If a + b + c = 13, a2+b2+c2=69 then find the ab + bc + ca : 10 30 50 70 a + b +

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Question
If a + b + c = 13, a2+b2+c2=69 then find the ab + bc + ca :
Options
A. 10
B. 30
C. 50
D. 70

Correct Answer

50

Explanation

${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$

$2 (a b + b c + c a) = {(a + b + c)}^{2} - (a^{2} + b^{2} + c^{2}) = 169 - 69 = 100 = (a b + b c + c a) = 50$

Simplification problems

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1. If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to :
Options
A. 22
B. 23
C. 24
D. 25

2. A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed :
Options
A. 30 birds
B. 60 birds
C. 72 birds
D. 90 birds

3. If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?
Options
A. 500
B. 1000
C. 1500
D. 2000

4. In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :
Options
A. 35
B. 38
C. 40
D. 42

5. Dev lent Rs. 8000 to Jairam for 17 years and Rs. 4700 to Karnik for 16 years on simple interest at the same rate of interest and received Rs. 21120 in all from both of them as interest. The rate of interest per annum is:
Options
A. 10.5 percent
B. 10 percent
C. 11 percent
D. 11.5 percent

6. The difference of 18 and its reciprocal is equal to :
Options
A. 1/8
B. 4/3
C. 15/16
D. 105/304

7. To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ?
Options
A. 52.5
B. 62.5
C. 72.5
D. 82.5

8. A tank is 2/5 full. If 16 litres of water is added to the tank, it becomes 6/7 full. The capacity of the tank is:
Options
A. 28 litres
B. 32 litres
C. 35 litres
D. 42 litres

9. Simplify the following equation. 1943 + 12 + 13 + 11 + 14
Options
A. 43/19
B. 1
C. 38/19
D. None of these

10. In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
Options
A. 160
B. 175
C. 180
D. 195

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