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#meritnation, , Mathematics, , TOP, 100, , Questions & Solutions, , , , Class 10

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#meritnation, , , , Meritnation Top 100 Questions, Class - 10, , , , Real Numbers, 93, , 1. Without performing actual division, state whether the rational number 600 will have a, terminating or non-terminating decimal expansion., , 2. Find the HCF of 1488 and 37888 using Euclid’s division algorithm., , 3. Use Euclid’s division lemma to show that the square of any positive integer is either of the, form 3p or 3p + 1, where p is an integer., , 45-9, 4. Prove that ( ) is an irrational number., , 5. On a circular track of length 1080 m, Srikant is walking at a speed of 90 m/min, Venkat at 72, m/min, and Bala at 60 m/min. If all of them start walking at 5:30 a.m. in the same direction from, same starting point, then at what time will they all meet each other at the starting point?, , Polynomials, , 6. If two of the zeroes of the polynomial p(x) = 3x* + 7x5 — 7x? — 21x — 6 are 3 and 3 ;:, then find the other zeroes of p(x)., , 7. Find the zeroes of the quadratic polynomial, p(x) = 6x” + 18x, and verify the relationship, between the zeroes and the coefficients., , 8. Ifa and f are the zeroes of the polynomial f(x) =x? ~ Sx + k such that a ~ f= 1, then find the, value of k., , Pair of Linear Equations in Two Variables, , 9. For what value of & will the system of equations x + 2y = 3 and 5x + ky = —7 have a unique, solution?, , 10. A group of students are seated in rows in such a way that the number of students in each row, is the same. If the number of students in each row is increased by 15, then number of rows, decreases by 5. If the number of students in each row is increased by 6, then the number of rows, decreases by 3. How many students were there in the group?, , , , [email protected] | 011-40705070

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#meritnation, , , , Meritnation Top 100 Questions, Class - 10, , , , 11. What is the value of & for which the pair of linear equations kx + 5y — (k — 5) = 0 and 20x +, ky — k= 0 has infinite many solutions?, , 12. Three men and eight women can complete a piece of work together in 10 hours. Eleven men, and thirteen women can complete the same piece of work together in 4 hours. How long will one, man alone and one woman alone take to complete the same work?, , 13. Solve the following pair of equations by algebraic method., 4 1, , (2x43) (2x-3y), a.) eg, (2x+3y) (2x-3y) _, , Quadratic Equations, , 14, For what value(s) of k does the quadratic equation 25x” — 10kx + 49 = 0 have equal roots?, 15. Find the roots of the equation 2x° — 7x + 3 = 0 using the method of completing the square., 16. For an excursion, Rs 12,900 is collected from a group of students such that same amount of, , money was contributed by each student. Had there been 14 students more, each of them would, have contributed Rs 21 less. How much amount of money is contributed by each student?, , 17, Determine the nature of the roots of the quadratic equation 5x’ -2V3x-7=0 ‘, , 18. The total cost of a certain length of a piece of cloth is Rs 200. If the piece was 5 m longer and, each metre of cloth costs Rs 2 less, the cost of the piece would have remained unchanged. How, long is the piece and what is its original rate per metre?, , 19. Solve the given quadratic equation for x : 9x” — 9(a + b)x + (2a° + Sab + 2b*) = 0., , 20. Solve for x :, 1 1, , z, Cie-2 ewes, , , , [email protected] | 011-40705070

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#meritnation, , , , Meritnation Top 100 Questions, Class - 10, , , , Arithmetic Progressions, =a 5, 21. Find the 25" term of the AP "2°" 2°",, , 22. The sum of 8" and 17" term of an AP is 36. Find the sum of first 24 terms of the AP., , 23. The students from five schools in a locality thought of planting trees to reduce air pollution., It was decided that the number of trees that each class of each school will plant will be the same, as the class in which they are studying. For e.g., class I will plant one tree, class II will plant two, trees and so on till class XII., , (i) How many trees will be planted by the students?, , (ii) Write values reflected in the question., , 24. For what value of & will the consecutive terms 3k + 2, 44 + 5 and 6k — 4 form an AP?, , 25. The ratio of the 21* term and 29" term of an arithmetic progression is 2 : 1. What is the 37", term of the arithmetic progression?, , 26. A thief runs with a uniform speed of 100 m/min. After one minute, a policeman runs after the, thief to catch him. He goes with a speed of 100 m/min in the first minute and increases his speed, by 10 m/min every succeeding minute. After how many minutes the policeman will catch the, thief., , 27. If the ratio of sum of the first m and terms of an AP is m’ : 1’, show that the ratio of its m'™, and n™ terms is (2m — 1): (2n- 1)., , 28. Find the sum of all three digit natural numbers, which are multiples of 11., , 29. If S, denotes the sum of the first 7 terms of an A.P., prove that S,)= 3 (S.) ~ Sj»)., , Triangles, AD 5, , 30. In the given AABC, DE|BC and AB 12 . If AC = 18 cm, then what is the length of EC?, , , , [email protected] | 011-40705070

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#meritnation, , , , Meritnation Top 100 Questions, Class - 10, , 31. The given figure shows an equilateral triangle ABC drawn on side BC of square BCED and, another equilateral triangle FDC drawn on diagonal DC of the square BCED., , A, , F, What is the ratio of the area of AABC to the area of AFDC?, , 32. The given figure shows a right-angled triangle PQR. S and T are the points on PQ and QR, 1 1, , respectively such that QS= 3 PQand QT= 3 QR., P., , s, , Q T R, Prove that 18(PT® + RS*) = 20PR’., , 33. State and prove the basic proportionality theorem., , , , [email protected] | 011-40705070