JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 25 July 2022, Shift 1, Maths Q24

Question 24 of 90 in this shift, Maths question 24 of 30, Section B.

Let

a,\ b

be two non-zero real numbers. If

p

and

r

are the roots of the equation

x^2-8ax+2a=0

and

q

and

s

are the roots of the equation

x^2+12bx+6b=0

, such that

\frac{1}{p},\frac{1}{q},\frac{1}{r},\frac{1}{s}

are in A.P., then

a^{-1}-b^{-1}

is equal to ______.

Official answer

NTA final key (2022 Session 2).

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: AP General Term

Same idea in other shifts

Asked 4× in all

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
5 Apr 2026, Shift 2 · Q6Let $A_1, A_2, A_3, \dots\dots, A_{39}$ be 39 arithmetic means between the numbers 59 and 159. Then the mean of $A_{25}, A_{28}, A_{31}$ …EasySingle correct
6 Sep 2020, Shift 2 · Q56The common difference of the A.P. $b_1, b_2, \ldots, b_m$ is 2 more than the common difference of A.P. $a_1, a_2, \ldots, a_n$ . If…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 42 of the 174 JEE Main shifts held from 2017 to 2026.