1. Find the cube root of (i) 456533 (ii) 157464 (iii) 474552 (iv) 614125
2. Find the smallest number by which the following numbers must be divided so that the quotient is a perfect cube. Also find the cube roots of the quotients so obtained.
(i) 3087 (ii) 33275 (iii) 29160
3. Find the smallest number to be multiplied with the given numbers to make them a perfect cube. Also find the cube roots of the products so found.
(i) 81 (ii) 100 (iii) 392
4. Three numbers in the ratio 1:2:3 .The sum of their cubes is 62208.Find the numbers.
5. 68 boxes of a certain commodity require a shelf length of 13.6 m . How many more boxes of the same commodity would occupy a shelf length of 20.4 m ? [answer: 34 more boxes]
6. Assuming that the height and the time taken by a H2 Balloon are in direct proportion. Find a, b, c, d.
Time( in minutes) / 2 / 3 / b / 25 / dHeight (in metres) / a / 36 / 84 / c / 1440
7. If x and y are in inverse proportion, find p, q , r, s.
x / 24 / 12 / q / 48 / sy / p / 8 / 6 / r / 0.5
8. A garrison has provisions for 900 men for 20 days.
(i) How many men must be transferred to another camp so that the provisions last for 30 days? (ii) If the food last only for 15 days, how many extra men joined the camp?
9. 15 % of the workers in a factory are female and the numbers of males are 850. Find the total workers and the ratio of female to male.
10. A shirt was sold for Rs. 442 at a discount of 15%. Another shirt was sold for Rs.240 at a discount of 25%. Find the total marked price of these two shirts. How much money will Raj save if he does the purchase of these two shirts?
11. A shopkeeper buys 80 articles for Rs. 2400, spends Rs. 100 as overhead charges and then sells them for a profit of 16%. Find the selling price of one article. [Answer: Rs.36.25 ]
12. The simple interest on a sum of money for 11/2 years at 6% p.a.is Rs. 900. What will be the compound interest on that sum at the same rate and for the same period if the interest is compounded half yearly? [ Answer: Rs. 10927.27]
13. An almirah costs Rs.29430 inclusive of tax. If the VAT charged is at the rate of 9%.Find the price of the almirah before VAT was added.
14. First simplify and then evaluate[ if a = 1 , b = (-1) , c = 2 ]
4c ( -a + b + c ) - 3a ( a + b + c ) + 2b ( a – b + c )
15. Find the product of ( x + 5y ) ( 2x – 3y + 4z )
16. Using identities expand the following :
(i) (3m + 23 n )2 (ii) ( 4g – 3h )2 (iii) ( x- 11 ) (x – 1 ) (iv) (x+3) (x+7) (v) (x+9) (x-2) (vi) (x-8) (x+5) (vii) ( 7yz + 2xy2 )( 7yz – 2xy2 )
17. Evaluate using Identities:
(i) 57 × 63 (ii) 1032 (iii) 992 (iv) 95 × 102 (v) 20.2 × 20.3
18. Show that ( 2p + 5 )2 – 20 p = ( 2p – 5 )2
19. A piece of wire is bent in the shape of an equilateral triangle of each side 6.6 cm. It is rebendt to form a circular ring. What is the diameter of the ring? How much area will it cover? Draw figure also.
20. Find the area of a rhombus whose two diagonals are 13m and 8m .
21. Diagonal of a quadrilateral shaped field is 120 m and the perpendiculars dropped on it from the remaining opposite vertices are 64 m and 29 m. Find the area of the field.
22. Area of a trapezium is 550 sq.m and its parallel sides measure 55m and 33m. Find the height of the trapezium.
23. Find the altitude of a rhombus whose area is 440m2 and the perimeter is 160m.
24. Find the lateral surface and the total surface area of a cube of each side 12.5cm.
25. Dimensions of a cuboid are 12m × 9m × 5m.Find its lateral surface and the total surface areas.