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llme Albwed : S to 3% Hoursl MODEL TEST PAPER 4 FIRST TERM (SA-I) MATHEMATICS (With Answers) CLASS X [Maxin~um Marks : 80 General Instructions : (i) All questions are compulsory.

SectionA comprises of 10 questions of 1 mark each, Section B comprises of 8 questions of 2 marks each, Section C compri+es of I0 questions of 3 marks each and.

$You have to attempt only one of the alternatives in all such questions. (v) Use of calculators is noipermitted. \ 1$

1 llme Albwed : S to 3% Hoursl MODEL TEST PAPER 4 FIRST TERM (SA-I) MATHEMATICS (With Answers) CLASS X [Maxin~um Marks : 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. SectionA comprises of 10 questions of 1 mark each, Section B comprises of 8 questions of 2 marks each, Section C compri+es of I0 questions of 3 marks each and. Section ~ D comprises of 6 questions of 4 marks each. (iii) Question numbqrs 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 has been'provided in 1 question of two marks, 3 questions of three marks each and 2 questions offour marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculators is noipermitted. \ 1 - Question numbers 1 to TO are of one mark each. 1. The least number that is divisible by all the numbers from 1 to 6 both inclusive is (a) 6 (b) 30 (c) 60 (d) In figure, the graph of a polynomialp(x) is shown. The number of zeroes of p(x) is ' Y (dl 4 BC 1 3. It is given that 4ABC - bdef and - = -. Then ar (mef) is kqual to EF 5 ar ( MC) 1 (a). 1 (c) - 25

2 ~ ~~ 4. If sin 0 - cos 0 = 0, then the value of sin8 0 + cos8 0 is 5. The value of cos Oo.cos lo.cos 2"... cos 89" is (a) 0 (b) - 1 (c) 1 6. (COS 0 + sin 0)2 + (COS 0 - sin el2 is equal to (a) 0 (b) - 1 (c) 1 (d)2 7. If sin (0 + 36") = cos 0, where " is an acute angle, then 0 is equal to (a) 9" (b) 18" (c) 27' (d) 36" 8. For a frequency distribution, mean, mode and median are connected by the relation (a) Mode = 3 Mean - 2 Median (b) Mode = 2 Median - 3 Mean (c) Mode = 3 Median - 2 Me& (d) Mode = 3 Median + 2 Mean 9. If the lines represented by the pair of linear equations 4~+ky-S=Oand3~-5y+7=0 are parallel, then the value of k is (dl The decimal expansion of - 21 will terminate after how many places of decimal? 1120 Question numbers I1 to 18 carry 2 marks.each. 11. If2 is a zero of both the polynomials 3x2 + m.x - 14 and 2x3 + I&' + x - 2, find the value of m - 2n. 12. Explain why 7 x 6 x 5 x 4 x 3 x 2 x is a composite number. 13. For what value of 'k' will the following pair of linear equations have %kite number of solutions. k+3y=k ky=k. 14. Prove that :

If sin 0 + cos 8 = fi sin (90" - 81, determine cot 8. 15. In figure, AABC is right angled at C and DE I AB. Prove that AABC - M E and hence find the lengths of AE and DE. - 12 nn ------*c 16.

3 If sin 0 + cos 8 = fi sin (90" - 81, determine cot In figure, AABC is right angled at C and DE I AB. Prove that AABC - M E and hence find the lengths of AE and DE nn *c 16. In figure, if ED LAC and CE I AB, prove that (i) AAEC - M B a? A. 17. The following cumulative frequency distribution gives daily wages of 60 workers : Daily wages (in Q More than or equal to 300 More than or equal to 250 More than or equal to 200 More than or equal to 150 More than or equal to 100 More than or equal to 50 More than or equal to :. No. of workers Write the above cumulative frequency distribution as frequency distribution. 18. Find the modal marks of the following distribution of marks obtained by 70 students Marksobtained Numb& of students ( / 40 ( Question numbers 19 to 28 carry 3 marks each. 19. Show that any positive odd integer is of the form 6q t 1 or 6q t 3 or 6q + 5, where q is a positive integer.

