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

The sum of first n even number is

• n2 A
• n(n+1) B
• n+1 C
• n+2 D

The expansion of (1 + 2x)^-2is valed if

• | x | < 1/2 A
• | x | < 1 B
• | x | < 2 C
• | x | < 3 D

The expansion of (1 - 3x)^-1is valid if

• | x | < 1 A
• | x | < 3 B
• | x | < 1/3 C
• None of these D

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

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

The coefficient of the third term of (8a-b)^1/3, after simplification is

• -228 A
• 1/288 B
• 1/220 C
• -1/177 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

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 3 + 6 + 9 + ....+ 3n = ______

• 
  A
• 
  B
• 
  C
• 
  D

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

The coefficient of the second term of (a+b)⁴ is

• 1 A
• 9 B
• 3 C
• 5 D

• 28 / 81 A
• 28 / 243 B
• 81 / 28 C
• 243 / 82 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

• Even A
• Odd B
• Prime C
• None of these D

The term involving x⁴in the expansion of (3 - 2x)⁷is

• 120 A
• 1512 B
• 1250 C
• 15120 D

If the expansion of (1 + x)²⁰, then co-efficient of rth ad (r + 4)th term are equal, then r is

• 7 A
• 8 B
• 9 C
• 10 D

a + x is ______

• A trinomial A
• A binomial B
• A monomial C
• None of these D

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

• 
  A
• 
  B
• 
  C
• 
  D

If the exponent in the binomial expansion is 6, then the middle term is

• 2nd term A
• 3rd term B
• 4th term C
• 5th term 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 number of terms in the expansion of (a + x)¹²is

• 13 A
• 12 B
• 11 C
• 10 D

For n€ N,2^n>2 > n is to only when

• n<2 A
• n≤ 4 B
• n≥ 4 C

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

• 71 A
• -22 B
• 27 C
• 28 D

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

• 24 A
• 25 B
• 9 C
• 13 D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 2 A
• 7 B
• 8 C
• 12 D

The term independent of x is the expansion (x³+1/x)¹²

• 295 A
• 495 B
• 395 C
• 722 D

The sum of even coefficient in the binomial expansion is

• 2ⁿ⁺¹ A
• 2ⁿ B
• 2^n-1 C
• 2n D

• ⁿC_r A
• ⁿ⁺¹C_r+1 B
• ⁿC_r+1 C
• None D

The sum of co-efficient in (1+x-3x²)⁴¹⁶³is

• 0 A
• 1 B
• -1 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