Linear Inequations (p-2) — Maths (commerce) STD 11 Commerce / Arts — Question

The following table gives the distribution of females in an Indian village. Determine the median age graphically.

Age Group	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No. Of Females (In '000')	175	100	68	48	25	50	23	8	2	1

Calculate Karl Pearsonian’s coefficient of skewness Skp from the follow ing data:

Marks above	0	10	20	30	40	50	60	70	80
No of students	120	115	108	98	85	60	18	5	0

Find the equation of the line passing through the point of intersection of lines x + y – 2 = 0 and 2x – 3y + 4 = 0 and making intercept 3 on the X-axis.

Solve the following equations using Cramer’s Rule.

(i) x + 2y – z = 5, 2x – y + z = 1, 3x + 3y = 8

Akash, Sameer, and Sid took a house on rent for one year for ₹ 16,236 . They stayed together for 4 months and then Sid left the house. After 5 more months, Sameer also left the house.
How much rent should each pay?

The following is the distribution of 160 workers according to the wages in a certain factory:

Wages More Than (in ₹)	No. Of Workers
8000	160
9000	155
10000	137
11000	103
12000	57
13000	23
14000	10
15000	1
16000	0

Determine the values of all quartiles and interpret the results.

An amount of ₹ 5,000 is invested in three plans at rates 6%, 7% and 8% per annum respectively. The total annual income from these investments is ₹ 350. If the total annual income from first two investments is ₹ 70 more than the income from the third, find the amount invested in each plan by using Cramer’s Rule.