EXPECTED QUESTIONS FOR CLASS X MARCH -017 ONE MARK 1. SETS AND FUNCTIONS 1. For two sets A and B, A B = A if only if (A) B A (B) A B (C) A B (D) A B = Ø. If A B, then A B is (A) B (B) A\B ( C) A (D) B\A 3. For any two sets P and Q, P Q is A) { x : x ϵ P or x ϵ Q } (B) { x : x ϵ P and x Q } (C) { x : x ϵ P and x ϵ Q } (D) { x : x P and x ϵ Q} 4. In n[p(a)] = 64, then n(a) is [ M 13] (A) 6 (B) 8 (C) 4 (D) 5 5. For any three sets A, B and C, A (B C) is (A) (A B) (B C) (B) (A B) (A C) (C) A (B C) (D) (A B) (B C) 6. For any three sets A, B and C, B \ (A C) is (A) (A \ B) (A \ C) (B) (B \ A) (B \ C) (C) (B \ A) (A \ C) (D) (A \ B) (B \ C) 7. If n(a) = 0, n(b) = 30 and; n(a B) = 40;, then n(a B) is equal to [O 14] (A) 50 (B) 10 (C) 40 (D) 70 8. If { (x, ), (4, y) } represents an identity function, then (x, y) is (A) (, 4) (B) (4, ) (C) (, ) (D) (4, 4) 9. Given f(x) = (- 1) x is a function from N to Z. Then the range of f is (A) { 1 } (B) N (C) { 1, - 1} (D) Z 1 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
10. Let A = {1, 3, 4, 7, 11}, B = {- 1, 1,, 5, 7, 9} and f : A B be given by f = { (1, -1), (3, ), (4, 1), (7, 5), (11, 9) }. Then f is (A) one one (B) onto (C) bijective (D) not a function 11. C f D function 4 5 4 16 5 The given diagram represents (A) an onto function (B) a constant (C) an one one function (D) not a function 1. If A = { 5, 6, 7 }, B = { 1,, 3, 4, 5 } and f : A B is defined by f(x) = x, then the range of f is [J 1] (A) { 1, 4, 5 } (B) { 1,, 3, 4, 5 } (C) (, 3, 4 } (D) { 3, 4, 5 } 13. If the range of a function is a singleton set, then it is (A) a constant function (C) a bijective function (B) an identity function (D) an one one function 14. If f : A B is a bijective function and if n(a) = 5 then n(b) is equal to [O 13, M 15] (A) 10 (B) 4 (C) 5 (D) 5 TWO MARKS SETS [ONE QUESTION] 1. If A = {4, 6, 7, 8, 9}, B = {, 4, 6} and C = {1,, 3, 4, 5, 6} then find (i) A (B C) (ii) A (B C) (iii) A\(C \ B). **. If A = {10, 15, 0, 5, 30, 35, 40, 45, 50}, B = { 1, 5, 10, 15, 0, 30} and C = { 7, 8, 15, 0, 35, 45, 48} find A \ (B C). * 3. If U = { 4, 8, 1, 16, 0, 4, 8}, A = { 8, 16, 4} and; B = { 4, 16, 0, 8} Find (i) (A B) (ii) (A B) (iii) A B (iv) A B. 4. If A and B are any two sets and U is the universal set such that n(u) = 700, n(a) = 00, n(b) = 300 and; n(a B) = 100 find n(a B ). 5. Given n (A) = 85, n(b) = 195, n(u) = 500, n(a B) = 410. Find n(a B ) ** EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
6. For any three sets A, B and ; C if n(a) = 17, n(b) = 17, n(c) = 17, n(a B) = 7, n(b C) = 6, n(a C) = 5 kw;wk; n(abc) =, find n(abc). 7. Draw Venn diagram for the following: (i) A ( B C ) (ii) A (B \ C) (iii) (B C) \ A* (iv) C (B A)** (v) C (B \ A) FUNCTIONS [ONE QUESTION] 8. Verify that the relation f = { (1, ), (4, 5), (9, -4), (16, -4)} is a function from A = {1, 4, 9, 16} to B = { -1,, -3, -4, 5, 6} or not. In case of a function, write down its range. 9. Let A = {1,, 3, 4} and B = {1,, 3, 4,5, 6, 7, 9, 10, 11, 1}. Let R = {(1, 3), (, 6), (3, 10), (4, 9)} A B be a relation. Show that R is a function and find its domain, co-domain and the range of R. x if x 0 10. Let x =, where x R - x if x < 0. Does the relation x, y / y= x, x R define a function? Find its range.* 11. Is the relation f = { (1, - 4), (1, - 1), (9, - 3), (16, ) } a function from A = { 1, 4, 9, 16 } to B = { - 1,, - 3, - 4, 5, 6 }? 1. Let X = { 1,, 3, 4}. Examine whether the relation g = { (3, 1), (4, ), (, 1) } is a function from X to X or not. Explain.* 1 13. A = { -, - 1, 1, } and f = x, : x A. Write down the range of f. Is f a function x from A to A?* 14. Let f = { (, 7), (3, 4), (7, 9), ( - 1, 6), (0, ), (5, 3) } be a function from A = { - 1, 0,, 3, 5, 7 } to B = {, 3, 4, 6, 7, 9}. Is this (i) an one one function (ii) an onto function (iii) both one one and onto function? 15. If X = { 1,, 3, 4, 5 }, Y = { 1, 3, 5, 7, 9 } determine whether the relation R = { (1, 1), (, 1), (3, 3), (4, 3), (5, 5) } is a function from X to Y or not. If it is a function, state the type. * 16. Write the pre images of and 3 in the function f = { (1, ), (13, 3), (15, 3), (14, ), (17, 17) } If R = { (a, - ), ( - 5, b), (8, c), (d, - 1) } represents the identity function, find the values of a, b, c and d. * 17. The following table represents a function from A = { 5, 6, 8, 10 } to B = { 19, 15, 9, 11 } where f(x) = x 1. Find the values of a and b. * x 5 6 8 10 FIVE MARKS f(x) a 11 b 19 3 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
SETS [ONE QUESTION] 1. Use Venn diagrams to verify (i) A (B C) = (A B) (A C) * (ii) A (B C) = (A B) (A C)* (iii) A \ (B C) = (A \ B) (A \ C) * (iv) (A B) = A B. For A = { - 3, - 1, 0, 4, 6, 8, 10 }, B = { - 1, -, 3, 4, 5, 6 } and C = { - 1,, 3, 4, 5, 7 }. Verify A (B C) = (A B) (A C) by using Venn diagram* 3. For A = { - 3, - 1, 0, 4, 6, 8, 10 }, B = { - 1, -, 3, 4, 5, 6 } and C = { - 1,, 3, 4, 5, 7 }. Verify A (B C) = (A B) (A C) by using Venn diagram 4. For A = { - 3, - 1, 0, 4, 6, 8, 10 }, B = { - 1, -, 3, 4, 5, 6 } and C = { - 1,, 3, 4, 5, 7}, Show that A (B C) = (A B) (A C). 5. For A = { x / - 3 x < 4, x R}, B = { x/ x < 5, x N} and C = { - 5, - 3, - 1, 0, 1, 3}, show that A (B C) = (A B) (A C). * 6. Let A = { a, b, c, d, e, f, g, x, y, z }, B = { 1,, c, d, e } and C = { d, e, f, g,, y }. Verify A \ (B C) = ( A \ B) (A \ C) 7. Let A = { 1, 3, 5, 7, 9, 11, 13, 15 }, B = { 1,, 5, 7 } and C = { 3, 9, 10, 1, 13 }. Verify A \ (B C) = ( A \ B) (A \ C) 8. Let U = { -, - 1, 0, 1,, 3,, 10 }, A = { -,, 3, 4, 5 } and B = { 1, 3, 5, 8, 9 }. Verify De Morgan s laws of complementation. Let A = { - 5, - 3, -, - 1 }, B = { -, - 1, 0 } and C = { - 6, - 4, - }. Find A \ (B \ C) and (A \ B) \ C. What can we conclude about set difference operation? * In a survey of university students, 64 had taken mathematics course, 94 had taken computer science course, 58 had taken physics course, 8 had taken mathematics and physics, 6 had taken mathematics and computer science, had taken computer science and physics course and 14 had taken all the three courses. Find the number of students who were surveyed. Find how many had taken one course only. * 9. In a school of 4000 students, 000 know French, 3000 know Tamil and 500 know Hindi, 1500 know French and Tamil, 300 know French and Hindi, 00 know Tamil and Hindi and 50 know all the three languages. (i) How many know at least one language? (ii) How many do not know any of the three languages? (iii) How many know only two languages? 10. In a town 85% of the people speak Tamil, 40% speak English and 0% speak Hindi. Also, 3% speak English and Tamil, 13% speak Tamil and Hindi and 10% speak English and Hindi, find the percentage of people who can speak all the three languages. 4 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
