1. If $a_n$ be the nth term of an A.P and if $a_7$ = 15, then the value of the common difference that would make $a_2{a}_7{a}_{12}$, greatest is

2. Consider an A.P with first term ‘a’ and common difference ‘d’. Let $S_k$ denotes the sum of the first k terms. If $\raisebox{1ex}{$S_{\mathrm{kx}}$}\!\left/ \!\raisebox{-1ex}{$S_x$}\right.$ is independent of x, then

3. If the interior angles of a polygon are in A.P with common difference $5^0$ and smallest angles is ${120}^0$, then the number of sides of the polygon is

4. The A.M between two numbers exceeds their G.M by 15 and H.M by 27. The numbers are

5. If $\frac{\mathrm{bc}}{\mathrm{ad}}$=$\frac{b+c}{a+d}$=3$\left(\frac{b-c}{a-d}\right)$, then a, b, c, d are in

6. If a, b, c are in H.P., then the value of $\frac{b+a}{b-a}+\frac{b+c}{b-c}$ is

7. If a, b, c are in G.P and a + x, b + x, c + c in H.P., then the vlaue of x is (a, b, c are distinct numbers)

8. If $A_1$, $A_2$ be two A.M and $G_1$, $G_2$ be two G.M s between a and b, then $\frac{A_1+A_2}{{G_1+G}_2}$ is equal to

9. The maximum sum of the series 20 + 19$\frac{1}{3}$+18$\frac{2}{3}$ + .......... is

10. If a, b, c, d are in G.P., then ${(a^3+b^3)}^{-1}$ $,{(b^3+c^3)}^{-1}$,${(c^3+d^3)}^{-1}$are in

11. If a, b, c, d are in H.P., then ab + bc + cd is equal to

12. If a, b, c are unequal numbers such that a, b, c are in A.P and b - a, c - b, a are in G.P., then a : b : c is

13. A G.P consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, the common ratio will be

14. If $a_1$, $a_2$, $a_3$, .... are in A.P such that$a_1$+ $a_5$+ $a_{10}$$+a_{15}$+ $a_{20}$+ $a_{24}$ = 225, then $a_1$+ $a_2$+ $a_3$... $a_{23}$+ $a_{24}$ is equal to

15. Between 1 and 31 are inserted m arithmetic means, so that the ratio of the $7^{\mathrm{th}}$ and ${(m-1)}^{\mathrm{th}}$ means is 5 : 9. Then the value of m is

16. If the A.M of the roots of a quadratic equation is 8/5 and the A.M of their reciprocals is 8/7, then the quadratic equation is

17. If x > 1 and ${\left(\frac{1}{x}\right)}^a,$${\left(\frac{1}{x}\right)}^b,$${\left(\frac{1}{x}\right)}^c$ are in G.P., then a, b, c are in

18. If the numbers a, b, c, d, e form an A.P., then the value of a - 4b + 6c - 4d + e is

19. If 1, log${}_{y}x$, log${}_{z}y$, - 15 log${}_{x}z$ are in A.P then

20. In an A.P., the sum of terms equidistant from the beginning and end is equal to

21. A family of 4 brothers and 3 sisters is to be arranged in a row for a photograph. In how many ways can they be seated if all sisters sit together

22. If n+${2c}_8:n-2P_4=\frac{57}{16}\mathrm{then}n\mathrm{equal}\mathrm{to}$

23. If n$p_r=720n{c}_r\mathrm{then}r\mathrm{is}$

24. In two many ways can 5 red and 4 white balls be drawn from a bag containing 10 red and 8 white balls.

25. Seven women and seven men are to sit around a circular table such that there is a man on either side of every woman. The number of seating arrangement is

26. If n and r are two +ve integers such that n$\ge r\mathrm{then}{\mathrm{nc}}_{r-1}+{\mathrm{nc}}_r=$

27. The number of ways in which 5 boys and 3 girls be seated in a row so that each girls between two boys is

28. If ${43}_{r-6}={43}_{3r+1}\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}r\mathrm{is}$

29. How many words can be formed the letters of the word "COMMITTEE"

30. If the first term of AP is 2 and common difference is 4 then sum of its 40 term is

31. If a and b are two different +ve real numbers then which of the following statement is true

32. The sum of 10 terms of the series $\sqrt{2}+\sqrt{6}+\sqrt{18}+\mathrm{.....}\mathrm{is}$

33. The product (32) ${(32)}^{\frac{1}{6}}{(32)}^{\frac{1}{36}}\mathrm{......}\propto \mathrm{is}$

34. If the $p^{\mathrm{th}}\mathrm{term}\mathrm{of}\mathrm{an}\mathrm{AP}\mathrm{is}q\mathrm{and}{q}^{\mathrm{th}}\mathrm{term}\mathrm{is}p\mathrm{then}\mathrm{the}{r}^{\mathrm{th}}\mathrm{term}\mathrm{is}$

35. If p,q,r be AM,GM,HM resp. between any two rational numbers a and b then p-q is

36. The $n^{\mathrm{th}}\mathrm{term}\mathrm{of}\mathrm{the}\mathrm{series}3,\sqrt{3},1,\mathrm{......}\mathrm{is}\frac{1}{243}\mathrm{then}n\mathrm{is}$

37. 3+3$\propto +3{\propto }^2+\mathrm{........}\propto \mathrm{is}\mathrm{equal}\mathrm{to}\frac{45}{8}\propto \succ 0\mathrm{then}\propto \mathrm{is}$

38. If b+c, c+a, a+b are in HP then $a^2,b^2,c^2\mathrm{will}\mathrm{be}\mathrm{in}$

39. If the AM between the roots of a quadratic equation is 8 and GM is 5 then equation is

40. The value of $9^{\frac{1}{3}}\times 9^{\frac{1}{9}}\times 9^{\frac{1}{27}}\mathrm{.........}\propto \mathrm{is}$

41. The ${20}^{\mathrm{th}}\mathrm{term}\mathrm{if}\mathrm{the}\mathrm{series}2\times 4+4\times 6+6\times 8+\mathrm{..................}\mathrm{is}$

42. The $n^{\mathrm{th}}\mathrm{term}\mathrm{of}\mathrm{the}\mathrm{sequance}\frac{1}{2},\frac{1}{6}$,$\frac{1}{12},\mathrm{.........}\mathrm{is}$

43. $5^{\mathrm{th}}\mathrm{term}\mathrm{of}a\mathrm{GP}\mathrm{is}2,\mathrm{then}\mathrm{the}\mathrm{product}\mathrm{of}\mathrm{first}9\mathrm{terms}\mathrm{is}$

44. If the sum of first n terms of an Ap is pn+Q$n^2\mathrm{where}p\mathrm{and}q\mathrm{are}\mathrm{constant},\mathrm{then}\mathrm{common}\mathrm{difference}\mathrm{of}\mathrm{AP}\mathrm{will}\mathrm{be}$

45. If a, b, c,d, e,f are in AP then e-c is equal to

46. If a, b, c are in Ap then $3^a,3^b,3^c\mathrm{are}$

47. The next term of the sequence 1,5,14,30,55,....is

48. If 1+$\frac{1+2}{2}+\frac{1+2+3}{3}+\mathrm{....}\mathrm{to}n\mathrm{terms}\mathrm{is}S\mathrm{then}S\mathrm{is}\mathrm{equal}\mathrm{to}$

49. The number of terms of the AP 3, 7, 11, 15......to be taken so that the sum is 406 is

50. If the progressions 3, 10, 17,..........and 63, 65, 67,.... are such that their$n^{\mathrm{th}}$ terms are equal, then n is equal