Time Allowed : 3 hours Maximum Marks : 90. jsuniltutorial

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1 6KN77NA I, 0 SUMMATIVE ASSESSMENT I, 0 / MATHEMATICS X / Class X 90 Time Allowed : hours Maximum Marks : 90 General Instructions: All questions are compulsory The question paper consists of questions divided into four sections A, B, C and D. Section- A comprises of 8 multiple choice questions of mark each; Section-B comprises of 6 questions of marks each; Section-C comprises of 0 questions of marks each and Section- D comprises of questions of marks each. There is no overall choice in this question paper Use of calculator is not permitted. SECTION A 8 Question numbers to 8 carry mark each. (a) 65 (b) 0 Page of 9

2 (c) (d) 65 Which of the following rational numbers has a terminating decimal expansion? (a) (c) (b) (d) x y (A) x0 ; y (B) x ; y8 (C) x ; y5 (D) x0 ; y0 The values of x and y in the given figure are : (A) x0 ; y (B) x ; y8 (C) x ; y5 (D) x0 ; y0 axbya b bxay0 (xy) (a) a b (b) ba (c) ab (d) a b If axbya b and bxay0, then the value of (xy) is : (a) a b (b) ba (c) ab (d) a b p(x)ax (a) x a (A) (B) (C) (D) If is one zero of the polynomial p(x)ax (a) x, then the value of a is : (A) (B) (C) (D) 5 7 m 5 m 6 m Page of 9

3 (a) 0 m (b) 5 m (c) 9 m (d).5 m Two poles of height 7 m and 5 m stand on a plane ground. If the distance between their foot is 6 m then distance between their tops is : (a) 0 m (b) 5 m (c) 9 m (d).5 m 6 sin 60sin 0 (A) (B) (C) (D) The value of sin 60sin 0 is : (A) (B) (C) (D) 7 cot 0 cot 5cot 75 cot 80 : 8 (a) 0 (b) (c) (d) The value of cot 0 cot 5cot 75 cot 80is equal to : (a) 0 (b) (c) (d) cannot de determined (A) (B) (C) (D) Relationship among mean, median and mode is : (A) MedianMode Mean (B) MeanMedian Mode (C) ModeMean Median (D) Mode Mean Median / SECTION B 9 Question numbers 9 to carry marks each. 9, 8 LCM Find the LCM of, and 8 by prime factorisation. Page of 9

4 0 6x 8x 7x x7 x x axb a b When a polynomial 6x 8x 7x x7 is divided by another polynomial x x the remainder is in the form axb. Find a and b. Solve : : x y x y x y y and x ABC BC D ADCBAC. D is a point on side BC of a triangle ABC such that ADCBAC. Prove that C A c o t c o t If c o t, c o t then find the acute angle Convert the following frequency distribution to a more than type cumulative frequency distribution. Marks obtained No. of Students C A C D C D C B C A C B C A.. / SECTION C 5 Question numbers 5 to carry marks each. 5 n n n, Prove that (n n) is divisible by for every positive integer n. Page of 9

5 6 x y 7xy85, x7y89 Solve for x and y : 7xy85, x7y89 7 a b xy7 ; (ab)x (ab)yab For what values of a and b will the following system of linear equations has infinitely many solutions? xy7 ; (ab)x (ab)yab 8 x x, x x 7x x 9 Check whether x x is a factor of x x 7x x or not. PQR PQ PR S T PQR In a PQR, S and T are points on sides PQ and PR respectively such that P S PSTPRQ. Prove that PQR is an isosceles triangle. 0 ABC XY, BC ABC B X AB P S S Q P T T R PSTPRQ In ABC, XY is parallel to BC and it divides ABC into two parts of equal area, prove that B X AB S Q P T T R and x sin y cos sincos x sinycos x y If x sin y cos sincos and x sinycos prove that x y coscotcosec sin Page 5 of 9 Find the value of coscotcosec, if sin.

6 X Find the mean of the following data which represent the height (in cm) of 50 girls of class X of a school : Height Total (in cm) Number of girls 0 x x If the mode of the given data is 0, find the missing frequency x for the following data : Classes Frequen cy x / SECTION D 5 Question numbers 5 to carry marks each. Page 6 of 9

7 5 0 5 n x y x, y n A class of 0 boys and 5 girls is divided into n groups so that each group has x boys and y girls. Find x, y and n. What values are reffered in a class? 6 f(x)x x x 9x6 Obtain other zeroes of the polynomial f(x)x x x 9x6, if two of its zeroes are and 7 km 9 km Rajiv walks and cycles at uniform speeds. When he walks for hrs and cycles for hr, distance travelled is km. When he walks for hr and cycles for hrs, distance travelled is 9 km. Find his speed of walking and cycling. If he walked and cycled for equal time in hrs how much distance does he cover? 8 5 cm 5 cm Hypotenuse of a right triangle is 5 cm and out of the remaining two sides, one is longer than the other by 5 cm. Find the lengths of the other two sides. 9 FEC GDB ADE ~ ABC In the fig. FEC GDB And Prove that ADE ~ ABC Page 7 of 9

