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

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

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

• 13 A
• 12 B
• 11 C
• 10 D

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

• 2 A
• 3 B
• 4 C
• 5 D

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

• 295 A
• 495 B
• 395 C
• 722 D

• ¹⁰C₆ A
• ¹⁰C₅ B
• ¹⁰C₄ C
• None D

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

• 10 A
• 12 B
• 11 C
• 9 D

If n is any positive integer then n! > n²for

• 
  A
• 
  B
• 
  C
• 
  D

The 5th term of (3a-2b) ^-1 is

• 77b²/a⁵ A
• 16b² /243 a⁵ B
• 17b⁴/43a⁵ C
• 25b³/43a⁵ D

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

• 1 A
• 9 B
• 3 C
• 5 D

The sum of first n even number is

• n2 A
• n(n+1) B
• n+1 C
• n+2 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

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

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

• 4 A
• 5 B
• 2 C
• 3 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

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

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

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

For≥ -2 , 1+3+5+......+(2n+5)

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

• 2 A
• 7 B
• 8 C
• 12 D

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

There are two middle terms in the expansion of (a+x)n if n is

• Even +ve integer A
• +ve integer B
• Odd +ve integer C
• All D

The middle term of (x-y)⁸is

• 25 x⁴y⁴ A
• 70 x⁴y⁴ B
• 120 x⁴y⁴ C
• 97x⁴y⁴ D

If n∈Z+ then(a+x)n is a/an

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

(1 - x)³= ______

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

The greatest integer which divides the number 101¹⁰⁰- 1 is

• 100 A
• 1000 B
• 10000 C
• 100000 D

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

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

(0.90)^1/2is equal to

• 0.99 A
• 0.90 B
• 0.80 C
• 0.88 D