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#### Binomial Theorem, Sequences and Series Two Marks Question

11th Standard

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. Expand $\left( { 2x }^{ 2 }-3\sqrt { 1-{ x }^{ 2 } } \right) ^{ 4 }+({ 2x }^{ 2 }+3\sqrt { 1-{ x }^{ 2 }) } ^{ 4 }$

2. Show that the sum of (m + n)th and (m - n)th term of an A.P is equal to twice the mth term.

3. Using binomial theorem, indicate which of the following two number is larger (1.01)1000000 (OR)10, 000

4. Find the last two digits of the number 3600

5. In the binomial expansion of (a+b)n the coefficients of the 4th and 13th terms are equal to each other, find n.

6. Find the middle term in ${ \left( x-\frac { 1 }{ 2y } \right) }^{ 10 }$

7. Find the greatest term in (1 + 2x)8 when x = 2.

8. If H be the H. M. between a and b, then show that (H - 2a) (H - 2b) = H2

9. Find the nth term of the series 3 - 6 + 9 -12 + ...

10. Find the middle term in the expansion of (x +y)6.

11. Find the middle terms in the expansion of (x +y)7.

12. Which two consecutive terms in the expansion (1 +x)15have equal coefficients.

13. Find $\sum_{k=1}^{n}{1\over k(k+1)}.$

14. Find a positive value of m for which the coefficient of x2 in the expansion of (1+x)m is 6.

15. Find the $\sqrt [ 3 ]{ 126 }$ approximately to two decimal places.