Mathematical induction and binomial theorem

Written by Hassan Raza (Mathematics)

Class 11 · Mathematics · 8 questions

Name: ____________________   Date: ____________

1. The number of terms in the expansion of (a + b)⁸ is:

   • A 10
   • B 8
   • C 9
   • D 16

2. The coefficient of x² in (1 + x)⁵ is:

   • A 15
   • B 5
   • C 20
   • D 10

3. The sum of the binomial coefficients in (1 + x)⁴ is:

   • A 8
   • B 4
   • C 16
   • D 32

4. Mathematical induction is used to prove statements for:

   • A Real numbers
   • B Only even numbers
   • C All natural numbers
   • D Fractions

5. The middle term of (a + b)⁶ is the:

   • A 4th
   • B 3rd
   • C 7th
   • D 5th

6. The expansion of (1 + x)³ is:

   • A 1 + 3x + 3x² + x³
   • B 1 + 3x + x³
   • C 1 + 2x + x²
   • D 1 + x³

7. The general term in (a + b)^n is:

   • A a^n + b^n
   • B nPr a b
   • C n a^r b
   • D nCr a^(n-r) b^r

8. The coefficient of x³ in (1 + x)⁴ is:

   • A 4
   • B 1
   • C 3
   • D 6