FUNCTIONS [ONE QUESTION] Let A = { 0, 1,, 3 } and B = { 1, 3, 5, 7, 9 } be two sets. Let f: A B be a function given by f(x) = x + 1. Represent this function as (i) a set of ordered pairs (ii) a table (iii) an arrow diagram and (iv) a graph* x - 3 11. Let A = { 6, 9, 15, 18, 1 }, B = { 1,, 4, 5, 6 } and f : A B be defined by f(x) = 3. Represent f by (i) an arrow diagram, (ii) a set of ordered pairs, (iii) a table (iii) a graph 1. A function f : [1, 6 ) R defined as follows * 1 + x, 1 x < f(x) = x - 1, x < 4 3x - 10, 4 x < 6 Find the value of (i) f(5) (ii) f(3) (iii) f(1) (iv) f() f(4) (v) f(5) 3 f(1) ONE MARK. SEQUENCES AND SERIES OF REAL NUMBERS 1. Which one of the following is not true? (A) A sequence is a real valued function defined on N (B) Every function represents a sequence (C) A sequence may have infinitely many terms (D) A sequence may have a finite number of terms. If a, b, c are in A.P. then a - b is equal to [O 1, M 14] b - c (A) a b (B) b c (C) a c (D) 1 3. If the sequence a 1, a, a 3,. is an A.P., then the sequence a 5, a 10, a 15, is (A) a G.P. (B) an A.P. (C) neither A.P. nor G.P. (D) a constant sequence 4. If k +, 4k 6, 3k are the three consecutive terms of an A.P. then the value of k is (A) (B) 3 (C) 4 (D) 5 5. If a, b, c, l, m, n are in A.P. then 3a + 7, 3b + 7, 3c + 7, 3l + 7, 3m + 7, 3n + 7 for [O 13] (A) a G.P. (B) an A.P. (C) a constant sequence (D) neither A.P. nor G.P. 6. If a, b, c are in G.P. then a - b b - c is equal to [M 13, J 14, J 16] (A) a b (B) b a (C) a c (D) c b 7. If x, x +, 3x + 3 are in G.P. then 5x, 10x + 10, 15x + 15 form 5 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
(A) an A.P. (B) a G.P. (C) a constant sequence (D) neither A.P. nor G.P. 8. If the product if the first four consecutive terms of a G.P. is 56 and if the common ratio is 4 and the first term is positive, then its 3 rd term is [J 13} (A) 8 1 (B) 16 (C) 1 3 (D) 16 9. In a G.P. t = 3 5 and t 3 = 1. Then the common ratio is [O 13] 5 (A) 1 5 (B) 1 3 (C) 1 (D) 5 10. If x 0, then 1 + secx + sec x + sec 3 x is equal to (A) (1 + sec x)(sec x + sec 3 x + sec 4 x) (B) ( 1 + sec x)(1 + sec x + sec 4 x) (C) ( 1- sec x)(sec x + sec 3 x + sec 5 x) (D) 91 + Sec x)(1 + Sec 3 x + Sec 4 x) 11. If the nth term of an A.P. is t n = 3 5n, then the sum of the first n terms is [M 14] n n n (A) 1 5n (B) n(1 5n) (C) 1 5n 1 n 1. The common ratio of the G.P. a m n, a m, a m + n is [M 15] (A) a m (B) a - m (C) a n (D) a - n (D) TWO MARKS I ARITHMETIC PROGRESSION 1. The first term of an A.P. is 6 and the common difference is 5. Find the A.P. and the general term.. Find the common difference and 15 th term of the A.P. 15, 10, 115, 110,..* 3. Find the 17 th term of the A.P. 4, 9, 14,.. 4. How many two digit numbers are divisible by 13 [M 1] 5. Three numbers are in the ratio : 5 : 7. If the first number, the resulting number on the subtraction of 7 from the second number and the third number form an arithmetic sequence, then find the numbers.* 6. If a, b, c are in A.P. then prove that (a c) = 4(b ac). II ARITHMETIC SERIES 7. Find the sum of the arithmetic series (i) 5 + 11 + 17 +. + 95. (ii) 38 + 35 + 3 +.. +. 8. Find the sum of the first 30 terms of an A.P. whose nth term is 3 + n. 9. The sum of first n terms of a certain series is given as 3n n. Show that the series is an arithmetic series. 6 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
10. Find the S n for the following arithmetic series described. (i) a = 5, n = 30, l = 11 (ii) a = 50, n = 5, d = - 4. * If a clock strikes once at 1 o clock, twice at o clock and so on, how many times will it strike in a day? * III GEOMETRIC PROGRESSION 11. Which term of the geometric sequence 5,, 4 5, 8 5, is 18 1565? 1. The fifth term of a G.P. is 1875. If the first term is 3, find the common ratio.* IV GEOMETRIC SERIES 13. Find the sum of the first 5 terms of the geometric series 16 48 + 144 43 +..* 14. Find the sum of the first 7 terms of the geometric series 1 1 1... 9 7 81 15. Find Sn for each of the geometric series described below. (i) a = 3, t 8 = 384, n = 8.* (ii) a = 5, r = 3, n = 1. 16. How many consecutive terms starting from the first term of the series (i) 3 + 9 + 7 +. would sum to 109? (ii) + 6 + 18 +.. would sum to 78? V SPECIAL SERIES 17. Find the sum of the following seires: (i) 1 + + 3 +. + 45 (ii) + 4 + 6 + + 100 (iii) 6 + 7 + 8 +. + 60* (iv)1 + + 3 3 +. + 5 (v)1 3 + 3 + 3 3 +.. + 0 3 18. If 1 3 + 3 + 3 3 +.. + n 3 = 36100, then find 1 + + 3 +. + n* 19. If 1 + + 3 +. + p = 171, then find 1 3 + 3 + 3 3 +.. + p FIVE MARKS I ARITHMETIC PROGRESSION 1. If 9 th term of an A.P. is zero, prove that the 9 th term is double the 19 th term.. The sum of three consecutive terms in an A.P. is 6 and their product is 10. Find the three numbers. 3. If m times the m th term of an A.P. is equal to n times its n th term then show that the (m + n) th term of the A.P. is zero* 4. If a x = b y = c z, x 0, y 0, z 0 and b = ac, then show that 1 x, 1 y, 1 are in A.P. z 7 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
II ARITHMETIC SERIES 5. Find the sum of all 3 digit natural numbers, which are divisible by 8 * 6. Find the sum of all 3 digit natural numbers, which are divisible by 9 7. Find the sum of all natural numbers between 300 and 500 which are divisible by 11 8. Find the sum of all numbers between 100 and 00 which are not divisible by 5 9. Find the sum of the first 40 terms of the series 1 + 3 4 +.. 10. Find the sum of the first n terms of the series 1 + 3 4 +..* 11. If there are (n + 1) terms in an arithmetic series, then prove that the ratio of the sum of odd terms to the sum of even terms is (n + 1) : n.* III GEOMETRIC PROGRESSION 1. The sum of the first three terms of a geometric sequence is 13 and their product is 1. 1 Find the common ratio and the terms. 13. If the product of three consecutive terms in G.P. is 16 and sum of their products in pairs is 156, find them.* 14. If a, b, c, d are in a geometric sequence, then show that (a b + c)(b + c + d) = ab + bc + cd* 15. If a, b, c, d are in geometric sequence, then prove that (b c) + (c a) + (a b) = (a d) IV GEOMETRIC SERIES 16. Find the sum of the first n terms of the series 6 + 66 + 666 + * 17. Find the sum of the first n terms of the series 7 + 77 + 777 +. 18. Find the sum of the first n terms of the series 0.4 + 0.94 + 0.994 + * 19. Find the sum of the finite series 1 + 11 + 111 + to 0 terms 0. A geometric series consists of even number of terms. The sum of all terms is 3 times the sum of odd terms. Find the common ratio. V SPECIAL SERIES 1. Find the sum of 16 + 17 + 18 + + 5 *. Find the sum of 5 + 7 + 9 +.. + 39 3. Find the sum of 16 3 + 17 3 +. + 35 3 4. Find the total area of 14 squares whose sides are 11 cm, 1 cm,., 4 cm respectively.* 8 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
