VIVEKANANDA VIDYALAYA MATRIC HR SEC SCHOOL, RAMESWARAM. Lesson 1 & 7 & Exercise 9.1 ( Unit Test -1 ) 10th Standard

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1 VIVEKANANDA VIDYALAYA MATRIC HR SEC SCHOOL, RAMESWARAM Lesson 1 & 7 & Exercise 9.1 ( Unit Test -1 ) 10 Standard Date : 6-Oct-18 MATHEMATICS Reg.No. : Time : 01:30:00 Hrs Total Marks : 50 I. CHOOSE THE BEST ANSWER WITH CORRECT OPTION:- 8 x 1 = 8 1) For any two sets A and B, (A B) (B A) (A B) is (a) ( A B (c) A B (d) A B ) If n(a) = 0, n(b) = 30 and n (A B) = 40, en n (A B) is equal to (a) 50 ( 10 (c) 40 (d) 70 3) 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 ( onto (c) bijective (d) not a function 4) If U ={x x N, x < 10} and A = {x x N, x < 6} en (A ) is (a) {1, 6, 7, 8, 9} ( {1,, 3, 4} (c) {, 3, 4, 5} (d) { } sin 1 θ 5) = 1+cosθ (a) cosθ ( tanθ (c) cotθ (d) cosecθ 6) If x = a secθ, y = b tanθ, en e value of = (a) 1 ( -1 (c) θ (d) tan cosec θ x a y x 7) 8) A man is 8.5 m away from a tower. His eye level above e ground is 1.5 m. The angle of elevation of e tower from his eyes is 45. Then e height of e tower is (a) 30 m ( 7.5 m (c) 8.5 m (d) 7 m The value of x if cosx=sin60 cos30 -co.s60 sin30 is (a) 15 ( 30 (c) 45 (d) II. ANSWER ANY 6 OF THE FOLLOWING:- Q.NO 15 IS COMPULSORY:- 6 x = 1 9) If A and B are two sets and U is e Universal set such at n (U) = 700, n (A) = 00, n (B) = 300, and n (A B) = 100, find n ( A B ). 10) Represent e function f = { ( 1, ), ( 3, 1), ( 5, 6), ( 4, 3) } as (i) a table (ii) an arrow diagram 11) Give an example for a function which is not a sequence. 1 cosθ 1) Prove e identity = cosec θ cot θ 13) 1+cosθ Prove e identity (si n 6 θ + co s 6 θ) = 1 3si n θ cos θ

2 14) A ladder leaning against a vertical wall, makes an angle of 60 wi e ground. The foot of e 15) a) ladder is 3.5 m away from e wall. Find e leng of e ladder. A simple pendulum of leng 40 cm subtends 60 at e vertex in one full oscillation. What will be e shortest distance between e initial position and e final position of e bob? Let x = { x, x 0, where x R. Does e relation {(x,y) y = x, x R define a x x < 0 function? Find its range. III. ANSWER ANY 4 OF THE FOLLOWING:- Q.NO 0 IS COMPULSORY:- 4 x 5 = 0 16) Use Venn diagrams to verify De Morgan s law for set di erence A (B C) = (A B) (A C). 17) In a residential area wi 600 families 3/5 owned scooter, 1/3 owned car, 1/4 owned bicycle, 10 families owned scooter and car, 86 owned car and bicylce while 90 families owned scooter and bicylce. If /15 of families owned all e ree types of vehicles, en find (i) The number of families owned atleast two types of vehicle. (ii) The number of families owned no vehicle. 18) Prove e identity (sin θ + cosec θ ) + (cos θ + sec θ ) = 7 + ta n θ + co t θ 19) If sin θ, cos θ and tan θ are in G.P., en prove at co t 6 θ cot θ = 1 0) a) Prove e following identities. (1 + cot θ cosec θ)(1 + tanθ + sec θ) = A function f : [1, 6) R is defined as follows f (x) = 1 + x, 1 x < x 1, x < 4 ([1,6)={{x R:1 x< 6:}) 3x 10, 4 x < 6 Find e value of (i) f (5) (ii) f(3) (iii) f(1) (iv) f() - f(4) (v) f(5) - 3 f(1) IV. ANSWER THE FOLLOWING:- 1 x 10 = 10 1) a) Draw a circle of radius 3. cm At a point P on it, draw a tangent to e circle using e tangent-chord eorem. Draw a circle of diameter 10 cm. From a point P, 13 cm away from its centre, draw e two tangents PA and PB to e circle, and measure eir lengs. ***************************************** 0

