JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 30 January 2024, Shift 1, Maths Q6

Question 6 of 90 in this shift, Maths question 6 of 30, Section A.

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) $405$
(2) $395$ Official answer
(3) $390$
(4) $410$

Official answer

Option 2

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: AP Sum of n terms

Same idea in other shifts

Asked 31× in all

2 Apr 2026, Shift 2 · Q5The sum $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \ldots$ up to 8 terms, is:MediumSingle correct
4 Apr 2026, Shift 1 · Q7The first term of an A.P. of $30$ non-negative terms is $\frac{10}{3}$ . If the sum of this A.P. is the cube of its last term, then its…MediumSingle correct
6 Apr 2026, Shift 1 · Q6The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal…MediumSingle correct
8 Apr 2026, Shift 2 · Q5Let $\alpha = 3 + 4 + 8 + 9 + 13 + 14 + \ldots$ up to 40 terms. If $(\tan\beta)^{\frac{\alpha}{1020}}$ is a root of the equation…MediumSingle correct
2 Apr 2025, Shift 1 · Q19Let $a_1, a_2, a_3,\ldots$ be in an A.P. such that $\sum_{k=1}^{12}a_{2k-1}=-\frac{72}{5}a_1$ , $a_1\neq0$ . If $\sum_{k=1}^{n}a_k=0$ , then…MediumSingle correct
7 Apr 2025, Shift 2 · Q6Let $a_n$ be the $n^{\mathrm{th}}$ term of an A.P. If $S_n=a_1+a_2+a_3+\ldots+a_n=700$ , $a_6=7$ and $S_7=7$ , then $a_n$ is equal to :MediumSingle correct
5 Apr 2024, Shift 1 · Q25Let $a_1, a_2, a_3, \ldots$ be in an arithmetic progression of positive terms. Let…HardNumerical value
6 Apr 2024, Shift 2 · Q7A software company sets up $m$ number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.