SUMMATIVE ASSESSMENT I (011) Lakdfyr ijh{kk&i MATHEMATICS / xf.kr Class X / & X 60018 Time allowed : 3 hours Maximum Marks : 80 fu/kkzfjr le; % 3?k.Vs : 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections A,B,C and D. Section A comprises of 10 questions of 1 mark each, section B comprises of 8 questions of marks each, section C comprises of 10 questions of 3 marks each and section D comprises 6 questions of 4 marks each. (iii) Question numbers 1 to 10 in section A are multiple choice questions where you are to select one correct option out of the given four. (iv) There is no overall choice. However, internal choice have been provided in 1 question of two marks, 3 questions of three marks each and questions of four marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculator is not permitted. lkeku; funsz k % (i) lhkh iz u vfuok;z gsaa (ii) bl iz u i= esa 34 iz u gsa, ftugsa pkj [k.mksa v, c, l rfkk n esa ckavk x;k gsa [k.m & v esa 10 iz u gsa ftuesa izr;sd 1 vad dk gs, [k.m & c esa 8 iz u gsa ftuesa izr;sd ds vad gsa, [k.m & l esa 10 iz u gsa ftuesa izr;sd ds 3 vad gs rfkk [k.m & n esa 6 iz u gsa ftuesa izr;sd ds 4 vad gsaa (iii) [k.m v esa iz u la[;k 1 ls 10 rd cgqfodyih; iz u gsa tgka vkidks pkj fodyiks a esa ls,d lgh fodyi pquuk gsa (iv) bl iz u i= esa dksbz Hkh lokszifj fodyi ugha gs, ysfdu vkarfjd fodyi vadksa ds,d iz u esa, 3 vadksa ds 3 iz uksa esa vksj 4 vadks a ds iz uksa esa fn, x, gsaa izr;sd iz u es a,d fodyi dk p;u djsaa (v) dsydqysvj dk iz;ksx oftzr gsa Section-A Question numbers 1 to 10 carry one mark each. For each questions, four alternative choices have been provided of which only one is correct. You have to select the correct choice. Page 1 of 9

1. Which of the following numbers has terminating decimal expansion? 37 4 1 3 6 17 49 89 3 37 4 1 3 6 17 49 89 3. The sum and the product of the zeroes of a quadratic polynomial are respectively, then the polynomial is : 1 and 1 x x 1 x x 1 x x 1 x x 1 1 1 3. x x 1 x x 1 x x 1 x x 1 A vertical stick 30 m long casts a shadow 1 m long on the ground. At the same time, a tower casts a shadow 7 m long on the ground. The height of the tower is : 10 m 100 m m 00 m 30 1 7 10 100 00 4. If cos A cos A 1, then sin A sin 4 A is : 1 0 1 cos A cos A 1 sin A sin 4 A 1 0 1. If 6 cot cosec cot cosec, then cos is : 4 3 3 4 6 cot cosec cot cosec, cos 4 3 3 4 6. The value of tan sec is : 1 0 tan sec 1 0 Page of 9

7. Which of the following rational numbers have a terminating decimal expansion? 1 441 77 10 1 1600 19 7 1 441 77 10 1 1600 19 7 8. The pair of linear equations 4x 6y 9 and x 3y 6 has No solution Many solutions Two solutions One solution. 4x 6y 9 x 3y 6 9. If cos 3, then sec tan 7 is equal to : 1 0 3 4 cos 3 sec tan 7 1 0 3 4 10. The median of the following data is : x : 10 0 30 40 0 f : 3 3 1 30 40 3 31 x : 10 0 30 40 0 f : 3 3 1 30 40 3 31 Section-B Questions numbers 11 to 18 carry two marks each. Page 3 of 9

11. Find the HCF of 867 and, using Euclid s division algorithm. 867 HCF 1. What must be subtracted from the polynomial 8x 4 14x 3 x 7x 8 so that the resulting polynomial is exactly divisible by 4x 3x? 8x 4 14x 3 x 7x 8 4x 3x 13. For what value of k, the pair of equations kx 3y k 3, 1x ky k has unique solution. k kx 3y k 3, 1x ky k 14. If tan =4, find the value of sin 3 cos sin cos. sin 3 cos tan 4 sin cos If A, B, C are the interior angles of ABC, then prove that : A B C cosec sec A, B C, ABC A B C cosec sec 1. In ABC, D and E are the points on the side AB and AC respectively such that DE BC. If AD 6x 7, DB 4x 3, AE 3x 3 and EC x 1, then find the value of x. ABC D E, AB AC DE BC, AD 6x 7, DB 4x 3, AE 3x 3 EC x 1, x 16. In the given figure ST and UV are intersecting at O such that the lengths of OS, OT, OU and OV (in centimeters) are 4., 6.3, 1. and 1.8. Prove SU VT. ST UV O OS, OT, OU OV 4. cm, 6.3 cm, 1. cm 1.8 cm SU VT. Page 4 of 9

