**Q1. The radius of a circle is 13 cm and the length of one of its chord is 24 cm. find the distance of chord from centre.**

**(a) 10 cm (b) 8 cm (c) 5 cm (d) 5.5 cm**

**Ans. (c) Solution:- from Figure;-**

**OD**

^{2}= (AO^{2}– AD^{2)}= (13^{2}– 12^{2}) = 25, OD = 5 cm**Q2. On dividing a number by 4, 5 and 6 we get 2, 3 and 4 as remainder find the highest possible three digit number.**

**(a) 958 (b) 858 (c) 959 (d) 956**

**Ans. (a) Solution: - Given number : 4 5 6**

**Remainder : 2 3 4**

**Which is equal to (4-2) (5-2) (6-2)**

**Hence number will be: LCM of [4, 5, 6] – 2 = 60-2 = 58**

**Highest possible three digit = 958**

**Q3. The average of three 3 number is 17 and that of the first two is 16. Find the third number.**

**(a) 15 (b) 16 (c) 17 (d)19**

**Ans. (d) Solution:- since sum of 3 number = 3*17 = 51**

**Sum of first 2 number = 2*16 = 32**

**Third number = 51-32 = 19**

**Q4. The age of Mitali and Pooja is in the ratio 2 : 6, after 5 years the ratio of their ages will becomes 6 : 8. Find the average of their ages after 10 years.**

**(a) 12 (b) 13 (c) 14 (d) 15**

**Ans. (a) Solution:- let present age of Mitali and Pooja be 2x and 6x**

**After 5 years , (2x+5)/(3x+5) = 6/8 or 16x +40 = 18x + 30 or x = ½**

**So Present age are 1 year and 3 years hence after 10 years it becomes 11 and 13 years.**

**Average = (11+13)/2 = 12**

**Q5. The income of Ramesh increase by 10%, 20%, and 30% successively in three years. Find change in his income if present income is 150000 Rs. Per annum.**

**(a) 120080 (b) 575000 (c) 257400 (d) 250000**

**Ans. (c) Solution:- Percent change in income = 150000* [(1+10/100)(1+20/100)(1+30/100)]**

**= 150000* 110/100 * 120/100 * 130/100**

**= 257400 Rs**

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