SUMMATIVE ASSESSMENT I (2011) Lakdfyr ijh{kk&i. MATHEMATICS / xf.kr Class X / & X. Time allowed : 3 hours Maximum Marks : 80 fu/kkzfjr le; % 3?k.

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1 For more sample papers visit : SUMMATIVE ASSESSMENT I (20) Lakdfyr ijh{kk&i MATHEMATICS / xf.kr Class X / & X 600 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 0 questions of mark each, section B comprises of 8 questions of 2 marks each, section C comprises of 0 questions of 3 marks each and section D comprises 6 questions of 4 marks each. (iii) Question numbers to 0 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 question of two marks, 3 questions of three marks each and 2 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 0 iz u gsa ftuesa izr;sd vad dk gs, [k.m & c esa 8 iz u gsa ftuesa izr;sd ds 2 vad gsa, [k.m & l esa 0 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 ls 0 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 2 vadksa ds,d iz u esa, 3 vadksa ds 3 iz uksa esa vksj 4 vadks a ds 2 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 to 0 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 of

2 . H.C.F. of two consecutive even numbers is : (A) 0 (B) (C) 4 (D) 2 (A) 0 (B) (C) 4 (D) 2 2. The graph of y p(x) is given below. The number of zeroes of p(x) are : (A) 0 (B) 3 (C) 2 (D) 4 y p(x) p(x) (A) 0 (B) 3 (C) 2 (D) 4 3. In figure, DE BC then x equals to : (A) 2. cm (B) 2 cm (C).4 cm (D) 4 cm DE BC x Page 2 of

3 (A) 2. (B) 2 (C).4 (D) 4 4. If sin cos, then value of is : (A) 0 (B) 4 (C) 30 (D) 90 sin cos (A) 0 (B) 4 (C) 30 (D) 90. If a cot b cosec p and b cot a cosec q then p 2 q 2 is equal to : (A) a 2 b 2 (B) b 2 a 2 (C) a 2 b 2 (D) b a a cot b cosec p b cot a cosec q p 2 q 2 (A) a 2 b 2 (B) b 2 a 2 (C) a 2 b 2 (D) b a 6. In figure, AC 3 cm, BC 2 cm, then sec equals : (A) 3 2 (B) 2 (C) 2 3 (D) 3 AC 3 BC 2 sec Page 3 of

4 (A) 3 2 (B) 2 (C) 2 3 (D) 3 7. If the HCF of 8 and 3 is expressible in the form 8n 3, then value of n is : (A) 3 (B) 2 (C) 4 (D) 8 3 HCF 8 n 3 n (A) 3 (B) 2 (C) 4 (D) 8. One equation of a pair of dependent linear equations is x 7y 2, the second equation can be : (A) 0x 4y 4 0 (B) 0x 4y 4 0 (C) 0x 4y 4 0 (D) 0x 4y 4 (A) 0x 4y 4 0 (B) 0x 4y 4 0 (C) 0x 4y 4 0 (D) 0x 4y 4 9. The value of tan.tan2.tan3... tan89 is : (A) 0 (B) (C) 2 (D) tan.tan2.tan3... tan89 x 7y 2 (A) 0 (B) (C) 2 (D) 2 0. The mean and median of same data are 24 and 26 respectively. The value of mode is : (A) 23 (B) 26 (C) 2 (D) (A) 23 (B) 26 (C) 2 (D) 30 2 Section-B Questions numbers to 8 carry two marks each.. Divide (2x 2 x 20) by (x 3) and verify the result by division algorithm. 2x 2 x 20 (x 3) 2. It being given that is one of the zeros of the polynomial 7x x 3 6. Find its other zeros. Page 4 of