17. Find the mean of the following data. Class 1 3 3 7 7 9 9 11 Frequency f 7 8 1 1 3 3 7 7 9 9 11 18. 7 8 1 The wickets taken by a bowler in 10 cricket matches are as follows : 6 4 0 1 3 3 Find the mode of the data. 10 6 4 0 1 3 3 Section-C Questions numbers 19 to 8 carry three marks each. 19. Prove that 3 is irrational. 3 0. Use Euclid s division lemma to show that the cube of any positive integer is of the form 9m, 9m 1 or 9m 8. 9m, 9m 1 9m 8 Page of 9

Prove that 3 is an irrational number. 3 1. Solve : 3 13 x y x 4 x, y 0 y 3 13 x y x 4 x, y 0 y x takes 3 hours more than y to walk 30 km. But if x doubles his pace, he is ahead of y by 1½ hours. Find their speeds of walking. 30 km x y 3 x y 1½. Find all the zeroes of p(x) x 3 9x 1x 0, if (x ) is a factor of p(x). p(x) x 3 9x 1x 0 (x ) 3. Prove that (sina coseca) (cosa seca) 7 tan A cot A. 4. (sina coseca) (cosa seca) 7 tan A cot A If sin (A B) 1 and cos (A B) 1, 0 <(A B) 90, A>B. Find A and B. sin (A B) 1 cos (A B) 1, 0 < (A B) 90, A > B, A B. In given figure, ABC, PQ BC and BC 3PQ. Find the ratio of the area of PQR and area of CRB where PC and BQ intersect at R. ABC PQ BC BC 3PQ PC BQ R PQR Page 6 of 9

CRB 6. In the given figure, PQR is a right angled triangle in which Q 90. If QS SR, show that PR 4PS 3PQ PQR Q 90 QS SR PR 4PS 3PQ 7. Calculate the mode of the following data : Classes 0 10 10 0 0 30 30 40 40 0 0 60 60 70 Frequency 10 18 30 0 1 0 10 10 0 0 30 30 40 40 0 0 60 60 70 10 18 30 0 1 Find the median of the following frequency distribution : Classes : 0 10 10 0 0 30 30 40 40 0 Frequency f : 7 8 0 8 7 0 10 10 0 0 30 30 40 40 0 f 7 8 0 8 7 8. Find the mean marks by step deviation method from the following data Page 7 of 9

9. Section-D Questions numbers 9 to 34 carry four marks each. Obtain all other zeroes of the polynomial x 4 3x 3 x 9x 6, if two of it s zeroes are 3 and 3. x 4 3x 3 x 9x 6, 3 3 30. Prove that the ratios of areas of two similar triangles is equal to the square of the ratio of their corresponding sides. PQRS is a trapezium with PQ SR. Diagonals PR and SQ intersect at M. PMS QMR. Prove that PS QR. Page 8 of 9

PQRS PQ SR PR SQ M PMS QMR PS QR 31. Show that n (m 1) m, if sin cos m and sec cosec n. sin cos m sec cosec n n (m 1) m. Simplify : cot (90 ) tan cosec (90 ) sec cos (0 ) cos (40 ) sin 1 cos 1 sec 78 cosec 7 tan 1 tan 37 tan 3 tan 7. cot (90 ) tan cosec (90 ) sec cos (0 ) cos (40 ) sin 1 cos 1 sec 78 cosec 7 tan 1 tan 37 tan 3 tan 7. 3. 33. Prove that cos A 1 sin A sec A. 1 sin A cos A cos A 1 sin A sec A. 1 sin A cos A Solve x y 6 and x y 0 graphically. Also find the area of the triangular region bounded by these lines and the x axis. x y 6 x y 0 x 34. Change the following frequency distribution to more than type distribution and draw its ogive and using it find its median. Classes 0 10 10 1 1 0 0 Frequency f 6 8 10 6 4 0 10 10 1 1 0 0 f 6 8 10 6 4 Page 9 of 9