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Q1. Find whether the number 3948 is divisible by 6 or not. Solution A number is divisible by 6 only if it is divisible by 2 and 3. Consider the number 3948. Since its units place digit is 8, which is even. So the number 3948 is divisible by 2. Again, sum of digits = 3 + 9 + 4 + 8 = 24. Since, 24 is divisible is 3. So the number 3948 is divisible by 3. Thus, the number is divisible by both 2 and 3. Hence, 3948 is divisible by 6. Q2. In the following addition, find A. Solution Consider: At one's place, A + 3 = _1 So think of a number which when added to 3 gives one's place as 1. Such a number is 8 as 8 + 3 = 11 Taking, A = 8, we obtain the addition as below: Q3. 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...
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Q1. A linear graph is given by the relation y = 3x + 6. Find the value of y if the value of x is 5.  1) 15 2) 21 3) 3 4) 18 Solution Put x = 5 in y = 3x + 6We get y = 21.  Q2. A bank gives 10% simple interest on the deposits. Draw a graph to show the relation between the sum deposited and the simple interest earned. Solution To draw the graph we assume the deposit sum to be Rs 1000, Rs 2000, Rs 3000 and Rs 4000. Now we calculate the SI for 1 year for the sum deposit. Sum deposit SI Rs 1000 Rs 2000 Rs 3000 Rs 4000 Plotting the points (1000, 100), (2000, 200), (3000, 300) and (4000, 400), we get the graph as below: Q3. Observe the graph:   What is the difference between the lowest marks of Rishit and Samyak?  ...
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14

Q1. What will be the value of a, if y + 2 is a factor of . Solution Since, y + 2 is a factor of , the remainder will be zero. Using Long Division, we have Now, 5a + 20 = 0 Q2. Find all the factors of 6xy. Solution All possible factors of 6 are: 1, 2, 3, 6 All possible factors of xy are: x, y, xy Hence all factors of 6xy are: 1, 2, 3, 6, x, y, xy, 2x, 2y, 2xy, 3x, 3y, 3xy, 6x, 6y, 6xy. Q3. Verify division algorithm, i.e., Dividend = Divisor x Quotient + Remainder for following: Dividend: Divisor: Solution Using Long Division, we have:   Verification: Dividend: Divisor: Quotient:  Remainder: 0 Now, Divisor x Quotient + Remainder Q4. Factorise: Solution Q5. Divide 27xy 2 (17x 2 - 68) by 51(x + 2). Solution Consider Thus, Q6. Divide by . Solution Q7. Factorise: x 2 + 8xy +16y 2 - 36  Solution Take Another Test
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13

Q1. Anusha has to prepare for her Maths exam. She has to study for 8 hours per day to complete the entire syllabus in 10 days. But because she had some relatives visiting, she was unable to study for two entire days. Now for how many hours should she study to finish the syllabus in the remaining 8 days? 1) None 2) 9 hours 3) 11 hours 4) 10 hours Solution 8 × 10 = 8 × x Q2. If the weight of 5 sheets of paper is 20 grams, how many sheets of the same paper would weigh 1 kg? Solution It is clear that the number of sheets and their corresponding weight vary directly. Also 1 kg = 1000 grams. Writing the information in the table, we have Number of sheets 5 x Weight (in grams) 20 1000 Now, in case of direct variation the ratio remains constant, so we have Hence, ...
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12

Q1. Subtract the number from the number . Solution To subtract the numbers, first we express the numbers with same power of 10. Consider Therefore, Q2. Simplify: Solution Q3. Write the following numbers in standard form: (i) (ii) 0.0000000014 Solution (i) (ii) Q4. If , find the value of x. Solution We have, Since, bases are equal, powers are also equal. Q5. Simplify: Solution Take Another Test
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