5 7x x For what value of p will the following system of equations have no solution p (2p ) x (p ) y 2p ; y 3x 0. (2p ) x (p ) y 2p y 3x 0 4. If tan (A B) 3 and tan (A B), 0 <A B 90 ; A > B, find A and B. 3 tan (A B) 3 tan (A B) 3 0 <A B 90 ; A > B A B If sin (A B) cos (A B) 3 2 A and B. OR / and A, B (A > B) are acute angles, find the values of sin (A B) cos (A B) 3 2 A, B (A > B) A B. X and Y are points on the sides PQ and PR respectively of a PQR. If the lengths of PX, QX, PY and YR (in centimeters) are 4, 4., 8 and 9 respectively. Then show XY QR. PQR PQ PR X Y PX, QX, PY YR cm 4, 4., 8 9 XY QR. 6. A pole of length 0 m casts a shadow 2 m long on the ground. At the same time a tower casts a shadow of length 0 m on the ground, then find the height of the tower. 0 m 2 m 0 m 7. The ages of employees in a factory are as follows : Age in years No. of employees Page of

6 Find the median age group of the employees The following is the daily pocket money spent by students. Pocket money (`) No. of students Find the mode of the above data. (`) Section-C Questions numbers 9 to 28 carry three marks each. 9. Prove that 2 3 is irrational Show that 4 n can never end with the digit zero for any natural number n. n 4 n Page 6 of

7 OR / If d is the HCF of 4 and 27, find x, y satisfying d 27x 4y 4 27 HCF, d x y d 27x 4y 2. Solve the following system of linear equations by cross multiplication method : 2(ax by) (a 4b) 0 2(bx ay) (b 4a) 0 2(ax by) (a 4b) 0 2(bx ay) (b 4a) 0 OR / In the figure below ABCDE is a pentagon with BE CD and BC DE. BC is perpendicular to CD. If the perimeter of ABCDE is 2 cm, find the value of x and y. ABCDE BE CD BC DE BC CD ABCDE 2 cm x y Page 7 of

8 22. On dividing the polynomial p(x) by a polynomial g(x) 4x 2 3x 2 the quotient q(x) 2x 2 2x and remainder r(x) 4 x 0. Find the polynomial p(x). p(x) g(x) 4x 2 3x 2 q (x) 2x 2 2x r(x) 4 x 0 p(x) 23. Prove that coseca sina seca cosa tana cota coseca sina seca cosa tana cota 24. If cosec (A B) 2, cot (A B) cosec (A B) 2, cot (A B), 0 < (A B) 90, A > B, then find A and B. 3, 0 < (A B) 90, A > B A B 3 2. Triangle ABC is right angled at B and D is mid point of BC. Prove that : AC 2 4AD 2 3AB 2. ABC B D, BC AC 2 4AD 2 3AB In figure, ABC is right angled at B and D is the mid point of BC. Prove that AC 2 4AD 2 3AB 2. ABC B D, BC AC 2 4AD 2 3AB 2. Page 8 of

9 27. Find the mean of the following frequency distribution, using step deviation method. Classes Frequency OR / The mean of the following distribution is 22, find the missing frequency f : Class Frequency f 9 22 f f Find the missing frequency f if the mode of the given data is 4. Class : Frequency : f f f 8 7 Page 9 of

10 Section-D Questions numbers 29 to 34 carry four marks each. 29. Obtain all the zeroes of the polynomial f (x) x 4 7x 3 0x 2 4x 2, if two of its zeroes are 2 and 2. f (x) x 4 7x 3 0x 2 4x Prove that in a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides : OR / If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. Prove it. 3. Prove that cota coseca cosa cota coseca sina cota coseca cosa cota coseca sina OR / Prove that tan 2 cot 2 2 sec 2 cosec 2 tan 2 cot 2 2 sec 2 cosec Prove that : (sin cosec ) 2 (cos sec ) 2 7 tan 2 cot 2 (sin cosec ) 2 (cos sec ) 2 7 tan 2 cot Draw the graph of 2x y 6 and 2x y 2 0. Shade the region bounded by these lines with x axis. Find the area of the shaded region. 2x y 6 2x y 2 0 x Page 0 of

11 34. Compute the median for the following data : For more sample papers visit : Page of

SUMMATIVE ASSESSMENT I (2011) Lakdfyr ijh{kk&i. MATHEMATICS / xf.kr Class X / & X. Time allowed : 3 hours Maximum Marks : 80 fu/kkzfjr le; % 3?k.

SUMMATIVE ASSESSMENT I (2011) Lakdfyr ijh{kk&i. MATHEMATICS / xf.kr Class X / & X. Time allowed : 3 hours Maximum Marks : 80 fu/kkzfjr le; % 3?k. 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.