B
• 2/3 and 9 C
• 3/2 and 6 D

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 D

The 8th term of (1+2x) ^-1/2is

• -221/16 x⁷ A
• -225/18 x⁷ B
• -407/9 x³ C
• -429/16 x⁷ D

The 5th term of (3a-2b) ^-1 is

• 77b²/a⁵ A
• 16b² /243 a⁵ B
• 17b⁴/43a⁵ C
• 25b³/43a⁵ D

If n is not natural number, then the expansion (1 + x)ⁿis valid for

• 
  A
• 
  B
• 
  C
• 
  D

n(n-1)(2n-1), for all natural numbers n, is divisible by

• 12 A
• 6 B
• 2 C
• 18 D

The coefficient of x¹⁸ in (ax⁴-bx)⁹ after expansion is

• 84a³ b⁶ A
• 22a³b⁶ B
• 27a⁴b⁵ C
• 28a³b⁶ D

If a statement S(n) is true for n = i where i is some natural number and the truth of S(n) for n = k > i implies the truth of S(n) for n = k +1 then S(n) is true for all positive integers

• 
  A
• 
  B
• 
  C
• 
  D

The middle term in the expansion of (a +x)¹²is

• 7th A
• 8th B
• 9th C
• 6th D

The sum of first n even number is

• n2 A
• n(n+1) B
• n+1 C
• n+2 D

For≥ -2 , 1+3+5+......+(2n+5)

• (n+2)² A
• (n-2)² B
• 2n+1 C
• (n+3)² D

There is no integer n for which 3n is

• Even A
• Prime B
• Odd C
• Real D

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 D

The general term in the expansion of (a+x)n is

• (r-1)th term A
• (r+1)th term B
• rth term C
• none D

The no of term is the expansion of (a+x)n-1 is

• n+1 A
• n-1 B
• n C
• n-2 D

The greatest integer which divides the number 101¹⁰⁰- 1 is

• 100 A
• 1000 B
• 10000 C
• 100000 D

The greatest term in the expansion of (3+2x)⁹, when x=1 is

• 4th A
• 4th and 5th B
• 5th C
• 6th D

1+3x+6x2 +10x3 +....=

• (1+x)-3 A
• (1-x)-2 B
• (1-x)-3 C
• (1+x)-2 D

When we expand (a + 2b)⁵then

• a⁵+ 10a⁴b + 40a³b²+ 80a²b³+ 80ab⁴+ 32b⁵ A
• a⁵+ a⁴b + a³b²+ a²b³+ ab⁴+ b⁵ B
• 5a⁵+ 4a⁴b + 3a³b²+ 2a²b³+ 1 ab⁴+ b⁵ C
• None D

The first three terms in the expansion of (1 + x)³are

• 1 + 3x +6x² A
• 1- 3x + 6x²\ B
• -3 -3x -6x² C
• 1- 3x -6x² D

For n€ N,2^n>2 > n is to only when

• n<2 A
• n≤ 4 B
• n≥ 4 C

Number of terms in the expansion of (a+x)ⁿis

• n - 1 A
• n + 1 B
• n + 2 C
• n + 3 D

If n is any positive integer then n! > 2^n-1for

• 
  A
• 
  B
• 
  C
• 
  D

• 405 / 256 A
• 504 / 259 B
• 450 / 263 C
• None D

(x³-1/2x)⁶ is

• 15/16 x² A
• 2/13 x² B
• 17/7 x² C
• 16/15 x² D

There is no integer n for which 3ⁿ is

• Odd A
• even B
• Natural C
• Prime D

• n < 8/5 A
• n < 5/8 B
• |n| < 8/5 C
• |n|>8/5 D

n² - 1 divisible by 8 when n is

• an odd integer A
• an even integer B
• Irrational C
• Prime Number D