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

• 3/8 A
• 7/8 B
• 1/8 C
• None D

The sum of coefficients in the binomial expansion equals to

• 2 A
• 2ⁿ⁺¹ B
• 2^n-1 C
• 2ⁿ D

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

• 2 A
• 3 B
• 4 C
• 5 D

For n€ N,2^n>2 > n is to only when

• n<2 A
• n≤ 4 B
• n≥ 4 C

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

• 7 A
• 6 B
• 3 C
• 0 D

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

• 6 A
• 3 B
• 4 C
• 8 D

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

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

a + x is ______

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

In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n=

• 12 A
• n=14 B
• 17 C
• n=15 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 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

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

There is no integer n for which 3n is

• Even A
• Prime B
• Odd C
• Real D

If n € N , then n(n+3) is always

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

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

• 71 A
• -22 B
• 27 C
• 28 D

For each natural number n, n (n+1) is

• an even A
• an odd B
• multiple of 3 C
• Irrational D

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

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

There is no integer n for which 3ⁿ is

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

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

• 295 A
• 495 B
• 395 C
• 722 D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 13 A
• 12 B
• 11 C
• 10 D

The no of term is the expansion of (a+x)n-1 is

• n+1 A
• n-1 B
• n C
• n-2 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

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