5. Find the total volume of 15 cubes whose edges are 16 cm, 17 cm, 18 cm,., 3cm respectively. 6. Find the value of k if 1 3 + 3 + 3 3 +.. + k 3 = 4356 7. Find the value of k if 1 3 + 3 + 3 3 +.. + k 3 = 6084* ONE MARK 3. ALGEBRA 1. A system of two linear equations is two variables is inconsistent, if their graphs [O 15] (A) coincide (B) intersect only at a point (C) do not intersect at any point (D) cut the axis. If one zero of the polynomial p(x) = (k + 4)x + 13x + 3k is reciprocal of the other, then k is equal to (A) (B) 3 (C) 4 (D) 5 3. The quotient when x 3 5x + 7x + 4 is divided by x 1 is (A) x + 4x + 3 (B) x 4x + 3 (C) x 4x 3 (D) x + 4x 3 4. The GCD of (x 3 + 1) and x 4 1 is (A) x 3 1 (B) x 3 + 1 (C) x + 1 (D) x 1 5. The LCM of x 3 a 3 and (x a) is (A) (x 3 a 3 )(x + a) (B) (x 3 a 3 )(x a) (C) (x a) (x + ax + a ) (D) (x + a) (x + ax + a ) 6. The lowest form of the rational expression (A) x 3 x 3 7. If a b 3 3 a b and a b a 3 b 3 (A) a ab b a ab b x 5 (B) x 3 x 3 x 5x 6 x x 6 9 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS is (C) x x 3 (D) x 3 x are the two rational expressions, then their product is (B) a ab b a ab b (C) a ab b a ab b (D) a ab b a ab b x 5 8. On dividing by is equal to [J 13] x 3 x 9 (A) (x 5)(x 3) (B) (x 5)(x + 3) (C) (x + 5)(x 3) (D) (x + 5)(x + 3) 9. If 3 3 a ab is added with b, then the new expression is b a (A) a + ab + b (B) a ab + b (C) a 3 + b 3 (D) a 3 b 3
10. The square root of x + y + z xy + yz zx (A) x y z (B) x y z (C) x y z (D) x y z 11. The square root of 11x 4 y 8 z 6 (l m) is (A) 11x y 4 z 4 l m (B) 11x 4 y 4 3 z L M (C) 11x y 4 z 6 l m (D) 11x y 4 3 z L M 1. If x + 5kx + 16 = 0 has no real roots, then [M 1, M 14] 8 (A) k > (B) k > - 8 (C) 8 5 5 5 < k < 8 (D) 0 < k < 8 5 5 13. A quadratic equation whose one root is 3 is (A) x 6x 5 = 0 (B) x + 6x 5 = 0 (C) x 5x 6 = 0 (D) x 5x + 6 = 0 14. The common root of the equations x bx + c = 0 and x +bx a = 0 is (A) c a (B) c a (C) c a (D) a b b b a c 15. If and are the roots of ax + bx + c = 0, then one of the quadratic equations whose roots are 1 and 1, is [O 13] (A) ax + bx + c = 0 (B) bx + ax + c = 0 (C) cx + bx + a = 0 (D) cx + ax + b = 0 16. Let b = a + c. Then the equation ax + bx + c = 0 has equal roots, if (A) a = c (B) a = - c (C) a = c (D) a = - c TWO MARKS (Two questions will be asked) I SOLVING TWO SIMULTANEOUS EQUATIONS 1. Solve by elimination method (i) 3x + 4y = - 5, x 3y = 6 (ii) x + y = 7, x y = 1. Using cross multiplication method, solve (i) 3x + 5y = 5; 7x + 6y = 30 * (ii) 3x + 4y = 4; 0x 11y = 47 II. SYNTHETIC DIVISION, GCD & LCM 3. Find the GCD of (i) x 4 7a 3 x, (x 3a) (ii) x x 1, 4x + 8x + 3 4. Find the quotient and remainder when the polynomial x 3 + x 7x 3 is divided by x 3 5. Find the quotient and remainder when the polynomial 3x 3 x + 7x 5 is divided by x + 3. III. RATIONAL EZPRESSIONS IN LOWEST FORM 6. Simplify: (i) 7. Simplify: (i) x 3x 5x x 3 3 4 (ii) 3 x 1 x x 1 x 81 x 6x 8 x 4 x 5x 36 (ii) x 3x 5x 4 (iii) x 1x x 3 x x * x 1 x 1 10 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
x x 3 8. Simplify: (i) x 3x 1 x x 3 9. Which rational expression should be added to (ii) x x 1 x 3 x 3 x 1 x to get 3 x x 3 x IV. SQUARE ROOT OF A POLYNOMIAL: 10. Find the square root of (i) (x y) + 4xy (ii) (x + 11) 44x* (iii) (x + 3y) 4xy (iv) x 4 1 + + (v) x 6 1 + - * 4 6 x x V. QUADRATIC EQUATIONS 11. Solve: (i) x + 1 x = 1 (ii) 15x 11x + 1 = 0 1. The sum of a number and its reciprocal is 1 5 5. Find the number. VI. NATURE OF ROOTS 13. Determine the nature of the roots of the following equations: (i) x 11x 10 = 0 (ii) x 3x + 4 = 0 * (iii) 9x + 1x + 4 = 0 14. Find the values of k for which the roots are real and equal in the equation x 10x + k = 0. IX. RELATIONS BETWEEN ROOTS AND COEFFICIENTS OF A QUADRATIC EQUATION 15. If and are the roots of the equation 3x 6x + 4 = 0, find the value of +.* 16. If and are the roots of the equation x 3x 1 = 0, find the values of (i) * (ii) 1 1 17. If the sum and product of the roots of the quadratic equation ax 5x + c = 0 are both equal to 10, then find the values of a and c. 18. If one of the roots of the equation 3x 10x + k = 0 is 1, then find the other root and 3 also the value of k. * 19. Form the quadratic equation whose roots are (i) 7 3, 7 3 (ii) 3 7,3 7 (iii) 4 7 FIVE MARKS I FACTORIZATION?*, 4 7 (Two questions will be asked) 1. Factorize: (i) x 3 x 5x + 6 (ii) x 3 10x x + 10 * (iii) x 3 + 11x 7x 6*. Factorize: (i) x 3-3x 3x + * (ii) x 3 9x + 7x + 6 (iii) x 3 + x + x 14 * (iv) x 3 5x x + 4 * 11 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
II RATIONAL EXPRESSION 3. Simplify: 4. Simplify: x 16 x 4 x 4x 16 3 x 3x x 64 x x 8 x 1 x 1 x x 1 x 1 x 1 x 5 x 1 3x 5. Simplify: x 1 x 1 * x 1 III TO FIND SQUARE ROOT OF POLYNOMIALS 6. Find the square root of (i) 5x 4-30x 3 + 9x - 1x + 4 (ii) x 4-4x 3 + 10x - 1x + 9* (iii) 9x 4-6x 3 + 7x - x + 1* (iv) 4 + 5x - 1x -4x 3 + 16x 4 7. Find the values of a and b if the following polynomials are perfect squares. (i) x 4 4x 3 + 10x - ax + b* (ii) ax 4 - bx 3 + 40x + 4x + 36 8. If m - nx + 8x + 1x 3 + 9x 4 is a perfect square, then find the values of m and n. 9. Find the square root of (i) (x 5)(x + 8x + 15)(x x 15)* (ii) (6x x )(3x 5x + )(x x 1) IV TO SOLVE THE QUADRATIC EQUATIONS 10. Solve the equation 1 4 x 1, where x + 1 0, x + 0 and x + 4 0 using x x 4 quadratic formula. 11. A car left 30 minutes later than the scheduled time. In order to reach its destination 150 km away in time, it has to increase its speed by 5 km/hr from its usual speed. Find its usual speed. * 1. A rectangular field is 0m long and 14m wide. There is a path of equal width all around it having an area of 111 sq. metres. Find the width of the path on the outside.* 13. One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son s age. Find their present ages. V NATURE OF ROOTS 14. Find the values of k so that the equation x x(1 + 3k) + 7(3 + k) = 0 has real and equal roots. VI AND PROBLEMS 15. If and are the roots of the equation x 3x 1 = 0, find the values of (i) + (ii) 4 + 4 16. If and are the roots of the equation x 3x 5 = 0, form a equation whose roots are and * 17. If and are the roots of the equation 3x 4x + 1 = 0, form a equation whose 1 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
