ECAT Pre Engineering MCQ Test With Answer for Chapter 10 Mathematics

In the expansion of (a + x)ⁿthe sum of exponents of a and x in each term of the expansion is

• n + 1 A
• n - 1 B
• n C
• 2n 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 sum of the cubes of three consecutive natural number is divisible by

• 9 A
• 6 B
• 5 C
• 10 D

The fifteenth term of (3-a)¹⁵ is

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

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

• 71 A
• -22 B
• 27 C
• 28 D

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

• 32 A
• 16 B
• 8 C
• 5 D

• 
  A
• 
  B
• 
  C
• 
  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

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

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 D

If the sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is

• 1594 A
• 792 B
• 924 C
• 2924 D

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

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

• 6 A
• 3 B
• 4 C
• 8 D

There is no integer n for which 3n is

• Even A
• Prime B
• Odd C
• Real D

The middle term of [1/x-x]¹⁰ is

• -152 A
• -252 B
• 371 C
• -421 D

If (1+x)ⁿ=C₀+ C₁x +C₂x²+ ......+C_nx¹then C₀C₂+ C₁C₃+ C₂C₄+ .....+C_n-2C_n=

• 
  A
• 
  B
• 
  C
• 
  D

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

The sum of first n even number is

• n2 A
• n(n+1) B
• n+1 C
• n+2 D

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

• 2 A
• 3 B
• 4 C
• 5 D

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

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

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

• 16 A
• 30 B
• 8 C
• 32 D

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

• 
  A
• 
  B
• 
  C
• 
  D

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

• 24 A
• 25 B
• 9 C
• 13 D

• 28 / 81 A
• 28 / 243 B
• 81 / 28 C
• 243 / 82 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 all positive integral value of n,3ⁿ< n! , when

• n> 6 A
• n< 6 B
• n<11 C
• n>11 D

If n∈Z+ then(a+x)n is a/an

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

a + x is ______

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

• 3/8 A
• 7/8 B
• 1/8 C
• None D

If the sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is

• 1594 A
• 792 B
• 924 C
• 2924 D