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Friday, 9 October

JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 8 April 2024, Shift 1, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

Let the positive integers be written in the form : 1 2 3 4 5 6 7 8 9 10 ... If the kthk^{\mathrm{th}} row contains exactly kk numbers for every natural number kk, then the row in which the number 5310 will be, is ____________.

The figure, in words

Triangular arrangement of positive integers: row 1 has 1; row 2 has 2, 3; row 3 has 4, 5, 6; row 4 has 7, 8, 9, 10; continued with dots.

Official answer

103

NTA final key.

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

Same idea in other shifts

Asked 15× in all
  1. 2 Apr 2026, Shift 2 · Q5The sum 131+13+231+3+13+23+331+3+5+…\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
  2. 4 Apr 2026, Shift 1 · Q7The first term of an A.P. of 3030 non-negative terms is 103\frac{10}{3}. If the sum of this A.P. is the cube of its last term, then its…MediumSingle correct
  3. 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
  4. 8 Apr 2026, Shift 2 · Q5Let α=3+4+8+9+13+14+…\alpha = 3 + 4 + 8 + 9 + 13 + 14 + \ldots up to 40 terms. If (tan⁡β)α1020(\tan\beta)^{\frac{\alpha}{1020}} is a root of the equation…MediumSingle correct
  5. 2 Apr 2025, Shift 1 · Q19Let a1,a2,a3,…a_1, a_2, a_3,\ldots be in an A.P. such that ∑k=112a2k−1=−725a1\sum_{k=1}^{12}a_{2k-1}=-\frac{72}{5}a_1, a1≠0a_1\neq0. If ∑k=1nak=0\sum_{k=1}^{n}a_k=0, then…MediumSingle correct
  6. 7 Apr 2025, Shift 2 · Q6Let ana_n be the nthn^{\mathrm{th}} term of an A.P. If Sn=a1+a2+a3+…+an=700S_n=a_1+a_2+a_3+\ldots+a_n=700, a6=7a_6=7 and S7=7S_7=7, then ana_n is equal to :MediumSingle correct
  7. 6 Apr 2024, Shift 2 · Q7A software company sets up mm number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start…MediumSingle correct
  8. 9 Apr 2024, Shift 1 · Q26If a function ff satisfies f(m+n)=f(m)+f(n)f(m+n)=f(m)+f(n) for all m,n∈Nm,n\in\mathbf{N} and f(1)=1f(1)=1, then the largest natural number λ\lambda such…MediumNumerical value

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. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.