Q.8. If the mean of the data
Class: 5-10, 10-15, 15-20, 20-25, 25-30, 30-35
Frequency: 2, k, 28, 54,

Q: What is the correct answer for JEE Main Mathematics Q8?

The correct answer is D. Sol. First, find the midpoints ($x_i$) for each class and calculate $\sum f_i x_i$ and $\sum f_i$. | Class | Frequency ($f_i$) | Midpoint ($x_i$) | $f_i x_i$ | |---------|-------------------|------------------|-----------------| | 5-10 | 2 | 7.5 | 15 | | 10-15 | k | 12.5 | 12.5k | | 15-20 | 28

Q: Q.8. If the mean of the data Class: 5-10, 10-15, 15-20, 20-25, 25-30, 30-35 Frequency: 2, k, 28, 54, k+1, 5 is 21, then k is one of the roots of the equation :

The correct answer is D. Sol. First, find the midpoints ($x_i$) for each class and calculate $\sum f_i x_i$ and $\sum f_i$. | Class | Frequency ($f_i$) | Midpoint ($x_i$) | $f_i x_i$ | |---------|-------------------|------------------|-----------------| | 5-10 | 2 | 7.5 | 15 | | 10-15 | k | 12.5 | 12.5k | | 15-20 | 28

Q: What are the options for this JEE Main Mathematics question?

A. 2x^2 - 23x - 10 = 0 · B. 4x^2 - 35x + 24 = 0 · C. 2x^2 - 19x - 10 = 0 · D. 2x^2 - 35x + 98 = 0

Question

Q.8. If the mean of the data
Class: 5-10, 10-15, 15-20, 20-25, 25-30, 30-35
Frequency: 2, k, 28, 54, k+1, 5
is 21, then k is one of the roots of the equation :

FirstInTest · Accepted Answer

Sol. First, find the midpoints ($x_i$) for each class and calculate $\sum f_i x_i$ and $\sum f_i$.

| Class   | Frequency ($f_i$) | Midpoint ($x_i$) | $f_i x_i$       |
|---------|-------------------|------------------|-----------------|
| 5-10    | 2                 | 7.5              | 15              |
| 10-15   | k                 | 12.5             | 12.5k           |
| 15-20   | 28                | 17.5             | 490             |
| 20-25   | 54                | 22.5             | 1215            |
| 25-30   | k+1               | 27.5             | 27.5(k+1) = 27.5k + 27.5 |
| 30-35   | 5                 | 32.5             | 162.5           |

$\sum f_i = 2 + k + 28 + 54 + (k+1) + 5 = 90 + 2k$

$\sum f_i x_i = 15 + 12.5k + 490 + 1215 + 27.5k + 27.5 + 162.5$
$= (15 + 490 + 1215 + 27.5 + 162.5) + (12.5k + 27.5k)$
$= 1910 + 40k$

Given that the mean is 21.
Mean $= \frac{\sum f_i x_i}{\sum f_i}$
$21 = \frac{1910 + 40k}{90 + 2k}$
$21(90 + 2k) = 1910 + 40k$
$1890 + 42k = 1910 + 40k$
$42k - 40k = 1910 - 1890$
$2k = 20$
$k = 10$

Now we check which equation has $k=10$ as a root:
(1) $2x^2 - 23x - 10 = 0$
$2(10)^2 - 23(10) - 10 = 200 - 230 - 10 = -40 
e 0$

(2) $4x^2 - 35x + 24 = 0$
$4(10)^2 - 35(10) + 24 = 400 - 350 + 24 = 74 
e 0$

(3) $2x^2 - 19x - 10 = 0$
$2(10)^2 - 19(10) - 10 = 200 - 190 - 10 = 0$
This is a root.

(4) $2x^2 - 35x + 98 = 0$
$2(10)^2 - 35(10) + 98 = 200 - 350 + 98 = -52 
e 0$

So, $k=10$ is a root of $2x^2 - 19x - 10 = 0$.

Answer

2x^2 - 23x - 10 = 0

Answer

4x^2 - 35x + 24 = 0

Answer

2x^2 - 19x - 10 = 0

Answer

2x^2 - 35x + 98 = 0

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