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

Digit in the unit place of the number 183! + 3¹⁸³

• 7 A
• 6 B
• 3 C
• 0 D

There is no integer n for which 3ⁿ is

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

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

• 1 A
• 9 B
• 3 C
• 5 D

(1 - x)³= ______

• 1 + 3x + 3x²+ x³ A
• 1 + x + x²+ x³ B
• 1 - x + x²- x³ C
• 1 - 3x + 3x²- x³ D

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

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

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

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

The 7th term of (3⁸ + 6⁴x)^11/4 is

• -19217/3 x⁶ A
• 189/2 6⁴x B
• 2227/12 x³ C
• -19712/3 x⁶ D

If n is any positive integer ,t hen 2+4+6+......+2 n=

• 2ⁿ-1 A
• 2ⁿ+1 B
• n²+1 C
• n(n+1) D

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

• 295 A
• 495 B
• 395 C
• 722 D

• 8 A
• 9 B
• 10 C
• 11 D

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

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

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

If n∈Z+ then(a+x)n is a/an

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

For n€ N,2^n>2 > n is to only when

• n<2 A
• n≤ 4 B
• n≥ 4 C

For every positive integers n 1+5+9+....+ (4n - 3) is

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

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

• 24 A
• 25 B
• 9 C
• 13 D

a + x is ______

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

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

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

The proposition S(n) is true∀n∈N,S(k+1) true when ______is true

• S(1) A
• Both a & c B
• S(k) C
• None D

The sum of the even coefficients in the expansion (1 + x)ⁿis

• n² A
• 2^n-2 B
• 2^n-1 C
• 2ⁿ D

The sum even binomial coefficient of (3+2x)5 is ______term

• 16 A
• 30 B
• 8 C
• 32 D

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

The sum of the cubes of three consecutive natural number is divisible by

• 9 A
• 6 B
• 5 C
• 10 D

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

• 2 A
• 3 B
• 4 C
• 5 D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 10 A
• 11 B
• 9 C
• 12 D

The coefficient of xn in the expansion of (1-2x)-1 is

• (-1)n2n A
• 2n B
• (-1)(n+1)xr C
• (n+1)2n D

• ab=-1 A
• ab = 1 B
• ab = 2 C
• None D