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MKVV INTERNATIONAL VIDYALAYA STD X ACADEMIC YEAR 2020 21 SUB MATHS PRELIMS MARKS 80 TIME 3hrs General instructions: 1. This question paper contains two parts A and B 2. Both Part A and Part B have internal choices Part- A 1. It consists of sections I and 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 sub parts PART - B 1. Question No 21 to 26 carry of 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 - 1 Section 1 has 16 questions of 1 mark each. 1. On comparing the ratios write weather the following pair of equation is consistent or not 3x + 4y +5 = 0 , 6x + 8y + 10 = 0 2. Two dice are thrown simultaneously .Find the probability of getting a sum 7 3 . Find the area of a quadrant of a circle where the circumference is 44cm OR If the diameter of a semi circular protractor is 14cm , then find its perimeter 4. Find the value of x if tan3x = sin 45 cos45 + sin30 5. If and are the zeros of the polynomial x - 5x + k , where = 1 , find the value of k 6 . If 2p + 1 , 13, 5p 3 are three consecutive terms of an A.P , then find the value of p OR th The 17 term of an A.P. exceeds its 10th term by 7. Find the common difference 7. Draw a line segment of length 8cm .Divide it internally in the ratio 3: 4 8. For what value of k, the following pairs of equations has no solutions 2x + 3y = 5 , 6x + ky = 15 9. Solve for x : 9x - 3( a + b) x + ab = 0 10 . The angle of elevation of the top of a tower from a point on the ground which Is 30m away from the foot of the tower is 30 . Find the height of the tower 0R A tower AB is 20m high and BC, its shadow on the ground is 20 3m long. Find The suns altitude 11. If two positive integers p and q can be expressed as p = ab and q = a b where a and b being prime numbers . Find the LCM ( p, q ) 12. Given PQ // BC and AP : PB =1/2 , find AP : AB 13 . Find the linear relation between x and y such that P ( x, y) is equidistant from the points A( 7, 0 ) and B ( 0,5) OR If A( 4, 9) , B ( 2,3) and C( 6, 5) are the vertices of ABC , then find the length of median through C 14. Given ABC ~ DEF, . BC = 3cm, EF = 4cm and area of ABC = 54cm , find the area of DEF 15. O is the centre of a circle and from an exterior point P tangents PA and PB are drawn to the circle . If AOP = 55 ,find APB 16 Find the quadratic polynomial whose zeros are 7 + 2 2 and 7 - 2 2 OR If the sum of zeros of the polynomial x - ( k + 3) x +( 5 k 3) is equal to one forth the product of the zeros , find the value of k Section II Case study based questions are compulsory. Attempt any 4 sub part of each question. Each sub part carries 1 mark Case study based 1 17 . For mathematics exam a different seating arrangement has been followed . Three student Ravi, Aarav and Karan are seated at the points A ,B ,and C respectively a) Sum of x co ordinates of points A, B, C is i) 11 ii) 12 iii) 7 iv) 6 b) Distance between origin and point C I) 15 ii) 19 iii) 21 iv) 26 c) The mid point of line joining points A and B is i) (2,1 ) ii) (1, 6 ) iii) ( 3, 3 ) iv) ( 2 , 5 ) d) The point which divides the line segment joining points A and C in the ratio 1: 2 is i) (3, 5/3 ) , ii) (2, 4/3 ) iii) (1 , 5/6 ) iv) (3, 4/5) e) Sum of distance BC and AC is i) 10 ii) 5 2 iii) 2 10 iv ) 2 5 Case study based 2 18) A model of a traffic signal on the road has a triangular base ABC with A =90 and with A red circular light within it as shown in figure. AB =12cm and BC = 20cm and R is the In centre of the ABC a) Area of ABC is i) 96 cm ii) 98cm iii) 140cm iv) 150cm b) In the figure AC is equal to i) 12cm ii) 14cm iii) 16cm iv ) 18cm c) Radius r is equal to i) 5cm ii) 6cm iii) 7cm iv) 4 cm d) Area used for red light is equal to i) 16 cm ii) 17 cm iii) 19 cm iv) 28 cm e) Area of CRB is equal to i) 40 cm ii) 80cm iii) 20 cm iv) 60 cm 19) case study based - 3 A stop watch is used to find the time that it took a