roots are and 18. If and are the roots of the equation 5x px + 1 = 0 and = 1, then find p.* ONE MARK 4. MATRICES 1. Matrix A = aij is a square matrix if m n (A) m < n (B) m > n (C) m = 1 (D) m = n. If a matrix is of order 3, then the number of elements in the matrix is [O 15] (A) 5 (B) 6 (C) (D) 3 3. If A is of order 3 4 and B is of order 4 3, then the order of BA is [M 1, J 1,O 1,M 14] (A) 3 3 (B) 4 4 (C) 4 3 (D) not defined 4. A is of order m n and B is of order p q, addition of A and B is possible only if (A) m = p (B) n = q (C) n = p (D) m = p, n = q 1 1 5. If A 0 = 1, then the order of A is [O 13, J 14] (A) 1 (B) (C) 1 (D) 3 6. If A and B are square matrices such that AB = I and BA = I, then B is (A) Unit matrix (B) Null matrix (C) Multiplicative inverse matrix of A (D) A 8 4 7. If = 4 1 then the value of x is x 8 1 (A) 1 (B) (C) 1 4 (D) 4 1 x 8. If 1 y = 4, then the values of x and y respectively, are (A), 0 (B) 0, (C) 0, - (D) 1, 1 a 3 5 9. If =, then the value of a is 1 1 0 (A) 8 (B) 4 (C) (D) 1 1 0a b 1 0 10. =, then the values of a, b, c and d respectively are 0 1c d 0 1 (A) 1, 0, 0, 1 (B) 1, 0, 0, 1 (C) 1, 0, 1, 0 (D) 1, 0, 0, 0 13 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
11. If A = 1 3 and B = 0 (A) 0 0 0 (B) 0 0 1 then A + B 3 1 1. If A = 3 4 and A + B = 0, then B is 1 (A) 3 4 7 13. If A = 1 3 1 0 (A) 0 1 1 (B) 3 4 (C) 14 (D) not defined 1 (C) 3 4 1 0 and A + B = 4, then the matrix B = [M 13] 6 (B) 3 1 14. If A = aij and a ij = I + j, then A = 1 (A) 3 4 15. If A = 3 (B) 3 4 is such that A = I, then 8 (C) 1 7 3 (C) 4 5 1 0 (D) 0 1 8 (D) 1 7 4 5 (D) 6 7 (A) 1 + + = 0 (B) 1 + = 0 (C) 1 = 0 (D) 1 + = 0 16. Which one of the following is true for any two square matrices A and B of same order? (A) (AB) T = A T B T (B) (A T B) T = A T B T (C) (AB) T = BA (D) (AB) T = B T A T TWO MARKS (Two questions will be asked) I. FORMATION OF A MATRIX 1. Construct a matrix A a ij whose elements are given by a ij = i j. Construct a 3 matrix A aij whose elements are given by i i 3j (i) aij (ii) aij j II. TO FIND THE UNKNOWN VALUES 14 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
3. Find the values of x, y and z x 5 4 (i) 5 9 1 = 3 5 z 5 y 1 1 x 0 x 0 4. Find the values of x and y if = 3 3 0 y 9 0 III. SOLVE BY FORMING EQUATIONS 5x y 4 1 6 (ii) 0 4z 6 = 0 y 6 x 5. Solve: (i) 3x 31 4y * (ii) x y 5 x 3y 13 (iii) 3 x 8 4 5 y 13 5 3 6. If A, 7 5 x 5 X and C and if AX = C, then find the values of x and y. y 11 1 10 7. Find a and b if a b * 3 1 5 IV. ADDITION AND SUBTRACTION OF MATRICES 3 8 1 8. Let A and B. Find the matrix C if C = A + B.* 5 1 4 3 4 8 9. If A and B find 6A 3B.* 5 9 1 3 3 1-0 0 10. If A = 5 1, B = 3 and O = 0 0 then verify: (i) A + B = B + A (ii) A + (- A) = O = (- A) + A V. MATRIX MULTIPLICATION 3-4 1 11. Find the product of (i) 5 1 7 8-7 1. If 9-3 A = - 4 and B = then find BA if exists 0 3 6-1 -5 3 5 5 13. Prove that and are multiplicative inverses to each other.* 1 1 3 VI TRANSPOSE OF A MATRIX AND ORDER OF A MATRIX 8 5 14. If A =, then find A T T and 1-3 4 A T 15 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
15. If 1-1 3 1 A = 5-4 7 4 6 0 9 8 Find (i) the order of the matrix (ii) write down the elements a 4 and a 3 (iii) in which row and column does the element 7 occur? FIVE MARKS é1-1ù 1. If A = then show that A 4A + 5I ê 3 ú = O * ë û é0ù é-1 1ù. If A =, B = 1 ê 1 3ú ë û êú ë û é- ù 3. If A = 4 ê 5 ú ë û 4. If A =, and C = [ 1] verify (AB)C = A(BC) * and B = [ 1 3-6 ], then verify that (AB) T = B T A T 1-4 - 1 6-3 and B = 3 -, then prove that (A + B) A + AB + B 3-5. Find X and Y if X + 3Y = and 3X + Y = * 4 0-1 5 x x - 9 6. Solve for x and y if + 3 =. y - y 4 5 3 x - 5 7. If A =, X = and C = and if AX = C, then find the values of x and y. 7 5 y - 11 ONE MARK 5. COORDINATE GEOMETRY 1. The point P which divides the line segment joining the points A(1, 3) and B ( 3, 9) internally in the ratio 1 : 3 is (A) (, 1) (B) (0, 0) (C) ( 5 3, ) (D) (1, ). If the line segment joining the points A(3, 4) and B (14, 3) meets the x axis at P, then the ratio in which P divides the segment AB is 16 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
(A) 4 : 3 (B) 3 : 4 (C) : 3 (D) 4 : 1 3. The centroid of the triangle with vertices at (, 5), (, 1) and (10, 1) is [M 15] (A) (6, 6) (B) (4, 4) (C) (3, 3) (D) (, ) 4. If (1, ), (4, 6), (x, 6) and (3, ) are the vertices of a parallelogram taken in order, then the value of x is (A) 6 (B) (C) 1 (D) 3 5. The angle of inclination of a straight line parallel to x axis is equal to (A) 0 0 (B) 60 0 (C) 45 0 (D) 90 0 6. Slope of the line joining the points (3, ) and ( 1, a) is 3, then the value of a is [O 13] (A) 1 (B) (C) 3 (D) 4 7. Slope of the straight line which is perpendicular to the straight line joining the points (, 6) and (4, 8) is equal to (A) 1 3 (B) 3 (C) 3 (D) 1 3 8. The point of intersection of the straight lines 9x y = 0 and x + y 9 = 0 is (A) ( 1, 7) (B) (7, 1) (C) (1, 7) (D) ( 1, 7) 9. The point of intersection of the straight lines y = 0 and x = 4 is [J 1, O 1, O 13] (A) (0, 4) (B) ( 4, 0) (C) )0, 4) (D) (4, 0) 10. The slope of the straight line 7y x = 11 is equal to [J 13] (A) 7 (B) 7 (C) 7 (D) 7 11. The equation of the straight line passing through the origin and perpendicular to the straight line x + 3y 7 = 0 is (A) x + 3y = 0 (B) 3x y = 0 (C) y + 5 = 0 (D) y 5 = 0 1. If the points (, 5), (4, 6) and (a, a) are collinear, then the value of a is equal to (A) 8 (B) 4 (C) 5 (D) 3 13. The x and y intercepts of the line x 3y + 6 = 0, respectively are [M 14] (A), 3 (B) 3, (C) 3, (D) 3, 14. The value of k if the straight lines 3x + 6y + 7 = 0 and x + ky = 5 are perpendicular is (A) 1 (B) 1 (C) (D) 1 TWO MARKS I.TO FIND THE COORDINATE OF A POINT 1. (i) Find the point which divides the line segment joining the points (3. 5) and (8, 10) internally in the ration : 3.* 17 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
