Binomial Theorem, Sequences and Series Three Marks Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
10 x 3 = 30
1. Find $\sqrt [ 3 ]{ 1001 }$ approximately. (two decimal places).

2. Prove that $\sqrt [ 3 ]{ { x }^{ 3 }+6 } -\sqrt [ 3 ]{ { x }^{ 3 }+3 }$ is approximately equal to $\frac { 1 }{ { x }^{ 2 } }$ when x is sufficiently large.

3. The first term of a G.P is 1 .The sum of third and fifth terms is 90.Find the common ration of the G.P

4. Find all the sequence which are simultaneously arithmetic and geometric progression.

5. If the mth term of a H.P. is n and nth term is m, then show that its pth  term is $\frac{mn}{p}$.

6. Find the sum: $1+{4\over5}+{7\over 25}+{10\over125}+.....$

7. Find the coefficient of the term involving x32 and x-17 in the expansion of $(x^{4}-\frac{1}{x^{3}})^{15}$.

8. If the sum of the coefficients in the expansion of (x+y)n is 4096.Then find the greatest coefficient in the expansion.

9. If the ratio of the sums of m terms and n terms of an A.P. be m2 : n2, prove that the ratio of its mth and nth terms is (2m - 1) : (2n - 1).

10. The sum of first three terms of a G.P. is to the sum of the first six terms as 125: 152. Find the common ratio of the G.P.