1. If the combined average of the expressions ???? − 3 , ???? − 1 , 7 , ???? , 2 ???? − 1 , and 3 ???? − 5 is 3.5, then what will be the median of these expressions?

(a) 3.5 (b) 4.5 (c) 5 (d) 5.5

2. If the combined mean of \(n\) quantities is \(\bar{x}\), and the sum of the first \((n-1)\) quantities is \(k\), then the \(n\)th quantity will be —

(a) \(k+n\) (b) \(\bar{x}+k\) (c) \(\bar{x}-k\) (d) \(n\bar{x}-k\)

3. If the data arranged in ascending order is 6, 9, 11, 12, x+2, x+3, 17, 20, 21, 24 and the median is 21, then the value of x will be —

(a) 13.5 (b) 15.5 (c) 18.5 (d) 21.5

4. If the mode and the combined mean of a statistical distribution are ₹12.30 and ₹18.48 respectively, then the median of the distribution will be —

(a) ₹ 16 (b) ₹ 17 (c) ₹ 16.42 (d) ₹ 17.42

5. If the current price of a machine is ₹\(b\) and its value depreciates by \(r\%\) every year, then after \(n\) years, the value of the machine will be ₹\(b\left(1 - \cfrac{r}{100}\right)^n\).

6. If the current population of a village is \(P\) and the annual population growth rate is \(2r\%\), then after \(n\) years the population will be ———.

7. If the average of the numbers \(7, x - 3, x + 3, 10, x - 5\) is \(15\), then their median will be \(10\).

8. If the population of a village is \(p\) and the annual growth rate is \(4r\%\), then after \(n\) years the population will be \[ p\left(1+\frac{r}{100}\right)^n \]

9. If the current population of a city is \(P\) and the annual population growth rate is \(r\%\), then after \(n\) years, the population of the city will be \(P\left(1-\frac{r}{100}\right)^n\).

10. If the population of a village is \(P\) and the annual population growth rate is \(4r\%\), then after \(n\) years, the population will be \(P\left(1-\cfrac{r}{25}\right)^n\).

11. If the population of a village is \(P\) and the annual growth rate of the population is \(2r\%\), then the population after \(n\) years will be ___.

12. If the population of a village is \(P\) and the annual population growth rate is \(2r\%\), then the population after \(n\) years will be:

(a) \(P\left(1+\cfrac{r}{100}\right)^n\) (b) \(P\left(1+\cfrac{r}{50}\right)^n\) (c) \(P\left(1+\cfrac{r}{100}\right)^{2n}\) (d) \(P\left(1-\cfrac{r}{100}\right)^n\)

13. If the combined average of the numbers 7, \(x - 3\), 10, \(x + 3\), and \(x - 5\) is 15, then the median is _____.

(a) 16 (b) 10 (c) 18 (d) 24

14. If the annual compound interest rate is \(r\%\), and the interest earned is _____, then the compound amount of \(p\) rupees in \(n\) years will be \(p\left(1+\cfrac{r}{400}\right)^{4n}\) rupees.

15. If the current population of a village is \(p\) and the annual population growth rate is \(2r\%\), then the population after \(n\) years will be _____.

16. If the population of a village is \(p\) and the annual population growth rate is \(2r\%\), then after \(n\) years, the population will be _____.

17. If the population of a village is \(p\) and the annual population growth rate is \(2r\%\), then the population after \(n\) years will be _____.

18. If the population of a village is \(p\) and the annual population growth rate is \(2r\%\), then the population after \(n\) years will be:

(a) \(p(1+\cfrac{r}{100})^n\) (b) \(p(1+\cfrac{r}{50})^n\) (c) \(p(1+\cfrac{r}{100})^{2n}\) (d) \(p(1-\cfrac{r}{100})^n\)

19. If the average of the first ten natural numbers is A and the median is M, then the relationship between A and M is —

(a) \(A\gt M\) (b) \(A\lt M\) (c) \(A=\cfrac{1}{M}\) (d) \(A=M\)

20. In a group of \(n\) numbers with an average of \(\bar{x}\), if the sum of the first \((n - 1)\) numbers is \(K\), then the \(n\)th number will be \((n - 1)\bar{x} + K\).

21. If the average of \( (p + q) \) numbers is \( x \), and the average of \( p \) of those numbers is \( y \), then the average of the remaining \( q \) numbers will be _____ .

22. If the average of the numbers 6, 7, x, 8, y, and 14 is 9, then

(a) x+y=21 (b) x+y=19 (c) x-y=21 (d) x-y=19

23. If the base radius of a right circular cone is 3 cm and the height is 4 cm, then the lateral surface area of the cone will be.

(a) \(10\pi \, cm^2\) (b) \(15\pi \, cm^2\) (c) \(12\pi \, cm^2\) (d) \(18\pi \, cm^2\)

24. The current price of a machine is rupees 2P, and if its price decreases by 2r% each year, then after 2n years, the price of the machine will be:

(a) \(P\left(1-\cfrac{r}{100}\right)^n\) (b) \(2P\left(1-\cfrac{r}{50}\right)^n\) (c) \(P\left(1-\cfrac{r}{50}\right)^{2n}\) (d) \(2P\left(1-\cfrac{r}{50}\right)^{2n}\)

25. If the 25th term of a sequence with 49 terms is 57 and the 26th term is 62, the median of the sequence will be?

(a) 59.5 (b) 57 (c) 62 (d) 57.5

26. If the ratio of the capital investments of A, B, and C is \(\cfrac{1}{2} : \cfrac{1}{3} : \cfrac{1}{4}\) and the total profit is ₹520, then C's share of the profit will be

(a) ₹120 (b) ₹160 (c) ₹180 (d) ₹140

27. If the ratio of the radii of two vertical solid circular cylinders is 2:3, and the ratio of their heights is 5:3, then the ratio of their curved surface areas will be –

(a) 2:5 (b) 8:7 (c) 10:9 (d) 16:9

28. If the average of the numbers 6, 7, x, 8, y, and 16 is 9, then—?

(a) x + y = 21 (b) x + y = 17 (c) x - y = 21 (d) x - y = 19

29. If the average of the quantities \(x_1, x_2, x_3,.......,x_{10}\) is 20, then the average of \(x_1+4, x_2+4, x_3+4,...., x_{10}+4\) will be—?

(a) 20 (b) 24 (c) 40 (d) 10

30. If a hemisphere and a cone have equal base areas and equal heights, then what will be the ratio of their volumes?

(a) 1:3 (b) 2:3 (c) 3:2 (d) 3:1