3 VIVEKANANDA VIDYALAYA MATRIC HR SEC SCHOOL Lesson & 4 & Exercise 9.3 ( Unit Test - )- 10 Standard Date : 07-Nov-18 MATHEMATICS Reg.No. : Time : 01:30:00 Hrs Total Marks : 50 I. CHOOSE THE BEST ANSWER WITH CORRECT OPTION:- 8 x 1 = 8 1) ) 3) 4) If a, b, c are in A.P. en a b b c a c a b b c (a) ( (c) (d) 1 The sequence 3, 3, 3, is is equal to (a) an A.P. only ( a G.P. only (c) neier A.P. nor G.P (d) bo A.P. and G.P. The common ratio of e G.P. a m n, a m, a m+n (a) a m ( a m (c) a n (d) a n The common di erence of an A.P. whose 6 term is 1 and 8 term is is (a) ( 3 (c) 5 (d) 4 5) Three numbers a, b, c are in A.P. if (a) a = c ( b = a + c (c) b = a + c (d) b = ac 6) If A ( ) = (1 ) en e order of A is (a) x 1 ( x (c) 1 x (d) 3 x 7) 8) ( 1 ) A( ) If A 3 4 and A + B = 0, en B is (a) 1 ( 1 (c) 1 (d) 3 4 ( 3 4 ) ( 3 4 ) ( ) A is order m x n and B is order p x q, addition of A and B is possible only if (a) m = p ( n = q (c) n = p (d) m = p, n = q II. ANSWER ANY 6 OF THE FOLLOWING:- Q.NO 16 IS COMPULSORY:- 6 x = 1 9) 10) In a flower garden, ere are 3 rose plants in e first row, 1 in e second row, 19 in e ird row and so on. There are 5 rose plants in e last row. How many rows are ere in e flower garden? Find e sum of e first 5 terms of e geometric series ) A sum of Rs.1000 is deposited every year at 8% simple interest. Calculate e interest at e end of each year. Do ese interest amounts form an A.P.? If so, find e total interest at e end of 30 years. 1) Find e indicated terms in each of e sequences whose 13) a n = ( 1) n n+3 (n + 1) ; a5, a8 y 6 x Solve : ( ) = ( ) 3x y is n terms are given by

4 14) Matrix A shows e weight of four boys and four girls in kg at e beginning of a diet programme to lose weight. Matrix B shows e corresponding weights a er e diet programme. B = ( 3 40 A = ( ) Boys ) Boys Girls Find e weight loss of e Boys and Girls. Girls 15) 1 3 If en verify AI=IA =A, where I is e unit matrix of order. 16) a) A = ( ), 9 6 Construct a 3x3 matrix aij = (i j) A = [ a ij ] whose elements are given by Which term of e arimetic sequence 4, 3,, 1,. is 3? 4 4 III. ANSWER ANY 4 OF THE FOLLOWING:- Q.NO IS COMPULSORY:- 4 x 5 = 0 17) In an arimetic series, e sum of first 14 terms is -03 and e sum of e next 11 terms is 57. Find e arimetic series. 18) If 1 en show 1 1 are in A.P. 19) 0) a x = b y = c z, x 0, y 0, z 0 and b = ac,,, x y z If ere are (n + 1) odd terms to e sum of even terms is (n + 1) : n. 3 terms in an arimetic series, en prove at e ratio of e sum of Find X and Y if X + 3Y = ( ) and 3X + Y = ( ) ) 1 1 If A =,B= and C = verify ) a) ( ) ( ) ( 1 ) (AB)C = A(BC) ( ) ( ) If A =, B = and C = find (A+B)C and AC+BC.Is (A+B)C=AC+BC? Find e sum of first 0 terms of e arimetic series in which 7 term is more an ree times its 3 rd term. ALL THE BEST... 3 rd term is 7 and IV. ANSWER THE FOLLOWING:- 1 x 10 = 10 3) a) Construct a cyclic quadrilateral PQRS, wi PQ = 6.5 cm, QR = 5.5 cm, PR = 7 cm and PS = 4.5 cm. Construct a cyclic quadrilateral PQRS such at PQ = 5.5 cm, QR = 4.5 cm QP R = o 45 and PS = 3 cm.

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4) If ax 2 + bx + c = 0 has equal roots, then c is equal. b) b 2. a) b 2

4) If ax 2 + bx + c = 0 has equal roots, then c is equal. b) b 2. a) b 2 Karapettai Nadar Boys Hr. Sec. School One Word Test No 1 Standard X Time: 20 Minutes Marks: (15 1 = 15) Answer all the 15 questions. Choose the orrect answer from the given four alternatives and write