8 0 5sin cos 5 sin co s 5 sin co s If 5sin cos, then find the value of 5 sin co s 5 sin co s ta n co t ta n co t co t ta n ta n co t Prove that : ta n co t co t ta n cota ta n ta n cos Asin A If cota, check whether ta n ta n cos Asin A or not Draw less than and more than ogives for the following distribution : Scores : Frequency : 8 0 Hence find the median. Verify the result through calculations. Page 8 of 9

9 Find the mean age (in years) from the frequency distribution given below : Class (age in years) frequency ***** Page 9 of 9

10 MARKING SCHEME 6KN77NA SUMMATIVE ASSESSMENT I, 0 MATHEMATICS Class X SECTION A Question numbers to 8 carry mark each. (c) (B) x ; y8 (c) (A) 5 (a) 0 m 6 (B) 7 (c) 8 (A) SECTION B Question numbers 9 to carry marks each LCM (,, 8) 79 x x 6x 6x 8x 8x 7 x x 7 to obtain r(x)5x By question 5xaxb a5 b xy66 xy (x) 6 x y8 x y 66 x6 y 9 x 7x 7x x 9 x 7 6 x 9 5 x solution : x6 y. Page of 7

11 Page of 7 In ADC and ABC ADCBAC CC ADC ~ BAC CA CB CD CA Given relation is taken as cot cot cot cot 60 Marks No. of students More than 0 0 More than 0 5 More than 0 6 More than 60 More than 80 6 SECTION C Question numbers 5 to carry marks each. 5 Identify the forms q or q If nq, solve, rearrange and show it is divisible by If nq, find (n n) and show it is divisible by 6 7 x y 85 7 x y 85 x 7 y 89 x 7 y x 58 y 7 x y 58 x y x y x y x y x y y x y x solution x y 7 a b c for infinitely many solutions. a b c

12 7 a b a b a b 7 a b a b a b a b ab6 a b 8 a b7 a7 b a b 6 ( a5 b0 () a 5 b 0 ( 6 b 6 b a 5 8 x x x x 7 x x x x 9 0 x x x ( ) ( ) x 5 x x x x x ( ) ( ) ( ) x x x 6 x 6 ( ) ( ) ( ) 7 x 7 x x is not a factor of x x 7x x Given that PS PT SQ TR QRST PSTPQR (Corresponding angles) Also given that PSTPRQ and PRQPQR PQPR PQR is isosceles Page of 7 AXY ABC (by AA )

13 area AXY AX area ABC AB AX AX AB AB AX AB BX AB x siny cos (given) y x cos () sin x sin y cos sin cos () sub. () in () y cos sin. sin y cos sin cos y cos sin y cos sin cos y cos [ sin cos ]sin cos ysin () Sub. () in () xcos x y cos sin 5 5 Finding cos 6 Cot 5 and cosec Finding value of the given exp Heights (in cm) f i x i xi f u i i u i h a f i u i Page of Mean height9.8 cm..

14 Since 0 is mode is modal class f f0 Mode l h f f0 f 0x x 0x x 5x005x x 8 SECTION D x6 Question numbers 5 to carry marks each. 5 HCF of 0 and 55 So number of groups5 0 5 Number of students in each group hence x and y 5 5 Values : Promote co-education, Promote and help to educate girl child, Role of activity in groups. 6 (x) and (x) are factors of f(x) (x)(x) is a factor Finding other zeroes as and 7 Let speed of walking x km/hr Speed of cycling y km/hr xy () xy () multiply () by x y 8 and x y 9 x 9 x km/hr y8 km/hr Speed of walking km/hr and cycling 8 km/hr Equal time of travel by walk and cycle km is distance travelled in hrs. Page 5 of 7

15 8 AC AB BC (5) (x5) x 65x 0x5x 600 x 0x 0 x 5x00 0 (x5)(x0) x0 or 5 cm. Hence x5, 9 FEC GDB ECBD (i) 0 AEAD (ii) From (i) and (ii) AE AD EC BD DEBC sides are 5 and 0 cm. ADE ~ ABC (A.A similarity) 5 sin cos sin tan cos 5 5 Dundery the N r & D r 5 sin cos of by cos 5 sin cos 5 tan 5 We get 5 5 tan tan cot cottan cot tan tan tan tan LHS : tan tan tan (tan ) tan tan (tan) (tan tan ) tancotrhs (tan) tan (tan) (tan ) k cota cot A k by Py. Theorem AC AB BC (k) (k) 5k AC 5k Page 6 of 7

16 LHS tan A tan A k k k k 9k 6k 9k 6k 7 5 cos Asin A k k 6k 9k 7k 7 5k 5k 5k 5k 5k 5 Less than series More than series Score Frequency Score Frequency Less than 0 8 More than 0 50 Less than 0 8 More than 0 Less than 50 More than 0 Less than 60 More than 50 8 Less than 70 8 More than 60 6 Less than More than 70 Correct graph of less than Correct graph of more than Median5 5 8 Verification : Classes frequency f i x i x u i i a h f i u i f i 70 f i u i 7 aassumed mean fu Meana i i h f. ½ i ½ Page 7 of 7

CBSE QUESTION PAPER CLASS-X MATHS

CBSE QUESTION PAPER CLASS-X MATHS SECTION - A Question 1:If sin α = 1 2, then the value of 4 cos3 α 3 cos α is (a)0 (b)1 (c) 1 (d)2 Question 2: If cos 2θ = sin(θ 12 ), where2θ and (θ 12 ) are both acute