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TAMRALIPTA PUBLIC SCHOOL Pre Final Examination: 2023-24 Sub: Mathematics Class-X F.M-80 Time-2hr. 30min. ----------------------------------------------------------------------------------------------------(Students are allowed additional 15 minutes for only reading the paper, they must not start writing during this time.) Attempt all questions for Section A and any four questions from Section B. All working, including rough work, must be clearly shown, and must be done on the same sheet as the rest of the answer. ----------------------------------------------------------------------------------------------------SECTION A (Attempt all questions from this Section) Question1. [15x1=15] i) If a matrix has 8 elements then its order may be a) 2x6 b) 4x4 c) 2x4 d) None. ii) If f(x) = 2x25x-7 then the value of f(3) is a) 4 b)-4 c) 40 d) None. iii) Statement I GST is always calculated on the amount after deducting discount, if any, from it. Statement II Discount is never allowed on amount inclusive of GST. a) Statement I is correct b) Statement II is correct only e) Both statements are correct d) Both are false statement iv) For finding Discriminant of a quadratic Equation ax2+bx+c=0 which must be follow a) a 0 b) b 0 c) c 0 d) a, b, c=0 v) In an A.P, if a18-b14=32, then the common difference is a) 8 b) -8 c) -4 d) 4 vi) If x, 12, 8 and 32 are in proportion, then the value of x is a) 6 b) 4 c) 3 d) 2 vii) Which of the following cannot be probability of an event a) 0.7 b) 2/3 c) -1.5 d) 15% viii) The volumes of two spheres are in the ratio 64:27. The ratio of their surface area is a) 3:4 b) 4:3 c) 9:16 d) 16:9 ix) It is given that ABC ~ PQR with then is equals to a) 9 b) 3 c) 1/3 d) 1/9 x) In a right triangle ABC; right angled at B, BC=12cm and AB=5cm, the radius of the circle inscribed in the triangle is a) 1cm b) 2cm c) 3cm d) 4cm xi) In similarity if the scale factor K=1 then the transformation of the image than the object is a) larger b) smaller c) congruent d) can't determine. xii) In a rectangle, the angle between a diagonal and a side is 30 and the length of this diagonal is 8cm. The area of the rectangle is a) 16cm2 b) 16/ cm2 c) 16 cm2 d) 8 cm2 xiii) If a matrix A is of order 5x3 and matrix B is of order 2x5, then the order of matrix BA is a) 5x2 b) 2x3 c)5x5 d) 5x3 xiv) If Nisha invests 19200 on 50 shares at a premium of 20%, then the number of shares she buy is a) 640 b) 384 c) 320 d) 160 xv) Which of the following is not a measure of central tendency? a) Mean b) Mode c) Median d) Range Question2. [3x4=12] i) A solid is in the shape of a cone mounted on a hemisphere of same base radius. If the curved surface areas of the hemispherical part and the conical part are equal then find the ratio of the radius and the height of the conical part. ii) Mr. Richard has a recurring deposit account in a post office for 3 years at 7.5% p.a. simple interest. If he gets 8,325 as interest at the time of maturity, then find i) The monthly installment ii) The amount of maturity iii) If = , find the value of Question3. i) If x = , then prove that ii) Two circles with radius 25cm and 9cm touch each other externally. Find the length of the direct common tangent. iii) The marks obtained by 120 students in a Mathematics test are given below Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 No of 5 9 16 22 26 18 11 6 4 3 Students Draw an ogire for the given distribution on a graph sheet and find i) The median ii) The number of students who obtained more than 75% marks in the test iii) The number of students who did not pass to in the test if the pass percentage 40 [4+4+5] SECTION B (Attempt any four questions) Question4. i) Find the matrix X of order 2x2 which satisfies the equation [ ][ ]+2x=[ ] ii) Using formulae solve x- = 6 and give your answer correct two significant figure. iii) A model of high rise building is made to a scale 1:50. i) If the height of the model is 0.8m find the height of the actual building. ii) If the floor area of a flat in the building is 20m , find the floor area of that in the model. [3+3+4] Question5. i) Calculate the mean of the following distribution by using step deviation method: Marks 0-10 10-20 20-30 30-40 40-50 50-60 No of 10 9 25 30 16 10 Students ii) A, B and c are three traders belonging to three different States. Trader A Sells some goods to trader B for 500 and trader B sells the same goods to trader C at a profit of 200. If the rate of GST is 12%. Calculate the tax liability on trader B. iii) In the given figure, PQRS is a cyclic Quadrilateral, PQ and SR produced meet at T i) prove that TPS ~ TRQ ii) Find SP if TP=18cm, RQ=4cm, and TR = 6cm. iii) Find the area of Quadrilateral PQRS if area of PTS=27cm [3+3+4] Question6. i) The product of first three terms of a G.P is 1000. If 6 is added to its second term and 7 add to its third term, then the terms become in A.P. Find the G.P. ii) Find the mode of the following distribution by drawing a histogram: Mid 12 18 24 30 36 42 48 Value Frequency 20 12 8 24 16 8 12 Also state the modal class. iii) The surface area of a solid metallic sphere is 2464cm2. It is melted and recast into solid right circular cones of radius 3.5cm and height 7cm calculate: i) The radius of the sphere ii) The number of cones recast [3+3+4] Question7. i) A straight line passes through P (2,1) and cuts the axes in points A, B if BP: PA=3:1 find a) The co-ordinates of A and B b) The equation of the line AB. c) Also find the Equation of a line perpendicular to P. ii) The distance between two vertical poles is 60m. The height of one of the poles is double the height of the other. The angles of elevation of the tops of the poles from the middle point of the line segment joining their feet are complementary to each other. Find [5+5] the heights of the poles. Question8. i) Solve the in equation , x R also represent it on number line. ii) ABC is a triangle with BC=6.4cm, CA=5.8cm and <B=600 , construct an inscribed circle of the triangle so formed. iii) Using properties of proportion solve for x. Given [3+3+4] Question9. i) The height of a cone is 30cm. A small cone is cut off at the top by a plane parallel to its base. If its volume be 1/27 of the volume of the given cone at what height above the base is the section cut? ii) If the equation (1 + m2)x2+2mcx+(c2-a2)=0 has equal roots, prove that c2=a2(1+m2) iii) Determine the ratio in which the line 2x+y-4=0 divides the line segment joining the points A(2, -2) and B(3,7). [4+3+3] Question10. i) Use factor theorem to factories x -13x-12. ii) The probability of selecting a red ball at random from a jar that contains only red, blue and orange ball is 1/4. The probability of selecting a blue ball at random from the same jar is 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar. iii) The point P(3,4) is reflected to P' in the x-axis and O' is the image of O(origin) in the line PP'. Find i) The co-ordinates of P' and O' ii) The length of segments PP' and OO' iii) The perimeter of the quadrilateral POP'O' [3+3+4]
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