1st Year Mathematics Chapter 8 TestUNIT 8: Mathematical induction and Binomial Theorem

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

1. The expansion of  is valid if ......:

   1. IxI<1

   2. IxI< 1/3

   3. IxI>1

   4. None of these

2. The inequality 4ⁿ>3ⁿ+2^n-1 is true for integral values of n if ......:

   1. n>0

   2. n>1

   3. n>2

   4. n<2

3. 1-x+x²-x³+.... is expansion equals:

   1. (1+x)^-2

   2. (1-x)^-2

   3. (1+x)^-1

   4. (1-x)^-1

4. If n is odd, then the expansion of (a+x)ⁿ has ......:

   1. Two middle terms

   2. 3 middle terms

   3. 4 middle terms

   4. 0 middle term

5. The inequality n!>2ⁿ-1 is true for interal values of a ......:

   1. n<4

   2. n<1

   3. N>2

   4. N>4

6. If n is positive integer, then n!>3^n-1 is true when:

   1. n<3

   2. n>2

   3. n<5

   4. None

7. In the expansion of (1+x)^-3 the 4th term is:

   1. -3x

   2. -10x³

   3. 6x²

   4. 10x³

8. 

   1. 

   2. 

   3. 

   4. 

9. if n is even, then the expansion of (a+x)ⁿ has ......:

   1. Two middle terms

   2. No middle term

   3. One middle term

   4. None of these

10. If IxI<1 then the expansion of  upto two terms is ......:

    1. 

    2. 

    3. 1-x

    4. 1+x