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

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

• 71 A
• -22 B
• 27 C
• 28 D

If x+y+z+......+2n = 2n+1-1∀n∈W,then cube root of xyz is equal to

• 1 A
• 4 B
• 2 C
• 8 D

The positive integer just greater than (1+0.0001)¹⁰⁰⁰⁰is

• 4 A
• 5 B
• 2 C
• 3 D

• ¹⁰C₆ A
• ¹⁰C₅ B
• ¹⁰C₄ C
• None D

If a statement S(n) is true for n = 1 and the truth of S(n) for n = k implies the truth of S(n) for = k + 1, then S(n) is true for all

• Real numbers n A
• Integers n B
• Positive integers n C
• None of these D

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

• 1 A
• 9 B
• 3 C
• 5 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

(51)⁴is equal to

• 7065201 A
• 8065201 B
• 6765201 C
• 6565201 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

(2.02)4 s equal to

• 16 A
• 16.6496 B
• 17 C
• 18 D

The coefficient of x¹⁰in the expansion (x³+3/x²)¹⁰is

• 1700 A
• 17023 B
• 17027 C
• 17010 D

The sum of coefficients in the binomial expansion equals to

• 2 A
• 2ⁿ⁺¹ B
• 2^n-1 C
• 2ⁿ D

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

• 6 A
• 3 B
• 4 C
• 8 D

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

• 2 A
• 3 B
• 4 C
• 5 D

The number of terms in the expansion of (a + x)¹²is

• 13 A
• 12 B
• 11 C
• 10 D

1st four terms of the expansion (1-x)^-2are

• 1 + 2x + 3x²+ 4x³ A
• 3x²+ 2x + 1 B
• 1 + 3x + 4x²+ 5x³ C
• None of these D

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

• 14 A
• 12 B
• 8 C
• 4 D

(1 + 2x)⁴= ______

• 1 + 4x + 6x²+ 4x³+ x⁴ A
• 1 - 4x + 6x²- 4x³+ x⁴ B
• 1 - 8x + 24x²- 32x³+ 16x⁴ C
• 1 + 8x+ 24x²+ 32x³+ 16x⁴ D

If in the expansion of (1+x)ⁿ, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x=

• 4 A
• 5 B
• 6 C
• 7 D

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

The term involving x4 the expansion (3-2x)7 is

• 217 x4 A
• 15120x4 B
• 313x4 C
• -25x4 D

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

• 295 A
• 495 B
• 395 C
• 722 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

If (1+x-2x³)⁶= 1+a₁x + a₂x²+ a₃x³+ ..... the the value of a₂+ a₄+ a₆+ .....+a₁₂will be

• 32 A
• 31 B
• 64 C
• 1024 D

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

• 10 A
• 12 B
• 11 C
• 9 D

If the 4th term in the expansion of (px + x^-1)^mis 2.5 for all x∈ R, then

• 
  A
• 
  B
• 
  C
• 
  D

If n is any positive integer then 2ⁿ> 2(n + 1) is true for all

• 
  A
• 
  B
• 
  C
• 
  D

If n∈Z+ then(a+x)n is a/an

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

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

• 
  A
• 
  B
• 
  C
• 
  D