CBSE Guess > Papers > Important Questions > Class XI > 2007 > Maths > Mathematics By Mr. Lt Col ( Retd ) IB Dutt Trig Function, Math Induction & Complex Numbers, Binomial and Sequence & Series Q. 1. Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length 15 cm. [TB 5 /7] [1] Q. 2. Prove that cot x cot 2x  cot 2x cot 3x  cot 3x cot x = 1 [TB 74/22] [1] Q. 3. Prove that if x and y are not odd multiple of where [1] Q. 4. Prove that cos ( A + B ) = cos A cos B  sin A sin B. [ TB 64/3] [2] Q. 5. Solve sin 2x  sin 4x + sin 6x = 0 [ TB 77/23 ] [2] Q. 6. [2] Q. 7. Prove by mathematical induction that for all 1^{2} + 2^{2} + 3^{2} + ................. + n^{2} = n(n + 1) (2n + 1) / 6 [TB 89/1] [2] Q. 8. Prove by mathematical induction that (2n + 7) < (n + 3)^{2}. [TB 95/24] [2] Q. 9. Prove by mathematical induction that: (1 + 3/1) (1 + 5/4) (1 + 7/9)................... [1 + (2n + 1) / n^{2}] = (n + 1)^{2} [TB 95/13] [2] Q. 10. Solve the equation x^{2}  x + 2 = 0 [TB 109/6] [2] Q. 11. Find the conjugate of (3  2t) (2 + 3t) / (1 + 2t ) (2  t) [ TB 109/12] [2] Q. 12. Find the number of non  zero integral solutions of the equation  1  t  ^{x} = 2^{x} [TB 113/18] [2] Q. 13. Find the middle term in the expansion of (1 + x)^{2n}, where n is a positive integer. [TB 168/6] [2] Q. 14. Write the general term in the expansion of [2] Q. 15. Find a positive value of m for which the coefficient of x^{2} in the expansion of (1 + x )^{m} is 6. [TB 171/12] [2] Q. 16. If the coefficient of a^{r  1}, a^{r} and a^{r + 1} in the expansion of (1 + a)^{n} are in arithmetic progression, prove that n^{2}  n(4r + 1) + 4r^{2}  2 = 0. [TB 172/11] [2] Q. 17. The sum of n terms of two arithmetic progressions are in the ratio (3n + 8) : (7n + 15). Find the ratio of their 12th terms. [TB 182/6] [2] Q. 18. Find the sum of the series 2 + 11 + 101 + 1001 + ............. To n terms. [2] Q. 19. Find the least n for which the sum of the series 1 + 2 + 4 + 8 + ........... is greater than 10000. [2] Q. 20. The sum of two numbers is 6 times their geometric means, show that the numbers arein the ratio [2] Q. 21. If S_{1}, S_{2}, S_{3} are the sum of thfirst n natural umbers, their squares and their cubes, respectively. Show that 9S_{2}^{2} = S_{3} (1 + 8S_{1}) [TB 200/24] Q. 22. Find sin x/2, cos x/2 and tan x/2 when [3] Q. 23. [3]

