Sequence & Series: JEE Main Mathematics Previous Year Questions

284 previous year questions from Sequence & Series. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. $A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more comput\dots$
2. $The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is \frac{27}{19} . Then the common ratio of this series is:$
3. $If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is$
4. $Let a_{1} = 1 and for n ⩾ 1, a_{n + 1} = \frac{1}{2} a_{n} + \frac{n ^{2} - 2 n - 1}{n ^{2} ( n + 1 ) ^{2}} . Then\dots$
5. $If 8 = 3 + \frac{1}{4} (3 + p) + \frac{1}{4 ^{2}} (3 + 2 p) + \frac{1}{4 ^{3}} (3 + 3 p) + \dots \infty, then the value of p is_____$
6. $If p (\frac{1}{q} + \frac{1}{r}), q (\frac{1}{r} + \frac{1}{p}), r (\frac{1}{p} + \frac{1}{q}) are in A.P., then p, q, r$
7. $The sum\dots$
8. $In an increasing geometric progression of positive terms, the sum of the second and sixth terms is \frac{70}{3} and the product of the third and fifth terms is 49 . Th\dots$
9. $If α, β and γ are three consecutive terms of a non-constant G . P . such that the equations\dots$
10. $If the first term of an A . P . is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of\dots$
11. $The number of 3 -digit numbers, that are divisible by 2 and 3 , but not divisible by 4 and 9 , is .$
12. $Let S_{n} denote the sum of the first n terms of an arithmetic progression. If S_{10} = 390 and the ratio of the tenth and the fifth terms is 15 : 7, t\dots$
13. $Let S_{n} denote the sum of the first n terms of an A . P . If S_{4} = 16 and S_{6} = - 48 then S_{10} is equal to :$
14. $Let a_{1}, a_{2}, a_{3} \dots be an A.P. If a_{7} = 3, the product a_{1} a_{4} is minimum and the sum of its first n terms is zero, then\dots$
15. $Let A = {n \in [100, 700] \cap N : n is neither a multiple of 3 nor a multiple of 4} . Then the number of elements in\dots$
16. $Let a_{1}, a_{2}, a_{3}, \dots . be a G.P. of increasing positive numbers. If a_{3} a_{5} = 729 and a_{2} + a_{4} = \frac{111}{4}, the\dots$
17. $Let S_{n} be the sum to n-terms of an arithmetic progression 3, 7, 11, \dots \dots If\dots$
18. $Let S be the sum of the first 9 terms of the series:\dots$
19. $If S_{n} = \frac{1}{6 \cdot 11} + \frac{1}{11 \cdot 16} + \frac{1}{16 \cdot 21} + \dots to n terms, then 6 S_{n} equals$
20. $If the sum of the first 10 terms of the series \frac{4 \cdot 1}{1 + 4 \cdot 1 ^{4}} + \frac{4 \cdot 2}{1 + 4 \cdot 2 ^{4}} + \frac{4 \cdot 3}{1 + 4 \cdot 3 ^{4}} + \dots . is\dots$
21. $The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7 is _______$
22. $If y = \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12} + \dots \infty, then$
23. $The value of\dots$
24. $Let α and β be the roots of the quadratic equation\dots$
25. $For positive integers n, if 4 a_{n} = (n^{2} + 5 n + 6) and S_{n} = \sum_{k = 1}^{n} (\frac{1}{a _{k}}), then the value of\dots$

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Sequence & Series: JEE Main Mathematics Previous Year Questions

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