ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 10

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 = 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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 7 A
• 6 B
• 3 C
• 0 D

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

• 9 A
• 6 B
• 5 C
• 10 D

(51)⁴is equal to

• 7065201 A
• 8065201 B
• 6765201 C
• 6565201 D

The proposition S(k+1) is true when ______ is true∀K∈N

• S(n) A
• S(k) B
• S(1) C
• S(k-1) D

If n is any positive integer then 3 + 6 + 9 + ....+ 3n = ______

• 
  A
• 
  B
• 
  C
• 
  D

(x3-1/x)12

• 295 A
• 495 B
• 395 C
• 722 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

If n € N , then n(n+3) is always

• Multiple of 3 A
• Multiple of 6 B
• odd C
• even D

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

• 16 A
• 30 B
• 8 C
• 32 D

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

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

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

• 405 / 256 A
• 504 / 259 B
• 450 / 263 C
• None D

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

The greatest integer which divides the number 101¹⁰⁰- 1 is

• 100 A
• 1000 B
• 10000 C
• 100000 D

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

n² - 1 divisible by 8 when n is

• an odd integer A
• an even integer B
• Irrational C
• Prime Number D

• ¹⁰C₆ A
• ¹⁰C₅ B
• ¹⁰C₄ C
• None D

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

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

There is no integer n for which 3ⁿ is

• Odd A
• even B
• Natural C
• Prime 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 number of terms in the expansion of (a + b)⁹is

• 10 A
• 11 B
• 9 C
• 12 D

• 8 A
• 9 B
• 10 C
• 11 D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

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

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

ⁿC₂= exists when n is ______

• 
  A
• 
  B
• 
  C
• 
  D

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

• 6 A
• 3 B
• 4 C
• 8 D