JEE Main 29 June 2022 Shift 1 Solved Paper

Mean (x)=‌

x1+x2+x3+x4+x5

5

Given, ‌

x1+x2+x3+x4+x5

5

=‌

24

5

⇒x1+x2+x3+x4+x5=24
Now, Mean of first 4 observation
=‌

x1+x2+x3+x4

4

Given, =‌

x1+x2+x3+x4

4

=‌

7

2

⇒x1+x2+x3+x4=14
From equation (1) and (2), we get
14+x5=24
⇒x5=10
Now, variance of first 5 observation
=‌

∑xi2

n

−(x)2

=‌

x12+x22+x32+x42+x52

5

−(‌

24

5

)2
Given,
‌

x12+x22+x32+x42+x52

5

−(‌

24

5

)2=‌

194

24

⇒x12+x22+x32+x42+x52=5(‌

194

25

+‌

576

25

)
⇒x12+x22+x32+x42+x52=154
⇒x12+x22+x32+x42+(10)2=154
⇒x12+x22+x32+x42=54
Now, variance of first 4 observation
=‌

x12+x22+x32+x42

4

−(‌

7

2

)2
Given,
‌

x12+x22+x32+x42

4

−(‌

7

2

)2=a
Given,
‌

x12+x22+x32+x42

4

−(‌

7

2

)2=a
⇒‌

54

4

−‌

49

4

=a
⇒a=‌

5

4

∴4a+x5
=4×‌

5

4

+10=15