group of students to run 100m race Time in Seconds No of Students 0 -- 20 8 20 40 10 40 60 13 60 80 80 -- 100 6 3 a) Estimate the mean time taken by a student to finish the race i) 54 ii) 63 iii) 43 iv ) 50 b) What is the mode of the given data i) 50 ii) 66 iii) 46 iv) 54 c) the difference between mean and mode is i) 3 ii) 2 iii) 1 iv) 4 d) How many students finished the race within 1 minute i) 18 ii) 37 iii) 31 iv) 8 e) The construction of cumulative frequency table is useful in determining the i) Mean ii) Median iii) Mode iv) All of the above Case study based 4 20) A carpenter makes tools for electricians with a square top of side 0.5 m and at a height 1.5m above the ground .Also ,each leg is inclined at an angle of 60 to the ground. There are two steps CD and EF which are parallel to the ground ( 3 = 1.732) a) the measure of leg AX is i) 2m ii) 3 m iii) m iv ) 3/2m b) Measure of step CD is i) 1.077 m ii) 2.011m iii) 1.732 m iv) 0.12m c) Area of rectangle ABSR is i) 1.75 m ii) 2.5 m iii ) 0.75 m iv) 1.5 m d) length of QF is i) 2 / 3m ii) 3/3 m iii ) 1/3 m iv 1/ 3 m e) If a sector is drawn from point x with radius 1cm , its area will be i) m ii) /6 m ii) /3m iv) /2m PART - B All questions are compulsory . In case of internal choices , attempt any one 21 . If x = a sin + b cos and y = a cos b sin prove that x + y = a + b 22. ABCD is a trapezium in which AB // DC and its diagonals intersect each other At the point O. Show that AO = CO BO DO OR Prove that the ratio of the areas of two similar triangles is equal to the square of ratio of their corresponding medians 23) Solve for x 2x + 9 + x = 13 OR If -5 is a root of the quadratic equation 2x + px 15 = 0 and the equation p( x +x) + k = 0 has equal roots , find the value of k 24) An A.P consists of 25 terms . If the 13th term is 50, find the sum of all terms of the A.P 25) Show that 3 - 2 5 is an irrational number 26) Three different coins are tossed together .Find the probability of getting i) at least two heads ii) not getting the same result in all the tosses 27) Draw a pair of tangents to a circle of radius ,which are inclined to each other at an angle of 60 28) Prove that when 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 29) The angle of elevation of the of a tower from a point A on the ground 30 .On moving a distance of 20 m towards the foot of the tower to a point B and the angle of elevation increases to 60 .Find the height of the tower and the distance of the tower from point A ( 3 = 1.732 ) 30) In ABC , AD is the median .Prove that AB + AC = 2AD + 2DC OR Given AB// PQ// CD. AB = x units , CD = y units PQ = z units Prove that 1 + 1 = 1 x y z A P C x z y D B Q 31) Solve for x and y 5 - 2 = -1 15 + 7 = 10 X+ y x y x+ y x - y 32) SinA ( 1 + tanA ) + cosA ( 1 + cot A) = Sec A + cosec A OR If sin + cos = 3 , then prove that tan + cot = 1 33) A Memento is made as shown in the figure . Its base PBCR is silver plated from the front side at the rate of Rs 20 per cm . Find the total cost of the Silver plating 34) The numerator of a fraction is 3 less than the denominator . If 2 is added to both The numerator and denominator , then the sum of new fraction and original Fraction is 29. Find the original fraction 20 35) The median of the following data is 16 . Find the missing frequencies x and y If the total frequency is 70 Class interval Frequency 0 -5 5 10 12 X 10 -15 12 15 20 20 -25 25 -30 15 y 6 30 - 35 6 35 -40 4 36) If the ratio of the 11th term of an A.P to its 18th term is 2: 3 , find the ratio of the sum of first five terms to the sum of its first 10 terms .Also find the sum of first 24 terms of an A.P whose n th term is given by an = 3 + 2n OR If the sum of first 4 terms of an A.P is 40 and that of first 14 terms is 280 , find the sum of Its first n terms. Hence find the sum of first 20 terms of the A.P
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