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

The sum of the coefficient in the expansion of (a + x)⁵is

• 32 A
• 16 B
• 8 C
• 5 D

The sum of the odd coefficients in the expansion of (a + x)⁴is

• 14 A
• 12 B
• 8 C
• 4 D

The first three terms in the expansion of (1 + x)^-2are ______

• 1 - 2x + 3x² A
• 1 - 2x - 3x² B
• 1 + 2x + 3x² C
• -2 -2x + 3x² D

For each even natural number n (n²-1) is divisible by

• 6 A
• 3 B
• 4 C
• 8 D

The proposition S(n) for any n∈ N is only true if k∈ N and

• S(k +1) is true A
• S(1) is true and S(k+1) is true whenever S (k) is true B
• S(k+1) is true whenever S (k) is true C
• S(k) is true D

If n is any positive integer then 4ⁿ>3ⁿ+ 4 is true for all

• 
  A
• 
  B
• 
  C
• 
  D

If | x | < 1, then the first two terms of (1 - x)^1/2are

• 
  A
• 
  B
• 
  C
• 
  D

If n is odd then the middle terms in the expansion of (a + x)ⁿare

• 
  A
• 
  B
• 
  C
• 
  D

The sum of even coefficient in the binomial expansion is

• 2ⁿ⁺¹ A
• 2ⁿ B
• 2^n-1 C
• 2n D

The exponent of x in 10th term in the expansion of (a+x)n

• 10 A
• 12 B
• 11 C
• 9 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

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

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

The middle term of [1/x-x]¹⁰ is

• -152 A
• -252 B
• 371 C
• -421 D

The last term of (1+2x)-2

• (-1)-2 (2x)-2 A
• (-1)-4(-2x)-2 B
• (-1)-3(2x)-3 C
• Does not exist D

The middle term of (x-y)⁸is

• 25 x⁴y⁴ A
• 70 x⁴y⁴ B
• 120 x⁴y⁴ C
• 97x⁴y⁴ D

For all positive integral value of n,3ⁿ< n! , when

• n> 6 A
• n< 6 B
• n<11 C
• n>11 D

• 8 A
• 9 B
• 10 C
• 11 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

If n∈Z+ then(a+x)n is a/an

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

The seventh term of (x3+1/x)8is

• 71 A
• -22 B
• 27 C
• 28 D

The number of terms in the expansion of (a + b)⁹is

• 10 A
• 11 B
• 9 C
• 12 D

The expansion (1 + x)^-3holds when

• |x| > 1 A
• |x| < 1 B
• x < 1 C
• x > 1 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

(2.02)4 s equal to

• 16 A
• 16.6496 B
• 17 C
• 18 D

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 D

For n€ N,2^n>2 > n is to only when

• n<2 A
• n≤ 4 B
• n≥ 4 C

If n is add the expansion (a + x)ⁿhas middle terms

• 2 A
• 3 B
• 4 C
• 5 D

The coefficient of xn in the expansion of (1-x)-1 is

• (-1)n2n A
• 1 B
• (-1)n(n+1) C
• (n+1) D

In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n=

• 12 A
• n=14 B
• 17 C
• n=15 D

The fifteenth term of (3-a)¹⁵ is

• -17a¹² A
• -945a¹³ B
• -941a¹³ C
• -515a¹² D