JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2025, Shift 2, Maths Q5

Question 5 of 75 in this shift, Maths question 5 of 25, Section A.

The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds the first by

\frac{21}{2}

. Then the number of terms which are integers in the A.P. is :

(1) $4$ Official answer
(2) $6$
(3) $8$
(4) $10$

Official answer

Option 1

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: AP Odd vs Even Index Sums

Same topic in other shifts

All AP and GP questions

2 Apr 2026, Shift 1 · Q5Let $A$ be the set of first $101$ terms of an A.P., whose first term is $1$ and the common difference is $5$ and let $B$ be the set of…MediumSingle correct
2 Apr 2026, Shift 2 · Q4Let $a_1, a_2, a_3, \ldots$ be an A.P. and $g_1, g_2, g_3, \ldots$ be an increasing G.P. If $a_1 = a_2 + g_2 = 1$ and $a_3 + g_3 = 4$ ,…MediumSingle correct
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
4 Apr 2026, Shift 2 · Q7Let $\alpha=\frac14+\frac18+\frac1{16}+\ldots\infty$ and $\beta=\frac13+\frac19+\frac1{27}+\ldots\infty$ . Then the value of…EasySingle correct
5 Apr 2026, Shift 1 · Q2Let the sum of the first $n$ terms of an A.P. be $3n^2 + 5n$ . Then the sum of squares of the first 10 terms of the A.P. is:EasySingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.