Sequences & Series · JEE Main previous year questions

2024 23 questions

1. Q72024 · 9 Apr 2024 · Shift 1

   If the sum of the series $\frac{1}{1\cdot (1+\mathrm{d})}+\frac{1}{(1+\mathrm{d})(1+2\mathrm{d})}+\cdots +\frac{1}{(1+9\mathrm{d})(1+10\mathrm{d})}$ is equal to 5, then $50\mathrm{d}$ is equal to :

   1. A.5
   2. B.10
   3. C.15
   4. D.20
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   Answer: A

2. Q182024 · 9 Apr 2024 · Shift 2

   Let $a,ar,a{r}^2,.........$ be an infinite G.P. If $\sum _{n=0}^{\infty }a{r}^n=57$ and $\sum _{n=0}^{\infty }{a}^3{r}^{3n}=9747$, then $a+18r$ is equal to

   1. A.27
   2. B.38
   3. C.31
   4. D.46
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   Answer: C

3. Q112024 · 8 Apr 2024 · Shift 2

   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. Then the sum of the $4^{\mathrm{th}},6^{\mathrm{th}}$ and $8^{\mathrm{th}}$ terms is equal to:

   1. A.78
   2. B.96
   3. C.91
   4. D.84
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   Answer: C

4. Q292024 · 8 Apr 2024 · Shift 2· Numerical answer

   An arithmetic progression is written in the following way $$\begin{array}{ccccccc}& & & 2& & & \\ & & 5& & 8& & \\ & 11& & 14& & 17& \\ 20& & 23& & 26& & 29\end{array}$$ The sum of all the terms of the $10^{\mathrm{th}}$ row is ____.

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   Answer: 1505

5. Q162024 · 5 Apr 2024 · Shift 2

   For $x\ge 0$, the least value of K, for which $4^{1+x}+4^{1-x},\frac{\text{K}}{2},16^x+16^{-x}$ are three consecutive terms of an A.P., is equal to :

   1. A.10
   2. B.4
   3. C.8
   4. D.16
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   Answer: A

6. Q142024 · 4 Apr 2024 · Shift 1

   Let the first three terms $2,p$ and $q$, with $q\ne 2$, of a G.P. be respectively the $7^{\text{th}},8^{\text{th}}$ and $13^{\text{th}}$ terms of an A.P. If the $5^{\text{th}}$ term of the G.P. is the $n^{\text{th}}$ term of the A.P., then $n$ is equal to:

   1. A.151
   2. B.177
   3. C.163
   4. D.169
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   Answer: C

7. Q22024 · 4 Apr 2024 · Shift 2

   If the coefficients of $x^4,x^5$ and $x^6$ in the expansion of $(1+x{)}^n$ are in the arithmetic progression, then the maximum value of $n$ is:

   1. A.28
   2. B.21
   3. C.7
   4. D.14
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   Answer: D

8. Q172024 · 4 Apr 2024 · Shift 2

   Let three real numbers $a,b,c$ be in arithmetic progression and $a+1,b,c+3$ be in geometric progression. If $a>10$ and the arithmetic mean of $a,b$ and $c$ is 8, then the cube of the geometric mean of $a,b$ and $c$ is

   1. A.120
   2. B.316
   3. C.312
   4. D.128
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   Answer: A

9. Q172024 · 1 Feb 2024 · Shift 1

   Let $3,a,b,c$ be in A.P. and $3,a-1,b+1,c+9$ be in G.P. Then, the arithmetic mean of $a,b$ and $c$ is :

   1. A.-4
   2. B.-1
   3. C.13
   4. D.11
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   Answer: D

10. Q242024 · 1 Feb 2024 · Shift 1· Numerical answer

    Let $3,7,11,15,\dots ,403$ and $2,5,8,11,\dots ,404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to ____.

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    Answer: 6699

11. Q72024 · 1 Feb 2024 · Shift 2

    Let $\alpha$ and $\beta$ be the roots of the equation $p{x}^2+qx-r=0$, where $p\ne 0$. If $p,q$ and $r$ be the consecutive terms of a non constant G.P. and $\frac{1}{\alpha }+\frac{1}{\beta }=\frac{3}{4}$, then the value of $(\alpha -\beta {)}^2$ is :

    1. A.8
    2. B.9
    3. C.$\frac{20}{3}$
    4. D.$\frac{80}{9}$
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    Answer: D

12. Q182024 · 1 Feb 2024 · Shift 2

    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 $15:7$, then $S_{15}-S_5$ is equal to :

    1. A.800
    2. B.890
    3. C.790
    4. D.690
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    Answer: C

13. Q292024 · 1 Feb 2024 · Shift 2· Numerical answer

    If three successive terms of a G.P. with common ratio $r(r>1)$ are the lengths of the sides of a triangle and $[r]$ denotes the greatest integer less than or equal to $r$, then $3[r]+[-r]$ is equal to ________ .

