**Q1. The arithmetic mean of the following numbers is **

**1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7**

(a) 4

(b) 5

(c) 14

(d) 20

**S1. Ans.(b)**

**Sol.** required mean

=(1×1+2×2+3×3+4×4+5×5+6×6+7×7)/(1+2+3+4+5+6+7)

=(1+4+9+16+25+36+49)/28

=140/28=5

**Q2. If the average of 6 consecutive even numbers is 25, the difference between the largest and the smallest number is:**

(a) 18

(b) 10

(c) 12

(d) 14

**S2. Ans.(b)**

**Sol.** Let, the numbers be x, x + 2, …, x + 10

∴ Required difference = x + 10 – x = 10

**Q3. The average age of the family of 5 members is 24. If the present age of youngest member is 8 years, then what was the average age of the family just before the birth of the youngest member?**

(a) 20 years

(b) 16 years

(c) 12 years

(d) 18 years

**S3. Ans.(a)**

**Sol. **Total age of the family of five numbers

= 24 × 5 = 120

Total age of the family of 5 members before 8 years

= 120 – 5 × 8

= 120 – 40 = 80

So, the required average age = 80/4 = 20 years.

**Q4. The difference between the simple and compound interest on a certain sum of money for 2 years at 4% per annum is Rs. 1. The sum is:**

(a) Rs. 676

(b) Rs. 675

(c) Rs. 625

(d) Rs. 700

**Q5. The simple interest accrued on an amount of Rs. 15500 at the end of three years is Rs. 5580. What would be the compound interest accrued on the same amount at the same rate in the same period?**

(a) Rs. 6726.348

(b) Rs. 6276.384

(c) Rs. 6267.834

(d) Rs. 6627.438

**S5. Ans.(b)**

**Sol.**Rate of interest = (5580 × 100)/(15500 × 3) = 12%

**Q10. There are some parrots and some tigers in a forest. If the total number of animal heads in the forest are 858 and total number of animal legs are 1746, what is the number of parrots in the forest?**

**S10. Ans.(b)**

**Let**total no. of parrots and tigers in the forest are p and t respectively

**Q11. In a group of 50 people, 35 speak Hindi, 25 speak both Hindi and English and all the people speak Hindi or English or both. The number of people who speak English only is:**

**Q12. A playground has the shape of a rectangle with two semi-circles on its smaller sides as diameters, added outside. If the sides of the rectangle are 36 m and 24.5 m, then the area of the playground is:**

**(use π=22/7)**

**Q13. The length of a rectangle is twice the diameter of a circle. The circumference of the circle is equal to the area of a square of side 22 cm. What is the breadth of the rectangle if its perimeter is 668 cm?**

**S13. Ans.(b)**

**Sol.**2(l + b) = 668

**Q14. The sum of the areas of the 10 squares, the lengths of whose sides are 20 cm, 21cm, …, 29 cm respectively is:**

**Q15. The number of coins of radius 0.75 cm and thickness 0.2 cm to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is:**