(ii) Find the coordinates of the point which divides the line segment joining (= 3, 5) and (4, 9) in the ratio 1 : 6 internally. (iii) Find the coordinates of the point which divides the line segment joining (3, 4) and ( 6, ) in the ratio 3 : externally.. Find the centroid of the triangle whose vertices are A(4, 6 ), B(3, ) and C(5, ). 3. The centre of a circle is at ( 6, 4). If one end of a diameter of the circle is at the origin, then find the other end. 4. If (7, 3), (6, 1), (8, ) and (p, 4) are the vertices of a parallelogram taken in order, then find the value of p.* II. Area of a triangle and collinear points 5. Find the area of the triangle whose vertices are (i) (1, ), ( 3, 4) and ( 5, 6)* (ii)( 4, 5 ), (4, 5) and ( 1, 6) 6. Vertices of the triangles taken in order and their areas are given below. In each of the following find the value of a. Vertices Area(in sq.units) (i) A(6, 7), B ( 4, 1), C(a, 9 ) 68 (ii) P(a, a), Q(4, 5), R(6, 1) 9 (iii) A(a, 3 ), B(3, a), C ( 1, 5) 1 * 7. Determine if the following set of points are collinear or not. (i) (4, 3), (1, ) and (, 1) (ii) (, ), ( 6, ) and (, ) 8. In each of the following, find the value of k for which the given points are collinear. (i) (k, 1 ), (, 1) and (4, 5)* (ii) (k, k), (, 3) and (4, -1) 9. If P(x, y) is any point on the line segment joining the points (a, 0) and (0, b), then prove that x y 1, where a,b 0.* a b III Angle of Inclination, Slope and Intercepts of a straight line 10. Find the angle of inclination of the line passing through the points (1, ) and (, 3). 11. Find the slope of the line which passes through the origin and the midpoint of the line segment joining the points (0, 4) and (8, 0).* 1. Find the slope and y- intercept of the line whose equation is 4x y + 1 = 0.* 13. Find the x and y intercepts of the straight line(s): (i) 5x + 3y -15 = 0 (ii) x y + 16 = 0 IV. EQUATION OF A STRAIGHT LINE 14. Find the equation of the straight line for the following details: 18 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
(i) angle of inclination 45, y intercept is 5 * (ii) Slope is 4 and passing through (1, )* (iii) Angle of inclination is 30 and passes through the midpoint of the line segment (4, ) and (3, 1). (iv) Passing through the points (, 5) and (3, 6). (v) Whose x and y- intercepts on the axes are given by and 3. V. PARALLEL AND PERPENDICULAR STRAIGHT LINES 15. Show that the following straight lines are parallel. (i) (i) 3x + y 1 = 0, 6x + 4y + 8 = 0 (ii) x + y + 1 = 0, 3x + 6y + = 0 16. Prove that the following straight lines are perpendicular to each other. (i) x + y + 1 = 0, x y + 5 = 0 (ii) 3x 5y + 7 = 0, 15x + 9y + 4 = 0 17. If the straight lines y x p and ax + 5 = 3y are parallel, then find a.* 18. Find the value of a if the straight lines 5x y 9 = 0, ay + x 11 = 0 are perpendicular to each other. 19. Find the equation of the straight line parallel to the line 3x y + 7 = 0 and passing through the point (1, -). 0. Find the equation of the straight line perpendicular to the straight line x y + 3 = 0 and passing through the point (1, ).* FIVE MARKS (Two questions will be asked) I.TO FIND THE COORDINATE OF A POINT 1. Let A( 6, 5) and B ( 6, 4) be two points such that a point P on the line AB satisfies AP = AB. Find the point P. 9. Find the points which divide the line segment joining ( 4, 0) and B(0, 6) into four equal parts. Area of a Quadrilateral 3. Find the area of the quadrilateral whose vertices are (i) ( 4, ). ( 3, 5), (3, ) and (, 3)* (ii) (6, 9), (7, 4), (4, ) and (3, 7) (iii) ( 3, 4), ( 5, 6), (4, 1) and (1, ) III. EQUATION OF A STRAIGHT LINE 4. The vertices of a ABC are A(, 1), B(, 3) and C(4, 5). Find the equation of the median through the vertex A.* 19 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
5. Find the equations of the straight lines each passing through the point (6, ) and whose sum of the intercepts is 5. 6. Find the equation of the straight lines passing through the point (3, 4) and has intercepts which are in the ration 3 : * 7. A straight line cuts the coordinate axes are A and B. If the midpoint of AB is (3, ), then find the equation of AB. 8. The vertices of ABC are A(, 1), B(6, 1) and C(4, 11). Find the equation of the straight line along the altitude from the vertex A. 9. If the straight line passing through the points (h, 3) and (4, 1) intersects the line 7x 9y 19 = 0 at right angle, then find the value of h. 10. Find the equation of the straight line passing through the point of intersection of the lines x + y 3 = 0 and 5x + y 6 = 0 and parallel to the line joining the points (1, ) and (, 1).* 11. Find the equation of the straight line which passes through the point of intersection of the straight lines 5x 6y = 1 and 3x + y + 5 = 0 and is perpendicular to the straight line 3x 5y + 11 = 0.* 1. If x + y = 7 and x + y = 8 are the equations of the lines of two diameters of a circle, find the radius of the circle if the point (0, ) lies on the circle.* ONE MARK 6. GEOMETRY 1. If a straight line intersects the sides AB and AC of a ABC at D and E respectively and is parallel to BC, then AE AC (A) AD (B) AD (C) DE (D) AD DB AB BC EC AB BD. In figure, if, B = 40 0 and C = 60 0, then BAD = AC DC A [O 14] (A) 30 0 (B) 50 0 (C) 80 0 (D) 40 0 40 0 60 0 B D C 3. In triangles ABC and DEF, B = E, C = F, then AB CA BC AB AB BC CA AB (A) (B) (C) (D) DE EF EF FD DE EF FD EF 4. If a vertical stick 1m long casts a shadow 8m long on the ground and at the same time a tower casts a shadow 40m long on the ground, then the height of the tower is 5. (A) 40m (B) 50m (C) 75m (D) 60m 0 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
6. In the figure, the value x is equal to A (A) 4. (B) 3. x 4 D 50 0 E (C) 0. 8 (D) 0. 4 8 10 50 0 B C 7. From the given figure, identigy the wrong statement A (A) Δ ADB ~ Δ ABC (B) Δ ABD ~ Δ ABC D (C) Δ BDC ~ Δ ABC (D) Δ ADB ~ Δ BDC B C 8. In the adjoining figure, chords AB and CD intersect at P. If AB = 16 cm. PD = 8 cm., PC = 6 cm and AP > PB, A D then AP = (A) 8 cm (B) 4 cm P P (C) 1 cm. (D) 6 cm C D 9. A point P is 6 cm away from the centre O of a circle and PT is the tangent drawn from P to the circle is 10 cm, then OT is equal to (A) 36 cm (B) 0 cm (C) 18 cm (D) 4 cm 10. The sides of two similar triangles are in the ratio : 3, then their areas are in the ratio (A) 9 : 4 (B) 4 : 9 (C) : 3 (D) 3 : [O 1, M 13, O 13, M 15] 11. Triangles ABC and DEF are similar. If their areas are 100 cm and 49 cm respectively and BC is 8. cm then EF = (A) 5.47 cm (B) 5.74 cm (C) 6. 47 cm (D) 6. 74 cm [J 15] 1. The perimeter of two similar triangles ABC and DEF are 36 cm and 4 cm respectively. If DE = 10 cm, then AB is (A) 1 cm (B) 0 cm (C) 15 cm (D) 18 cm 13. The areas of two similar triangles are 16 cm and 36 cm respectively. If the altitude of the first triangle is 3 cm, then the corresponding altitude of the other triangle is (A) 6.5 cm (B) 6 cm (C) 4 cm (D) 4. 5 cm TWO MARKS (One Question will be asked) I Basic proportionality theorem 1. In ABC, DE BC and AD =. If AE = 3.7 cm, find EC. DB 3 1 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
