I, SUMMATIVE ASSESSMENT I, / MATHEMATICS X / Class X

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1 I, SUMMATIVE ASSESSMENT I, / MATHEMATICS X / Class X : hours 90 Time Allowed: hours Maximum Marks: 90 JMYCH7I General Instructions: 1. All questions are compulsory.. The question paper consists of 1 questions divided into four sections A, B, C and D. Section-A comprises of questions of 1 mark each; Section-B comprises of 6 questions of marks each; Section-C comprises of 10 questions of marks each and Section-D comprises of 11 questions of marks each.. There is no overall choice in this question paper.. Use of calculator is not permitted. 1 1 Question numbers 1 to carry one mark each / SECTION-A 1 DEW, ABEW AD cm., DE1 cm. DWcm BD 1 In DEW, ABEW. If AD cm, DE1 cm and DW cm, then find the value of DB. cota, cosec Acot A 1 Page 1 of 9

2 If cota, then find the value of cosec Acot A sincos sin. tan. sin cos 1 cot 1 If sincos, find the value of sin. tan. sin cos 1 cot Find the sum of upper limit and lower limit of the class interval in which the 0 th observation of the following data lies : Class interval Frequency Question numbers 5 to 10 carry two marks each. / SECTION-B Find two numbers which on multiplication with numbers rational or irrational? 180 gives a rational number. Are these 6 1 n n 0 5 Show that 1 n cannot end with digits 0 or 5 for any natural number n. 7 6 Page of 9

3 ` ` 90 The Taxi charges in a city consists of a fixed charge together with the charge for the distance covered. For a distance of 6 km, the charges paid are Rs 58 while for a journey of 10 km, the charges paid are ` 90. Find the charge per km and the fixed charge. 8 ABC AB AC X Y YC6 cm XYBC AX 1, AY cm AB X and Y are points on the sides AB and AC respectively of a triangle ABC such that AX 1 AB, AY cm and YC6 cm. Find whether XYBC or not. 9 cos x (secxcosx)sin x Prove the following identity : cos x (secxcosx)sin x If mean of set of numbers is 15 and each observation is multiplied by, then find the mean of new set of observations Question numbers 11 to 0 carry three marks each. / SECTION-C Page of 9

4 Two tankers contain 60 litres and 80 litres of diesel respectively. Find the maximum capacity of a container which can measure the diesel of both the tankers in exact number of times. 1 x y xy6 xy0 Solve for x and y : xy6 xy0 1 x x Find the zeroes of the quadratic polynomial x zeroes and the coefficients. x and verify the relationship between the 1 x y xy0 xy70 Solve for x and y : xy0 xy70 15 ABC B90 AC BC ABC is an isosceles triangle. If B90, then prove that AC BC. Page of 9

5 16 ABC AD BC AD BDCD ABC In a ABC, AD is perpendicular to BC and AD BDCD, Prove that ABC is a right angled Triangle. 17 cos 71sin 57 tan Express cos 71sin 57 tan 6 in terms of trigonometric ratios of angles between 0 and sina (sec A tan A) 1 sina Prove that : 1 sina (sec A tan A) 1 sina x) x Following is the age distribution of cardiac patients admitted during a month in a hospital. Find the missing frequency, if the mode is given to be 58. Age (in years) Number patients of 5 1 x (kg/ha) Page 5 of 9

6 The following table gives the production yield per hectare of wheat of 100 farms of a village : Production yield (kg/ha) Number of farms Construct a more than type distribution and draw its ogive. 1 1 Question numbers 1 to 1 carry four marks each. / SECTION-D 1 x y xp q yp q HCF LCM LCM, HCF If two positive integers x and y are expressible in terms of primes as xp q and yp q, what can you say about their LCM and HCF. Is LCM a multiple of HCF? Explain. 8 Two years ago, a father was five times old as his son. Two years later from today his age will be 8 years more than three times the age of his son. Find their present ages. x 7x1, x 7x 7x pxq p q If a polynomial x 7x 7x pxq is exactly divisible by x 7x1, then find the value of p and q. NGO NGO x x 8x x7 xx Page 6 of 9

5x11 NGO A NGO decided to distribute books

the NGO which they donated to school for

Find the amount received by each student from

5 Prove that area of the equilateral triangle

7 5x11 NGO A NGO decided to distribute books and pencils to the students of a school running by some other NGO. For this they collected some amount from different number of people. The total amount collected is represented by x x 8x x7. The amount is equally divided between each of the students. The number of students, who received the amount is represented by xx. After distribution, 5x11, amount is left with the NGO which they donated to school for their infrastructure. Find the amount received by each student from the NGO. What value have been depicted here? 5 Prove that area of the equilateral triangle described on the side of square is half of area of the equilateral triangle described on its diagonal. 6 ABC DEBC AD : DB : 5 ar DFE ar CFB In a ABC, DEBC. If AD : DB : 5, then find ar DFE ar CFB. Page 7 of 9

8 7 sin(ab)sina.cosbcosa.sinb cos(ab)cosa.cosbsina.sinb (i) sin75 (ii) cos15 If sin(ab)sina.cosbcosa.sinb and cos(ab)cosa.cosbsina.sinb Find the value of (i) sin75 (ii) cos15 8 sin.sin sin.cos cos.sin cos.cos cosec cot 6 cot Simplify : sin.sin sin.cos cos.sin cos.cos cosec cot 6 cot 9 coseca cota q q 1 q 1 cosa0 If coseca cota q, then show that q 1 q 1 cosa Page 8 of 9

9 In a hospital, during the month of October 01, number of patients admitted for dengue and their ages are as follows : Age (in years) Number patients of Find the mean and median age of the patients In a village, number of members in 50 families are given in the following frequency distribution : Number of members Number of families Find the mode and mean of the above data. -o0o0o0o- Page 9 of 9

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