Usha Martin World School, Patna Session: QUESTION BANK. All questions are compulsory.

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1 Usha Martin World School, Patna Session: QUESTION BANK Class: VII Sub. : MATHS All questions are compulsory. Q1. There are number of rational numbers between two rational numbers. Q2. All rational numbers are integers. True/false Q3. In the standard form of a rational number, the common factor of numerator and denominator is always: (a) 0 (b) 1 (c) 2 (d) 2 Q4. If p= m t and q= n t, then p q =? Q5. A body floats 2 of its volume above the surface. What is the ratio of the body submerged volume to its exposed 9 volume? Re-write it as a rational number. Q6. From a rope 68 m long, pieces of equal size are cut. If length of one piece is 4 1 m, find the number of such 4 pieces. Q7. Simplify: Q8. List four rational numbers between 5 7 and 7 8 Q9. Represent the following rational numbers on a number line: Q10. In Fig. 9.10, ABCD is a parallelogram, in which AB = 8 cm, AD = 6 cm and altitude AE = 4 cm. Find the altitude corresponding to side AD. Q11. Circumference of a circle is 33 cm. Find its area. Q12. If two cubes of dimensions 2 cm by 2cm by 2cm are placed side by side, what would the dimensions of the resulting cuboids be? Q13. Rectangle ABCD is formed in a circle as shown in Fig If AE = 8 cm and AD=5 cm, find the perimeter of the rectangle. Q14. In reference to a circle the value of π is equal to Q15. A wall of a room is of dimensions 5 m 4 m. It has a window of dimensions 1.5 m 1m and a door of dimensions 2.25 m 1m. Find the area of the wall which is to be painted. Q16. Ratio of the area of WXY to the area of WZY is 3 : 4 (Fig. 9.33). If the area of WXZ is 56 cm 2 and WY = 8 cm, find the lengths of XY and YZ. Page 1 of 5

2 Q17. Find the area of a square inscribed in a circle whose radius is 7 cm (Fig. 9.45). Q18. Find the areas of the shaded region: Q19. An algebraic expression containing three terms is called a (a) Monomial (b) Binomial (c) Trinomial (d) All of these Q20. Number of terms in the expression 3x 2 y 2y 2 z z 2 x + 5 is (a) 2 (b)3 (c)4 (d) 5 Q21. Which of the following is a pair of like terms? (a) 7xy 2 z, 7 x 2 yz (b) 10xyz 2, 3xyz 2 (c) 3xyz, 3x 2 y 2 z 2 (d) 4xyz 2, 4x 2 yz Q22. b 0 is equal to (a) 1 b (b) 1 b 0 (c) 0 ( 1) b (d) b 0 1 Q23. The length of a side of square is given as 2x+ 3. Which expression represents the perimeter of the square? (a) 2x + 16 (b) 6x + 9 (c) 8x + 3 (d) 8x + 12 Q24. (x + y + z) is an expression which is neither monomial nor. Q25. On adding a monomial to 2 x+ 4y 2 + z, the resulting expression becomes a binomial. Q26. Write the following statements in the form of algebraic expressions and write whether it is monomial, binomial or trinomial. (a) X is multiplied by itself and then added to the product of x and y. (b) Two times q subtracted from cube of q. (c) Sum of the products of a and b, b and c and c and a. (d) The sum of square of x and cube of z. Q27. To what expression must 99x 3 33x 2 13 x 41 be added to make the sum zero? Q28. If A = 3x 2 4x+ 1, B = 5x x 8 and C = 4x 2 7x+ 3, then find: (i) (A + B) C (ii) B + C A Q29. Each symbol given below represents an algebraic expression: The symbols are then represented in the expression: Find the expression which is represented by the above symbols. Q30. A taxi service charges 8 per km and levies a fixed charge of `50. Write an algebraic expression for the above situation, if the taxi is hired for x km. Q31. A wire is (7x 3) metres long. A length of (3x 4) metres is cut for use. Now, answer the following questions: (a) How much wire is left? Page 2 of 5

3 (b) If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed? Q32. Out of the following, the number which is not equal to 8 27 is Q33. x is a non-zero rational number. Product of the square of x with the cube of x is equal to the (a) Second power of x (b) third power of x (c) Fifth power of x (d) sixth power of x Q34. Value of is (a) 10 (b) (c) 101 (d) Q35. If = K , then the value of K is (a) 1 (b) 2 (c) 3 (d) 4 Q36. Which of the following is not equal to 1? Q37. In standard form, the number is written as K 10 8 Where K is equal to (a) (b) (c) (d) Q38. Which of the following is not true? (a) 3 2 > 2 3 (b) 4 3 = 2 6 (c) 3 3 = 9 (d) 2 5 > 5 2 Q39. x 0 x 0 = x 0 x 0 is true for all non-zero values of x. Q40. Arrange in descending order: Q41. How many times of 30 must be added together to get a sum equal to 30 7? Q42. Express the following numbers in standard form: (a) (b) Q43. Write the number of seconds in scientific notation. Page 3 of 5

4 Q44. Bacteria can divide in every 20 minutes. So 1 bacterium can multiply to 2 in 20 minutes, 4 in 40 minutes, and so on. How many bacteria will there be in 6 hours? Write your answer using exponents. Q45. A net of a 3-D shape is a sort of skeleton - outline in 2-D, which, when folded results in the 3-D shape. (True/False) Q46. Draw all the lines of symmetry for the following letters if they exist. Q47. Draw the top, the front and the side views of the following solid figure made up of cubes. Q48. A triangle can be constructed by taking its sides as: (a) 1.8 cm, 2.6 cm, 4.4 cm (b) 2 cm, 3 cm, 4 cm (c) 2.4 cm, 2.4 cm, 6.4 cm (d) 3.2 cm, 2.3 cm, 5.5 cm Q49. A triangle can be constructed by taking two of its angles as: (a) 110, 40 (b) 70, 115 (c) 135, 45 (d) 90, 90 Q50. A solid that has only one vertex is (a) Pyramid (b) Cube (c) Cone (d) Cylinder Q51. Which of the following nets is a net of a cylinder? Q52. Draw two parallel lines at a distance of 2.2 cm apart. Q53. Construct an obtuse angled triangle which has a base of 5.5 cm and base angles of 30 and 120. Q54. By what minimum angle does a regular hexagon rotate so as to coincide with its original position for the first time? Q55. Match the nets with appropriate solids: Page 4 of 5

5 56. Tell whether each figure has rotational symmetry or not. Page 5 of 5