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Q1. Using the digits 4, 0 and 5, form all possible 3 digit numbers without repeating the digits. Also, classify them in a multiple of 2 and 3. Solution Digits are: 4, 0, 5 3 digit numbers are: 405, 450, 540, 504 A number is multiple of 2 if its unit place is even. Therefore, 450, 540 and 504 are multiples of 2. A number is multiple of 3 if the sum of digits is divisible by 3. For all the above 3 digit numbers, sum of digits is 9, which is divisible by 3. Hence all numbers are divisible by 3. Q2. Write all possible numbers using the digits 2, 4, 7 without repeating them. Solution All possible numbers with digits 2, 4 and 7 are: 247, 274, 427, 472, 742, 724. Q3. Write the following numbers in usual form: (i) 100 x 7 + 10 x 9 + 1 x 8 (ii) 1000 x 3 + 100 x 1 + 10 x 5 + 1 x 9 Solution (i) 100 x 7 + 10 x 9 + 1 x 8 = 700 + 90 + 8 = 798 (ii) 1000 x 3 + 100 x 1 + 10 x 5 + 1 x 9 = 3000 + 100 + 50 + 9 = 3159 Q4. Test the divisibility of 46602479 by 11. Sol...
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15

Q1. Two quantities x and y are related by the relation y = 5x + 3. Make a point table for 4 different values of x. Solution The relation is: y = 5x + 3 Taking x = 1, y = 5 x 1 + 3 = 8 Taking x = 2, y = 5 x 2 + 3 = 13 Taking x = 3, y = 5 x 3 + 3 = 18 Taking x = 4, y = 5 x 4 + 3 = 23 Table is: x 1 2 3 4 y 8 13 18 23 Q2. Write X-coordinate and Y-coordinate of the following points: (i) (8, -3) (ii) (4, 1) (iii) (-6, 4) Solution (i) In (8, -3) X-coordinate is 8 Y-coordinate is -3. (ii) In (4, 1) X-coordinate is 4 Y-coordinate is 1. (iii) In (-6, 3) X-coordinate is -6 Y-coordinate is 3. Q3. Which of the following points lie on y-axis? (0, 1), (-1, 0), (7, 0), (0, -4), (0, 4), (5, 0) Solution A point with zero x-coordinate lies on y-axis, i.e., a point of the form (0, b) lies on y-axis. Thus, points lying on y-axis are: (0, 1), (0, -4), (0, 4). Q4. Write the name of quadrant in which the following points lie: (i) (-8, 1) (ii) (-3, -1) (iii) (1,...
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12

Q1. Mass of earth is approximately 5,970,000,000,000,000,000,000,000 kg. Express this mass in standard form. Solution Mass of earth = 5,970,000,000,000,000,000,000,000 kg = 597 x 10000000000000000000000 kg = 597 x 10 22 kg = 5.97 x 10 24 kg Q2. Express the following in usual form: (i) 1.002 x 10 6 (ii) 5.54 x 10 7 Solution (i) 1.002 x 10 6 = 1.002 x 1000000 = 1002000 (ii) 5.54 x 10 7 = 5.54 x 10000000 = 55400000 Q3. Write the following in standard form. (i) 458000 (ii) 1780000 (iii) 85000 Solution (i) 458000 = 4.58 x 100000 = 4.58 x 10 5 . (ii) 1780000 = 1.78 x 1000000 = 1.78 x 10 6 . (iii) 85000 = 8.5 x 10000 = 8.5 x 10 4 . Q4. Compare the following pair of numbers. (i) 2.5 x 10 3 and 3.5 x 10 2 (ii) 2 5 and 5 2 Solution (i) 2.5 x 10 3 and 3.5 x 10 2 Or, 2.5 x 1...
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11

Q1. Find the surface area of cubes with edge (i) 5 cm (ii) 2.9 cm. Solution Surface area of cube = 6(Side) 2 . (i) Surface area of cube with edge 5 cm = 6(5) 2 = 6 x 25 = 150 cm 2 (ii) Surface area of cube with edge 2.9 cm = 6(2.9) 2 = 6 x 8.41 = 50.46 cm 2 Q2. If the area of a rectangle is 243 sq. m and the length is 27 m, what is the breadth of the rectangle? Solution Area of a rectangle is given by: Area = l x b, where l = length b = breadth Here, area is given as 243 m 2 and its length = 27 m Thus, Area = l x b 243 = 27 x b b = 9 Thus, breadth of the rectangle = 9 m Q3. Raju wants to fence the garden in his house which is in the shape of a rectangle having dimensions 25 m x 18 m. Find the cost of fencing at the rate of Rs 200 per metre. Solution The length of the fence required is the perimeter of the rectangular garden. Given ...
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9

Q1. Define monomial, binomial and trinomial and give two examples of each. Solution Monomial: An algebraic expression consisting only one term is called a monomial. Examples: x 2 y, -5xy 2 Binomial: An algebraic expression consisting two terms is called a binomial. Examples: y - 7x 2 , -6 + x 2 Trinomial: An algebraic expression consisting three terms is called a trinomial. Examples: 1 + x + x 2 , -1 + z 2 - z 2 x 2 , 3x + 2y - z Q2. Classify the following as monomial, binomial or trinomial: (i) 2x + 3y (ii) 2x 3 + 3y 2 - 1 (iii) 2xy + 10 (iv) -9x 4 yz Solution (i) 2x + 3y : Binomial (ii) 2x 3 + 3y 2 - 1 : Trinomial (iii) 2xy + 10 : Binomial (iv) -9x 4 yz : Monomial Q3. Write down the terms in the following expression: (i) -2x 2 y + 5xy + y 3 - 7 (ii) -9xy + 5x 2 y - 3 Solution (i) Terms in the expression -2x 2 y + 5xy + y 3 - 7 are: -2x 2 y, 5xy, y 3 , - 7 (ii) Terms in the expression -9xy + 5x 2 y - 3 are: -9xy, 5x 2 y, -3 Q4. Write the numeric...
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8

Q1. In a book fair 27.5% discount is offered on a book of Rs. 500, then find the discount. Solution Q2. A farmer borrows Rs. 7000 from a co-operative society for 2 years at the rate of 12%. How much does he has to pay at the end of two years? Solution Q3. The sales tax rate is 8%. If Rahul bought a new car and paid a sales tax of Rs 1,920, what was the cost of the car before the tax? Solution Let  us say the car costs Rs y.   That would mean that y multiplied by 8% is Rs 1920.  y(8%) = 1920 8% could also be expressed as 0.08 Thus, y(0.08) = 1920 y =Rs 24000 The car costs Rs 24000 without tax. Q4. Convert the following ratios into percentage: 1) 3 : 5 2) 1 : 4 Solution Q5. 15 boys earn Rs. 600 in 4 days, how much will 20 boys earn in 7 days? Solution Q6. Find the marked price of an article which is bought for Rs. 13489 after a discount of 18%. Solution Q7. The catalogu...
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