. In ABC, D and E are points on the sides AB and AC respectively such that DE BC. If AD = 6 cm, DB = 9 cm and AE = 8 cm, then find AC.* 3. In PQR, given that S is a point on PQ such that ST QR and PS = 3. If PR = 5.6 cm, SQ 5 then find PT. II Angle bisector theorem 4. In ABC, the internal bisector AD of A meets the side BC at D. If BD =.5 cm, AB = 5 cm and AC = 4. cm, then find DC 5. In ABC, AD is the internal bisector of A, meeting BC at D. If AB = 5.6 cm, AC = 6 cm and DC = 3 cm find BC. 6. In ABC, AE is the external bisector of A, meeting BC at E. If AB = 10 cm, AC = 6 cm and BC = 1 cm then find CE. * III Tangent chord theorem 7. Let PQ be a tangent to a circle at A and AB be a chord. Let C be a point on the circle such that BAC = 54 0 and BAQ = 6 0 Find ABC.* IV Two chords of a circle intersect either inside or outside of the circle 8. AB and CD are two chords of a circle which intersect each other internally at P. If CP = 4 cm, AP = 8 cm, PB = cm, then find PD. A 5 B 4 9. Find the value of x in the given diagram: x D P C 10. AB and CD are two chords of a circle which intersect each other externally at P. If AB = 4 cm, BP = 5 cm, PD = 3 cm then find CD. * 11. ABCD is a quadrilateral such that all of its sides touch a circle. If AB = 6 cm, BC = 6.5 cm and CD = 7 cm, then find the length of AD. * FIVE MARKS (One Question will be asked) 1. State and prove the following theorems: (i) Basic Proportionality Theorem (Thales Theorem) (ii) Converse of Basic Proportionality Theorem* (iii) Angle Bisector Theorem (iv) Pythagoras Theorem* EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
. ABCD is a quadrilateral with AB parallel to CD. A line drawn parallel to AB meets AB at P and BC at Q. Prove that AP BQ * PD QC 3. The internal bisector of A of ABC meets BC at D and the external bisector of A meets BC produced at E. Prove that BD CD BE CE 4. A man of height 1.8 m is standing near a Pyramid. If the shadow of the man is of length.7 cm and the shadow of the Pyramid is 10 m long at that instant, find the height of the Pyramid. 5. A girl of height 10 cm is walking away form the base of a lamp post at a speed of 0.6 m / sec. If the lamp is 3.6 m above the ground level, then find the length of her shadow after 4 seconds. D 6. A boy is designing a diamond shaped kite, as shown in A the figure where AE = 16 cm. He wants to use a straight cross bar BD. How long should it be? B C 7. In the figure, tangents PA and PB are drawn to a circle A with centre O from an external point P. If CD is a C tangent to the circle at E and AP = 15 cm, find the perimeter of PCD o. E P B D 8. A lotus is 0 cm above the water surface in a pond and its stem is partly below the water surface. As the wind blew, the stem is pushed aside so that the lotus touched the water 40 cm away from the original position of the stem. How much of the stem was below the water surface originally? ONE MARK 7. TRIGONOMETRY 1. sin 1 1 cos (A) cos (B) tan (C) cot (D) cosec 3 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
. cos 4 x sin 4 x = (A) sin x 1 (B) cos x 1 (C) 1 + sin x (D) 1 sin x 3. 0 0 sin(90 )sin cos(90 )cos tan cot (A) tan (B) 1 (C) 1 (D) sin 4. (1 + tan )(1 sin)(1 + sin) = (A) cos sin (B) sin cos (C) sin + cos (D) 0 5. 1 tan 1 cot (A) cos (B) tan (C) sin (D) cot 6. sin 1 + 1 tan = (A) cosec + cot (B) cosec cot (C) cot cosec (D) sin cos 7. 9tan 9 sec = [M 1, M 14] (A) 1 (B) 0 (C) 9 (D) 9 8. A man is 8.5 m away from a tower. His eye level above the ground is 1.5 m. the angle of elevation of the tower from his eyes is 45 0. Then the height of the tower is [J 1, O 1, O 14] (A) 30 m (B) 7. 5 m (C0 8. 5 m (D) 7 m 9. In the adjoining figure, ABC = C [M 13, O 15] (A) 45 0 (B) 30 0 (C) 60 0 (D) 50 0 100 3m A 100 m B x y 10. If x = a sec, y = b tan, then the value of [J 13, M 15] a b (A) 1 (B) 1 (C) tan (D) cosec 11. sin(90 0 )cos + cos(90 0 )sin = (A) 1 (B) 0 (C) (D) 1 TWO MARKS (Two questions will be asked) I To prove the identities 1. Prove the identity. Prove the identity sin cos 1* cosec sec 1 cos cosec cot * 1 cos 4 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
3 sin sin 3. Prove the identity 3 cos cos = tan * 4. Prove that sec + cosec = sec cosec sin 5. Prove that cosec cot 1 cos 6. Prove that 7. Prove that sec cosec tan cot 1 cos sin sin 1 cos = cot * 8. Prove that sec(1 sin)(sec + tan) = 1 * II Heights and Distances 9. A kite is flying with the string of length 00 m. If the thread makes an angle 30 0 with the ground, find the distance of the kite from the ground level. (Here assume that the string is along a straight line) * 10. A ladder leaning against a vertical wall, makes an angle of 60 0 with the ground. The foot of the ladder is 3. 5m away from the wall. Find the length of the ladder.* 11. A ramp for unloading a moving truck, has an angle of elevation of 30 0. If the top of the ramp is 0. 9 m above the ground level, then find the length of the ramp. 1. A pendulum of length 40 cm subtends 60 0 at the vertex in one full oscillation. What will be the shortest distance between the initial position and the final position of the bob? * FIVE MARKS [One Question will be asked] I To prove the identities tan sec 1 1 sin 1. Prove that tan sec 1 cos * tan cot. Prove that 1 + seccosec 1 cot 1 tan 3. If tan = cos sin, then prove that cos sin = tan m 1 n 1 4. If tan = n tan and sin = m sin, then prove that cos 3 = * 5. If sin, cos and tan are in G.P., then prove that cot 6 cot = 1 * II Heights and Distances 6. A vertical wall and a tower are on the ground. As seen from the top of the tower, the angles of depression of the top and bottom of the wall are 45 0 and 60 0 respectively. Find the height of the wall if the height of the tower is 90m. 3 1.73 * 5 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
