SUMMATIVE ASSESSMENT I (011) Lakdfyr ijh{kk&i MATHEMATICS / f.kr Class X / & X 56003 Time allowed : 3 hours Maimum 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 ;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,, gsaa izr;sd iz u es a,d fodyi dk p;u djsaa (v) dsydqysvj dk iz;ks 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 10
1. If the HCF of 65 and 117 is epressible in the form 65 m 117, then the value of m is : (A) 4 (B) (C) 3 (D) 1. 65 117 HCF 65 m - 117 m (A) 4 (B) (C) 3 (D) 1 The quadratic polynomial whose product and sum of the zeroes are 1 and 1, respectively is : (A) 1 (B) 1 1 (C) 1 (D) 1 1 1 1 (A) 1 (B) 1 1 (C) 1 (D) 1 1 3. In the given figure, value of (in cm) is : (A) 4 (B) 5 (C) 6 (D) 8 cm (A) 4 (B) 5 (C) 6 (D) 8 4. In ABC, C 90 then the value of cos A cos B is : (A) 1 (B) 0 (C) 1 (D) 3 ABC, C cos A cos B (A) 1 (B) 0 (C) 1 (D) 3 5. If sin A 1 and cos B 1, then the value of (A B) is equal to : (A) 0 o (B) 60 o (C) 90 o (D) 30 o Page of 10
sin A 1 cos B 1, (A B) 6. (A) 0 o (B) 60 o (C) 90 o (D) 30 o (seca tana) (1 sina) is equal to : 7. (A) seca (B) sina (C) coseca (D) cosa. (seca tana) (1 sina) (A) seca (B) sina (C) coseca (D) cosa. 31 The decimal epansion of the rational number. 5 will terminate after : (A) one decimal place (B) two decimal places (C) three decimal places (D) more than 3 decimal places 31. 5 (A) (C) (B) (D) 8. The point of intersection of the lines y 3 and 3y is : (A) (3, 0) (B) (0, 3) (C) (3, 3) (D) (0, 0) y 3 3y (A) (3, 0) (B) (0, 3) (C) (3, 3) (D) (0, 0) 9. sin 75 sec 75 can be epressed in terms of angles between 0 and 45 10. (A) sin 15 sec 15 (B) cos 15 sec 15 (C) cos 15 cosec 15 (D) sin 15 cosec 15 sin 75 sec 75 0 45 (A) sin 15 sec 15 (B) cos15 sec 15 (C) cos 15 cosec 15 (D) sin 15 cosec 15 If the mean and median of a distribution are 70 and 0 respectively, then the mode of the data is : (A) 10 (B) 0 (C) 80 (D) 370 70 0 (A) 10 (B) 0 (C) 80 (D) 370 Section-B Questions numbers 11 to 18 carry two marks each. Page 3 of 10
11. In the adjoining factor tree given below, find the numbers m, n : m n 1. Find a quadratic polynomial whose zeroes are 3 5 and 3 5. 3 5 3 5 13. Find the value of k for which the system of equations k 3y 1; 1 ky has no solution. k k 3y 1; 1 ky 14. It cosec 13, find the value of cot tan 1 cosec 13 cot tan 1 If sin (A B) cos (A B) 3 and A, B (A > B) are acute angles, find the values of A and B. sin (A B) cos (A B) 3 A, B (A > B) A B 15. In the given figure, find in terms of p, q and r. p, q r Page 4 of 10
16. Prove that the diagonals of a trapezium divide each other proportionally. 17. Find the mean of the following frequency distribution : Classes 0 4 4 6 6 8 Frequency f 5 8 5 0 4 4 6 6 8 f 5 8 5 18. The IQ of 50 students was recorded as follows. Find the mode. IQ score 80 90 90 100 100 110 110 10 10 130 130 140 Number of students 5 10 16 15 3 1 50 80 90 90 100 100 110 110 10 10 130 130 140 5 10 16 15 3 1 Section-C Questions numbers 19 to 8 carry three marks each. 19. If is rational and y is irrational, then prove that ( y ) is irrational. y ( y ) 0. Show that any positive odd integer is of the form 8q 1 or 8q 3 or 8q 5 or 8q 7, Page 5 of 10
where q is some integer. 8q 1 8q 3 8q 5 8q 7 q Prove that 5 3 is irrational. 5 3 1. Solve for and y : - 5 1 y 4 3 6 1 y 3 y 5 1 y 4 3 6 1 y 3. 3. Solve : 4 3 y 14, 3 4 y 3 4 3 3 y 14, 4 y 3 Find the zeroes of 3 13 6 and verify the relation between the zeroes and coefficients of the polynomial. 3 13 6 Prove that 4. Prove that, tan cot tan cot. sin cos tan cot tan cot sin cos cos 1 sin sec 1 sin cos. Page 6 of 10
cos 1 sin sec 1 sin cos 5. In given figure ABCD is a parallelogram such that diagonals AC, BD intersect at O. If P is mid point of CD and CQ 1 AC. Prove that R is mid - point of BC. 4 ABCD AC BD O P CD CQ 1 AC R BC 4 6. Two Isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 5. Find ratio of their corresponding heights. 16 : 5 7. Find the mean of the given frequency distribution table : 00 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows. Page 7 of 10
No. of letters 1 5 5 10 10 15 15 0 0 5 No. of surnames 0 60 80 3 8 Find the median. 00 1 5 5 10 10 15 15 0 0 5 0 60 80 3 8 8. Find the value of p if mean of the following distribution is 7.5. p 7.5 Section-D Questions numbers 9 to 34 carry four marks each. 9. Find all the zeroes of the polynomial 4 5 3 10 8, if two of its zeroes are,. 4 5 3 10 8 30. In the given figure, ABC is right angled at C and DE AB. Prove that ABC ADE and find the lengths of AE and DE. Page 8 of 10
ABC C DE AB ABC ADE AE DE Prove that the ratio of the areas of two similar triangles is equal to the squares of the ratio of their corresponding sides. 31. Prove that : (1 tanatanb) (tana tanb) sec A. sec B. (1 tanatanb) (tana tanb) sec A. sec B. Prove that : cosa sina 1 coseca cota. cosa sina 1 cosa sina 1 coseca cota cosa sina 1 3. Determine the value of such that cosec 30 sin 60 3 4 tan 30 10 cosec 30 sin 60 3 4 tan 30 10 Page 9 of 10
33. Determine graphically the vertices of the triangle formed by the lines y 1 0 ; 3 y 1 ; y 0. y 1 0 ; 3 y 1 ; y 0. 34. For the data given below draw more than ogive graph and find the value of median. Production (in tons) No. of labourers 0 10 8 10 0 18 0 30 3 30 40 37 40 50 47 50 60 6 60 70 16 70 80 7 Total 18 0 10 10 0 0 30 30 40 40 50 50 60 60 70 70 80 8 18 3 37 47 6 16 7 18 Page 10 of 10