JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 18 March 2021, Shift 2, Maths Q64

Question 64 of 90 in this shift, Maths question 4 of 30, Section A.

Let in a series of

2n

observations, half of them are equal to a and remaining half are equal to

-

a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of

a^2+b^2

is equal to :

(1) $925$
(2) $425$ Official answer
(3) $650$
(4) $250$

Official answer

Option 2

NTA final key.

Chapter: Statistics
Topic: Variance and SD
Idea tested: Effect of Linear Transformations

Same idea in other shifts

Asked 4× in all

8 Jan 2020, Shift 1 · Q67The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p…MediumSingle correct
9 Jan 2020, Shift 1 · Q68Let the observations $x_i(1\le i\le 10)$ satisfy the equations, $\sum_{i=1}^{10}(x_i-5)=10$ and $\sum_{i=1}^{10}(x_i-5)^2=40$ . If $\mu$ …MediumSingle correct
2 Sep 2020, Shift 1 · Q67Let $X=\{x\in\mathbf{N} : 1\le x\le 17\}$ and $Y=\{ax+b : x\in X$ and $a, b\in\mathbf{R}, a>0\}$ . If mean and variance of elements of Y…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.