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ISHA VIDHYA MATRICULATION SCHOOLS, REVISION EXAM- MATHEMATICS, TIME: 3 HRS, CLASS: 10, MARKS: 100, __________________________________________________________________________, PART- I, Note : i) Answer all the 14 questions, , ( 1 x 14 = 14), , ii) Choose the most suitable answer from the given four alternatives and write the, option code with the corresponding answer., 1. If the ordered pairs (a+2, 4) and (5,2a+b) are equal then (a,b) is, A) (2,-2), B) (5,1), C) (2,3), D) (3,-2), 2, 2. The range of the relation R= { (x, x ) | x is a prime number less than 13} is, A) {2,3,5,7}, B) {2,3,5,11}, C) {4,9,25,49,121}, , D) {1,4,9,25,49,121}, , 3. Let n(A) = m and n(B) = n then the total number of non- empty relations that can be, defined from A to B is, A) mn, B) nm, C) 2mn-1, D) 2mn, 4. The sum of the exponents of the prime factors in the prime factorisation of 1729 is, A) 1, B) 2, C) 3, D) 4, 5. If the HCF of 65 and 117 is expressible in the form of 65m-117, then the value of m is, A) 4, B) 2, C) 1, D) 3, 1, , 6. π¦ 2 +π¦ 2 is not equal to, A), , π¦ 4 +1, π¦2, , B) (y+1/y)2, , C) (y-1/y)2+2, , D) (y+1/y)2-2, , 7. If n(AxB) = 6 and A={1,3} then n(B) is, A) 1, B) 2, C) 3, D) 4, th, th, 8. If 6 times of 6 term of an A.P is equal 7 times the 7 term, then the 13th term of the, A.P is, A) 0, B) 6, C) 7, D) 13, 9. Given F1= 1, F2= 3 and Fn = Fn-1 + Fn-2 then F5 is, A) 3, B) 5, C) 8, D) 11, 2, 10. The nature of the roots of x - 25=0 is, A) no real roots, B) real and equal, C) real and unequal, , D) imaginary roots, , 11. The solution of (2x-1)2 = 9 is equal to, A) -1, , B) 2, , C) -1,2, , D) None of these
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12. The quotient when, , π₯ 2 β25, π₯+3, , π₯+5, , divided by, , π₯ 2 β9, , is, , A) (x-5) (x-3), , B) (x-5) (x+3), , B) (x+5) (x-3), , D) (x+5) (x+3), , 13. Which of the following should be added to make x4+64 a perfect square, A) 4x2, , B) 16x2, , C) 8x2, , D) -8x2, , 14. If ( x-6) is the HCF of x2-2x-24 and x2-kx-6 then the value of k is, A) 3, , B) 5, , C) 6, , D) 8, , PART β II, Note : i) Answer only 10 questions., ii) Question No. 28 is compulsory., , ( 10 x 2 = 20 ), , 15. If B x A = { (-2,3), (-2,4), (0,3), (0,4), (3,3), (3,4) } find A and B, 16. A Relation R is given by the set { ( x,y ) | y = x+3 , x Ο΅ { 0,1,2,3,4,5 } }. Find its domain, and range., 17. A man has 532 flower pots. He wants to arrange them in rows such that each row contains, 21flower pots. Find the number of completed rows and how many flower pots are left, over., 18. If 3+k, 18-k, 5k+1 are in A.P then find k., 19. Find the sum and product of the roots for the following quadratic equations., x2 + 8x - 65=0., 20. If 13824 = 2a x 3b then find a and b., 21. Find the LCM of 2x2-5x-3, 4x2-36., 22. Let A = { 1,2,3 } and B = { x / x is a prime number less than 10 }. Find A x B and B x A., 23. Solve the following quadratic equation by factorization method. 3 ( p2- 6) = p ( p + 5)., 24, , 24. If the difference between a number and its reciprocal is 5 , find the number., 25. Multiply, , π₯3, 9π¦ 2, , by, , 27π¦, π₯5, , .
