**Important Questions for Mathematics**

**1.A man on the top of a tower, standing on the seashore finds that a boat coming towards him takes 10 minutes for the angle of depression to change from 30 degree to 60 degreefind the time taken by the boat to reach the shore from this position.**

- 15 minutes
- 5 minutes
- 4 minutes
- none of the above

**Answer: (2)**

**2.The period of 2 sin x cos x is**

- 4 pi 2
- 2 pi
- 4 pi
- pi

**Answer: 4**

**3.The mean of a data set is equal to 10 and its standard deviation is equal to 1. If we add 5 to each data value, then the mean and standard deviation become**

- mean = 15 , standard deviation = 6
- mean = 10 , standard deviation = 6
- mean = 15 , standard deviation = 1
- mean = 10 , standard deviation = 1

**Answer: (3)**

**4.A hemisphere of iron of 6cm radius is cast in such a way of right circular cone of height 75cm.The radius of the base of the cone is**

- 1.2cm
- 2cm
- 2.6cm
- 2.4cm

**Answer: (4)**

**5.The population of a country increased by an average of 2% per year from 2000 to 2003. If the population of this country was 2 000 000 on December 31, 2003, then the population of this country on January 1, 2000, to the nearest thousand would have been**

- 1 846 000
- 1 852 000
- 1 000 000
- 1 500 000

**Answer: (1)**

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