7. 8. A girl standing on a lighthouse built on a cliff near the seashore, observe two boats due East of the lighthouse. The angles of depression of the two boats are 30 0 and 60 0. The distance between the boats is 300 m. Find the distance of the top of the lighthouse from the sea level.* 9. The angle of elevation of an aeroplane from a point A on the ground is 60 0. After a flight of 15 seconds horizontally, the angle of elevation changes to 30 0. If the aeroplane is flying at a speed or 00 m/s, then find the constant height at which the aeroplane is flying. 10. A boy is standing at some distance from a 30 m tall building and his eye level from the ground is 1.5 m. The angle of elevation forms his eyes to the top of the building increases from 30 0 to 60 0 as he walks towards the building. Find the distance he walked towards the building. 11. A straight highway leads to the foot of a tower. A man standing on the top of the tower spots a van at an angle of depression of 30 0. The van is approaching the tower with a uniform sped. After 6 minutes, the angle of depression of the van is found to be 60 0. How many more minutes will it take for the van to reach the tower?* 1. The angle of elevation of an artificial earth satellite is measured from two earth stations, situated on the same side of the satellite are in the same vertical plane. If the distance between the earth stations is 4000 km, find the distance between the satellite and earth 3 1.73 * 13. The angle of elevation of a hovering helicopter as seen from a point 45m above a lake is 30 0 and the angle of depression of its reflection in the lake, as seen from the same point and at the same time is 60 0. Find the distance of the helicopter from the surface of her lake. ONE MARK 8. MENSURATIONS 1. If the total surface area of a solid right circular cylinder is 00 cm and its radius is 5 cm, then the sum of its height and radius is (A) 0 cm (B) 5 cm (C) 30 cm (D) 15 cm. The curved surface area of a right circular cylinder whose radius is a units and height is b units, is equal to (A) a b sq.cm (B) ab sq.cm (C) Sq.cm (D) sq.cm 3. Radius and height of a right circular cone and that of a right circular cylinder are respectively, equal. If the volume of the cylinder is 10 cm 3, then the volume of the cone is equal to (A) 100 cm 3 (B) 360 cm 3 (C) 40cm 3 (D) 90 cm 3 6 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
4. If the diameter and height of a right circular cone are 1 cm and 8 cm respectively, then the slant height is (A) 10 cm (B) 0 cm (C) 30 cm (D) 96 cm 5. If the circumference at the base of a right circular cone and the slant height are 10 cm and 10 cm respectively, then the curved surface area of the cone is equal to (A) 100 cm 3 (B) 600 cm 3 (C) 300 cm (D) 600 cm 6. If the volume and the base area of a right circular cone are 48 cm 3 and 1 cm respectively, then the height of the cone is equal to (A) 6 cm (B) 8 cm (C) 10 cm (D) 1 cm 7. The surface areas of two spheres are in the ratio of 9 : 5. Then their volumes are in the ratio (A) 81 : 65 (B) 79 : 1565 (C) 7 : 75 (D) 7 : 15 8. The total surface area of a solid hemisphere whose radius is a units, is equal to (A) a sq.units (B) 3a sq.units (C) 3a sq.units (D) 3a sq,units 9. If the surface area of a sphere is 100 cm, then its radius is equal to (A) 5 cm (B) 100 cm (C) 5 cm (D) 10 cm 10. If the total surface area of a solid hemisphere is 1 cm then its curved surface area is equal to (A) 6 cm (B) 4 cm (C) 36 cm (D) 8 cm 11. The ratios of th respective heights and the respective radii of two cylinders are 1 : and : 1 respectively. then their respective volumes are in the ratio. [M 15] (A) 4 : 1 (B) 1 : 4 (C) : 1 (D) 1 : 1. Two right circular cones have equal radii. If their slant heights are in the ratio 4 : 3, then their respective curved surface areas are in the ratio [O 13] (A) 16 : 9 (B) : 3 (C) 4 : 3 (D) 3 : 4 13. If the radius of a sphere is half of the radius of another sphere, then their respective volumes are in the ratio. [O 15] (A) 1 : 8 (B) : 1 (C) 1 : (D) 8 : 1 14. If the radius of a sphere is cm, then the curved surface area of the sphere is equal to (A) 8 cm (B) 16 cm (C) 1 cm (D) 16 cm 15. If the surface area of a sphere is 36 cm, then the volume of the sphere is equal to (A) 1 cm (B) 36 cm (C) 7 cm 3 (D) 108 cm 3 TWO MARKS (Two questions will be asked) I CYLINDER 1. A solid right circular cylinder has radius 7 cm and height 0 cm. Find its CSA and TSA. 7 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
. The radii of two right circular cylinders are in the ratio of 3 : and their heights are in the ratio 5 : 3. Find the ratio of their curved surface areas. 3. Find the volume of a solid cylinder whose radius is 14 cm and height 30 cm 4. A lead pencil is in the shape of right circular cylinder. The pencil is 8 cm long and its radius is 3 mm. If the lead is of radius 1 mm, then find the volume of the wood used in the pencil. II CONE 5. Radius and slant height of a solid right circular cone are 35 cm and 37 cm respectively. Find the curved surface area and total surface area of the cone,. ( Take = 7 ) 6. The volume of a solid right circular cone is 498 cu.m. If its height is 4 cm, then find the radius of the cone. ( Take = 7 )* 7. The volume of a cone with circular base is 16 cu.cm. If the base radius is 9 cm, then find the height of the cone. * 8. A right angled ABC with sides 5 cm, 1 cm and 13 cm is revolved about the fixed side of 1 cm. Find the volume of the solid generated. III SPHERE AND HOLLOW SPHERE 9. A hollow sphere in which a circus motorcyclist performs his stunts, has an inner diameter of 7 m. Find the area available to the motorcyclist for riding. 10. Find the volume of a sphere shaped metallic shot put having diameter of 8. 4 cm.* 11. If the volume of a solid sphere is 741 1 cu.cm, then find its radius * 7 1. The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of volumes of the balloon in the two cases. * IV HEMI SPHERE 13. Total surface area of a solid hemisphere is 675 sq.cm. Find the curved surface area of the solid hemisphere. 14. Radii of two solid hemispheres are in the ratio 3 : 5. Find the ratio of their curved surface areas and the ratio of their total surface areas. 15. A cone, a hemisphere and cylinder have equal bases. If the heights of the cone and a cylinder are equal and are same as the common radius, then find the ratio of their respective volumes. (Two questions will be asked) FIVE MARKS I CYLINDER & HOLLOW CYLINDER 1. The ratio between the base radius and the height of a solid right circular cylinder is : 5. If its curved surface area is 3960 sq.cm, find the height and radius. 7 8 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
