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M.K.V.V. International Vidyalaya Prelim II (2020-21) Subject: Mathematics Std: X Marks: 80 Time: 3 Hrs General instructions: 1) This question paper contains parts A and B. 2) Both Part A and Part B have internal choices. Part A 1) It consists of section I and section II 2) Section I has 16 questions of 1 mark each. 3) Section II has 4 questions on case study. Each case study has 5 case-based sub parts. Attempt any 4 out of 5 Part B 1) Question No. 21 to 26 carry 2 marks each 2) Question No. 27 to 33 carry 3 marks each 3) Question No. 34 to 36 carry 5 marks each. PART A Section I Q.1 Write fundamental Theorem of Arithmetic. Q.2 Check 14 ends with zero or not? Q.3 Write a quadratic polynomial whose zeros are ( 2 + 2) (2 2) Q.4 Write nature of linear equation: 3 + 5 = 7 10 + 6 = 10 Q. 5 Solve: 2 X2 - (3/ 2) X + (1/ 2) Q.6 Which term of the AP : 27, 24, 21 is zero. OR In an AP if d = - 4, n= 7, an = 4 , then find a. Q.7 If ABC is similar to PQR and their areas are 6400 cm2 and 14400 cm2. Find ratio of their corresponding sides. Q.8 Two cones have their heights in the ratio 1:3 and radii in the ratio 3:1 Find the ratio of their volume. OR A new solid sphere is made by melting 27 small sphere of equal radius r. Find radius of new sphere. Q. 9 If = 2 2 = 2 2 + 1, then find ( + ). Q.10 If two tangents are inclined each other at 90 find angle between radii. Q.11 A piece of wire 22 cm long is bend into the form of an arc of a circle subtending an angle of 60 at its center, find radius of the circle. Q.12 Find value of 3 ,if 3 = (30 + ) OR If cos A = (1/2) then evaluate sin A 2 Q.13 Find value of x, if the distance between the points A (0,0) and B (x, - 4) is 5 units. Q.14 If radius of a circle is 7cm find the distance between two parallel Tangents. Q.15 A die is thrown once. Find the probability of getting an odd prime number. Q.16 If point P divides AB in the ratio 4 : 5 then find value of BP : AB Case study Questions from Q.no. 17 to Q.no. 20 Q.21 Write decimal expansions of (3/8) and (13/125) Q.22 Find the zeros and verify the relationship between the zeros and their Coefficients of 2 7 18 = 0 Q.23 Solve 0.2 x + 0.3y = 1.3 0.4 x + 0.5y = 2.3 1 Q.24 Solve + = 3 Q.25 Two poles of height 9 m and 14 m stand on a plane ground. IF distances between their feet is 12 m, find the distance between their tops. Q.26 Find perimeter of a triangle with vertices (0,5), (0,0) and (12,0) OR If the points A (6,1) , B (8,2), C (9,4) and D (p , 3) are the vertices of the parallelogram, taken in the order, find the value of p. Q.27 Prove that tangents at any point of a circle is perpendicular to the radius through the point of contact. OR Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals. Q.28 Find the area of the shaded region, where ABCD is square of side 10cm and semicircles are drawn with each side of the square as diameter. Q.29 Water is flowing at 5km/hr through a pipe of diameter 14cm into a rectangular tank in which length is 5m and breadth is 44 m. Find time in which water level rise by 7cm. OR A metallic sphere of radius 10.5 cm is melted and recast into smaller cones, each of radius 3.5 cm and height 3cm. How many number of cones will be formed. Q.30) 8 men and 12 boys can finish a piece of work in 10 days. While 6 men and 8 boys can finish it in 14 days. Find the time taken by one man alone and that by one boy alone to finish the work. Q.31 The angle of elevation of a cloud from a point 80 m above a lake is 30 and the angle of depression of the reflection of cloud in the lake is 60 . Find the height of the cloud. Q.32 A bag contains cards numbered from 2 to 25 and a card is drawn at Random. Find probability that: a] it is a multiple of 4 b] it is perfect square number c] it is a multiple of 5 or 10 Q 33 Draw a circle of radius 3cm take any point P at distance of 3 times radius from center, construct the pair of tangents to the circle and measure their lengths. Q.34 a] If 5tan = 4 . Then find 5 4 5 + 4 b] If + = and = , show that 2 2 = 4 Q.35 The sum of 3rd and 7th term of an A.P. is 6 and their product is 8. Find the sum of first 16 terms of A.P. OR Divide 32 into 4 parts which are in A.P., such that the ratio of the product of extremes to the product of means is 7:15. Q. 36 The marks in science of 80 students of class X are given below. Find mean, mode and median of the marks obtained by the students in science. Marks Frequency 0 10 3 10-20 5 20-30 16 30-40 12 40-50 13 50-60 20 60-70 5 70-80 4 80-90 1 90-100 1
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