Prove that 3& is an irrational. 5 21. The sum of a two digit number and the number formed by interchanging the digits is 132.

4 Prove that 3& is an irrational The sum of a two digit number and the number formed by interchanging the digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number. or A fraction is such that if the numerator is multiplied by 3 and the denominator reduced by , we get -, but if the numerator is increased by 8 and the denominator is doubled, we get Find the fraction. 22. If a and p are the zeroes of the polynomial :p(x) = x2-5x + k such that a - = 1, find the value of k If cot B = -, prove that : tar?^ - sin2 B = sin4 B sec2 B. 5 - cota+coseca-1 l+cosa 24. Show that : - cot A - cosec A + 1 sin A ' 25. In figure, U3 c 90" andad I BC. Prove that A C~ - AB' + BC' - 2BC.BD. I: B D C 26. E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that AABC - ACFB. 27. Find mean of the following frequency distribution using step-deviation method : t Classes Class-Interval ( Frequency 22 The mean of the following frequency distrlbutlon is Find the value ofp. 35 / Frequency P

28. Find the median of the following distribution : - Marks Frequency - 0-100 I 2 Question numbers 29

Prove that, in a right triangle, the square of the hypotenuse is equal to the s,m of squares of other two sides.

5 28. Find the median of the following distribution : - Marks Frequency I 2 Question numbers 29 to 34 carry 4 marks each. 29. Find the zeroes of the polynomial :p(x) = x3-5x2-2x + 24, if it is given that the product of its two zeroes is Prove that, in a right triangle, the square of the hypotenuse is equal to the s,m of squares of other two sides... Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. 31. J.f'cGec 8 -sin 0 = a and see 0 -tan 8 = b, prove that a2b2 (a2 + b" 3) = 1. Evaluate : cot 10" cot 36" cot 54" cot 60" cot 80" +tan (55" 0) -cot (35" + 8) + cos (40" + 0) - sin (50" - 8) + cos2 39" + cos2 51" sin2 39" + sin2 51" x Y. x. Y 32. If- coso+- smo=land- sm8-- coso=-l,provethat:?+-=l. x2 y2 a b - a b a. h The lengths of40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table : Length (in b) , Number of leaues Draw a more than type ogive for the given data. Hence, obtain the median length of the leaves from the graph and verify the result by using the formula.

A 17. Daily wages Number of workers (in Q frequency 0-50 1 50-100 6 100-150 9 150-200 23 200-250 9 250-300 12 18. Mode = 37.5 Section 'C' 12 21. Number = 48 Fractionis - 22.

6 34. Solve the following system of equations graphically : x-2y=-3 2x+y=4 Find the points where the lines intersect x-axis. Section 'A' 1. (c) 2. (a) 3. (dl 4. (c) 5. (d) 6. (dl 7. (c) 8. (c) 9. (b) 10. (d) Section 93' 11. m-2n= x 6 x 5 x 4 x 3 x 2 x = 5 x 1009 is a composite number as product of prime occur AE = - cm, DE = - cm A 17. Daily wages Number of workers (in Q frequency Mode = 37.5 Section 'C' Number = 48 Fractionis k = Mean = p = Median = 525 Section 9' 29. Zeroes of the given polynomial are 3,4 and - 2. & Median = &. 3 3?. x = 1 and y = 2; (- 3,O) and (2,O)

MODEL TEST PAPER 9 FIRST TERM (SA-I) MATHEMATICS (With Answers)

MODEL TEST PAPER 9 FIRST TERM (SA-I) MATHEMATICS (With Answers) CLASS X llme Allowed, : 3 to 3% Hours] LMaximum Marks : 80 General Instructions : (i) All are compulsory. (ii) The question paper consists