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26. Find all positive integers, when divided by 3 leaves remainder 2., 27. If a polynomial p(x) = x2-5x-14 is divided by another polynomial q(x) we get, , π₯β7, π₯+2, , ,, , find q(x)., 28. If A = { 1,3,5 } and B = { 2,3 } show that n ( A x B ) = n ( B x A) = n ( A) x n ( B ), (OR), If Ξ± and Ξ² are the roots of x2+7x+10 = 0 find the value of Ξ±2 + Ξ²2, , PART β III, Note : i) Answer only 10 questions., ii) Question number 42 is compulsory., , ( 10 x 5 = 50 ), , 29. Let A = { x Ο΅ W | x < 2 } , B = { x Ο΅ N | 1 < x β€ 4 } and C = { 3,5 }. Verify that, A x ( B β© C ) = ( A x B ) β© ( A x C )., 30. Let A = The set of all natural numbers less than 8, B = The set of all prime numbers less, than 8, C = The set of even prime number. Verify that, ( A β© B ) x C = ( A x C ) β© ( B x C)., 31. Represent the given relation { ( x,y ) | y = x+3, x,y are natural numbers < 10 }, by ( a) an arrow diagram, ( b ) a graph and ( c ) a set in roster form., 32. Let A = { x Ο΅ N | 1 < x < 4 } , B = { x Ο΅ W | 0 β€ x < 2 } and C = { x Ο΅ N | x < 3 }. Then, verify that A x ( B U C ) = (A x B ) U ( A x C)., 33. In a winter season let us take the temperature of Ooty from Monday to Friday to be in, A.P. The sum of temperatures from Monday to Wednesday is 0β and the sum of the, temperatures from Wednesday to Friday is 18β. Find the temperature on each of the five, days., 34. If ( m + 1 )th term of an A.P. is twice the ( n + 1 )th term, then prove that ( 3m + 1 )th term, is twice the ( m + n + 1 )th term.
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π2 β1, th, , 35. Find a8 and a15 whose n term is an = {, , π+3, π2, 2π+1, , ; π ππ ππ£ππ, πππ, ., , ; π ππ πππ, ππ π, , 36. In an A.P. sum of four consecutive terms is 28 and their sum of their squares is 276. Find, the four numbers., 37. Solve the following system of linear equations in three variables 3x β 2y + z = 2,, 2x + 3y β z = 5, x + y + z = 6., 38. If A =, , π₯, π₯+1, , ,B=, , 1, π₯+1, , , prove that, , ( π΄+π΅ )2 +( π΄βπ΅ )2, π΄Γ·π΅, , =, , 2 ( π₯2 + 1 ), π₯ ( π₯ +1 )2, , 39. Find the GCD of 6x3- 30x2 + 60x - 48 and 3x3- 12x2 + 21x β 18., 40. Find the square root of 64x4 β 16x3 +17x2 β 2x + 1 by division method ., 41. A ladder 17 feet long is leaning against a wall. If the ladder, vertical wall and the floor, from the bottom of the wall to the ladder form a right triangle, find the height of the wall, where the top of the ladder meets if the distance between bottom of the wall to bottom of, the ladder is 7 feet less than the height of the wall ?, 42. If the roots of the equation ( c2 β ab ) x2 β 2( a2 β bc )x + b2 β ac = 0 are real and equal, prove that either a = 0 ( or ) a3 + b3 + c3 = 3abc., , (OR), , Determine the general term of an A.P. whose 7th term is -1 and 16th term is 17., PART β IV, Note : i) This section contains one question with two alternatives., ii) Answer the given question choosing either of the alternatives., 43. Discuss the nature of solutions of the quadratic equation x2 + 2x + 5 = 0, , ( 2 x 8 = 16 ), (OR), , Discuss the nature of solutions of the quadratic equation x2 β 6x + 9 = 0, , 44. Draw the graph of y = 2x2 and hence solve 2x2 β x β 6 = 0, Draw the graph of y = x2 + 3x + 2 and use it to solve x2 + 2x + 1 = 0, , (OR)