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    Answer: 1

14. Q102024 · 31 Jan 2024 · Shift 1

    The sum of the series $\frac{1}{1-3\cdot 1^2+1^4}+\frac{2}{1-3\cdot 2^2+2^4}+\frac{3}{1-3\cdot 3^2+3^4}+\dots$ up to 10 -terms is

    1. A.$\frac{45}{109}$
    2. B.$-\frac{55}{109}$
    3. C.$\frac{55}{109}$
    4. D.$-\frac{45}{109}$
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    Answer: B

15. Q142024 · 31 Jan 2024 · Shift 2

    Let $2^{\text{nd}},8^{\text{th}}$ and $44^{\text{th}}$ terms of a non-constant A. P. be respectively the $1^{\text{st}},2^{\text{nd}}$ and $3^{\text{rd}}$ terms of a G. P. If the first term of the A. P. is 1, then the sum of its first 20 terms is equal to -

    1. A.990
    2. B.980
    3. C.960
    4. D.970
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    Answer: D

16. Q192024 · 30 Jan 2024 · Shift 1

    Let $S_n$ denote the sum of first $n$ terms of an arithmetic progression. If $S_{20}=790$ and $S_{10}=145$, then $S_{15}-S_5$ is :

    1. A.405
    2. B.390
    3. C.410
    4. D.395
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    Answer: D

17. Q52024 · 29 Jan 2024 · Shift 1

    If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to

    1. A.7
    2. B.6
    3. C.5
    4. D.4
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    Answer: B

18. Q72024 · 29 Jan 2024 · Shift 1

    In an A.P., the sixth term $a_6=2$. If the product $a_1{a}_4{a}_5$ is the greatest, then the common difference of the A.P. is equal to

    1. A.$\frac{2}{3}$
    2. B.$\frac{5}{8}$
    3. C.$\frac{3}{2}$
    4. D.$\frac{8}{5}$
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    Answer: D

19. Q112024 · 29 Jan 2024 · Shift 2

    If ${\log }_{e}a,{\log }_{e}b,{\log }_{e}c$ are in an A.P. and ${\log }_{e}a-{\log }_{e}2b,{\log }_{e}2b-{\log }_{e}3c,{\log }_{e}3c-{\log }_{e}a$ are also in an A.P, then $a:b:c$ is equal to

    1. A.$6:3:2$
    2. B.$9:6:4$
    3. C.$25:10:4$
    4. D.$16:4:1$
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    Answer: B

20. Q162024 · 29 Jan 2024 · Shift 2

    If each term of a geometric progression $a_1,a_2,a_3,\dots$ with $a_1=\frac{1}{8}$ and $a_2\ne a_1$, is the arithmetic mean of the next two terms and $S_n=a_1+a_2+\dots +a_n$, then $S_{20}-S_{18}$ is equal to

    1. A.$-2^{15}$
    2. B.$2^{15}$
    3. C.$-2^{18}$
    4. D.$2^{18}$
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    Answer: A

21. Q202024 · 29 Jan 2024 · Shift 2

    Let $A=\left[\begin{array}{ccc}2& 1& 2\\ 6& 2& 11\\ 3& 3& 2\end{array}\right]$ and $P=\left[\begin{array}{ccc}1& 2& 0\\ 5& 0& 2\\ 7& 1& 5\end{array}\right]$. The sum of the prime factors of $|P^{-1}AP-2I|$ is equal to

    1. A.66
    2. B.27
    3. C.23
    4. D.26
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    Answer: D

22. Q162024 · 27 Jan 2024 · Shift 1

    The number of common terms in the progressions $4,9,14,19,\dots \dots ,$ up to $25^{\mathrm{th}}$ term and $3,6,9,12,\dots \dots ,$ up to $37^{\mathrm{th}}$ term is :

    1. A.9
    2. B.8
    3. C.5
    4. D.7
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    Answer: D

23. Q92024 · 27 Jan 2024 · Shift 2

    The $20^{\text{th}}$ term from the end of the progression $20,19\frac{1}{4},18\frac{1}{2},17\frac{3}{4},\dots ,-129\frac{1}{4}$ is :

    1. A.$-115$
    2. B.$-100$
    3. C.$-110$
    4. D.$-118$
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    Answer: A