. The total surface area of a solid right circular cylinder is 1540 cm. If the height is four times the radius of the base, then find the height of the cylinder.* 3. Base area and volume of a solid right circular cylinder are 13.86 sq.cm and 69.3 cu.cm respectively. Find its height and curved surface area. 4. A rectangular sheet of metal foil with dimension 66 cm 1 cm is rolled to form a cylinder of height 1 cm. Find the volume of the cylinder.* 5. The outer curved surface area of a hollow cylinder is 540 sq.cm. Its internal diameter is 16 cm and height is 15 cm. Find the total surface area. 6. A hollow cylindrical iron pipe is of length 8 cm. Its outer and inner diameters are 8 cm and 6 cm respectively. Find the volume of the pipe and weight of the pipe if 1 cu.cm of iron weighs 7 gm. * II CONE & FRUSTUM 7. The radius and height of a right circular cone are in the ratio : 3. Find the slant height if its volume is 100.48 cu.cm * 8. A sector containing an angle of 10 0 is cut off from a circle of radius 1cm and folded into a cone. Find the curved surface area of the cone. 9. A vessel is in the form of a frustum of a cone. Its radius at one end and the height are 8 cm and 14 cm respectively. If its volume is 5676 cm 3, then find the radius at the other end. * 3 10. The perimeter of the ends of a frustum of a cone is 44 cm and 8.4 cm. If the depth is 14 cm, then find its volume. * III SPHERE & HEMISPHERE 11. The inner curved surface area of a hemispherical dome of a building need to be painted. If the circumference of the base is 17.6 m, find the cost of painting it at the rate of Rs. 5 per sq.m 1. The volume of a solid hemisphere is 115 cu.cm. Find its curved surface area. IV COMBINATION OF SOLIDS 13. A solid wooden toy is in the form of a cone surmounted on a hemisphere. If the radii of the hemisphere and the base of the cone are 3.5 cm each and the total height of the toy is 17.5cm, and then finds the volume of wood used in the toy.* 14. A play top is in the form of a hemisphere surmounted on a cone. The diameter of the hemisphere is 3.6 cm. The total height of the play top is 4. cm. Find its total surface area. 15. A hollow sphere of external and internal diameters of 8 cm and 4 cm respectively is melted and made into another solid in the shape of a right circular cone of base diameter of 8 cm. Find the height of the cone. * 9 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
16. A right circular cylinder having diameter 1 cm and height 15 cm is full of ice cream. The ice cream is to be filled in cones of height 1 cm and diameter 6 cm, having a hemispherical shape on top. Find the number of such cones which can be filled with the ice cream available.* 17. A cylindrical bucket of height 3 cm and radius 18 cm is filled with sand. The bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 4 cm, find the radius and slant height of the heap. 18. A container with a rectangular base of length 4.4 m and breadth m is used to collect rain water. The height of the water level in the container is 4 cm and the water is transferred into a cylindrical vessel with radius 40 cm. What will be the height of the water level in the cylinder? 19. Through a cylindrical pipe of internal radius 7 cm, water flows out at the rate of 5 cm /sec. Calculate the volume of water (in litres) discharged through the pipe in half an hour. * ONE MARK 11. STATISTICS 1. The range of the first 10 prime numbers, 3, 5, 7, 11, 13, 17, 19, 3, 9 is (A) 8 (B) 6 (C) 9 (D) 7. For a collection of 11 items, x = 13, then the arithmetic mean is (A) 11 (B) 1 (C) 14 (D) 13 3. If the variance of 14, 18,, 6, 30 is 3, then the variance of 8, 36, 44, 5, 60 is (A) 64 (B) 18 (C) 3 (D) 3 4. Given x x = 48, x = 0 and n = 1. The coefficient of variation is (A) 5 (B) 0 (C) 30 (D) 10 5. The least value in a collection of data is 14. 1. If the range of the collection is 8. 4, then the greatest value of the collection is [ J 1] (A) 4. 5 (B) 43. 5 (C) 4. 4 (D) 4. 1 6. The greatest value of a collection of data is 7 and the least value is 8 [O 13] (A) 44 (B) 0.7 (C) 0.44 (D) 0.8 7. For any collection of n items, x x = [J 15] (A) n x (B) (n ) x (C) (n 1) x (D) 0 x x [M 14] (A) x (B) x (C) n x (D) 0 8. For a collection of n items, 30 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS
9. If the variance of a data is 1. 5, then the S.D. is (A) 3. 5 (B) 3 (C). 5 (D) 3. 5 10. Variance of the first 11 natural numbers is [M 13] (A) 5 (B) 10 (C) 5 (D) 10 TWO MARKS [One question will be asked] 1. Find the range and coefficient of range of the data 41., 33.7, 9.1, 34.5, 5.7, 4.8, 56.5, 1.5 *. The weight (in kg) of 13 students in a class is 4.5, 47.5, 48.6, 50.5, 49, 46., 49.8, 45.8, 43., 48, 44.7, 46.9, 4.4. Find the range and coefficient of range. 3. The smallest value of a collection of data is 1 and the range is 59. Find the largest value of the collection of data. * 4. The largest of 50 measurements is 3.84 kg. If the range is 0.46 kg, find the smallest measurement. 5. Find the standard deviation of the first 10 natural numbers 6. Mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and the sum of the squares of all the items. * 7. If n = 10, x = 1 and x = 1530, then calculate the coefficient of variation. * 8. A group of 100 candidates have their average height 163.8 cm with coefficient of variation 3.. What is the standard deviation of their heights? FIVE MARKS [One question will be asked] 1. Calculate the standard deviation of the data 10, 0, 15, 8, 3, 4 *. Find the standard deviation of the numbers 6, 58, 53, 50, 63, 5, 55 3. Calculate the coefficient of variation of the data 0, 18, 3, 4, 6 4. Calculate the variance of the following data x 4 6 8 10 1 14 16 f 4 4 5 15 8 5 4 5 5. Calculate the standard deviation of the following data * x 70 74 78 8 86 90 f 1 3 5 7 8 1 6. Length of 40 bits of wire, correct to the nearest centimeter is given below. Calculate the variance. Length cm 1 10 11 0 1 30 31 40 41 50 51 60 61 70 No. of bits 3 8 1 9 5 1 31 EXPECTED QUESTIONS FOR MARCH 017 EXAMINATION X MATHEMATICS