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Class 10 CBSE 10th Board 2016 : Mathematics (J K Public School, )

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Anirudh Singh
J K Public School

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Y6I7ZNS II, (2015-2016) SUMMATIVE ASSESSMENT II MATHEMATICS / Class X / X 90 Maximum Marks : 90 (i) (ii) 31 6 1 3 / SECTION-A UN (iii) (iv) 4 All questions are compulsory. The question paper consists of 31questions divided into four sections A, B, C and D. Section-A comprises of 4 questions of 1 mark each, Section-B comprises of 6 questions of 2 marks each, Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11 questions of 4 marks each. There is no overall choice. Use of calculator is not permitted. IL (i) (ii) 4 10 TU T General Instructions : 2 11 (iii) (iv) OR IA L 3 Time allowed : 3 hours 1 4 1 Question numbers 1 to 4 carry one mark each. 2 A.P. : 11, 8, 5, 2, . 150 Is 150 a term of the A.P. :11, 8, 5, 2, . ? JS 1 9m 1 16 m The angle of elevations of a building from two points on the ground 9 m and 16 m away from the foot of the building are complementary. Find the height of the building. http://jsuniltutorial.weebly.com/mathematics.html Page 1 of 6 1 3 1 A die is thrown once. Find the probability of getting a number which has at least 2 factors. P 4 Q (3, 4) P 1 / SECTION-B OR IA 5 10 2 Question numbers 5 to 10 carry two marks each. L If the line segment joining the points P and Q (3, 4) is bisected at origin, find the coordinates of P. 5 2 8 6 TU T One day, I asked the son of my close friend about his age. The child replied in a different way : He said, One year ago, my dad was 8 times as old as me and now his age (in years) is equal to the square of my age . Represent the above situation in the form of a quadratic equation. AP m am2 bm If the sum of first m terms of an AP is am2 bm, find its common difference. O 7 P PA PB 2 PA 2.8 2 IL APB 60 AB If PA and PB are two tangents drawn to a circle with centre O, from an external point P such that PA 2.8 cm and APB 60 . Find the length of chord AB. 2 JS UN 8 DE'F' . DX 5 cm D3E' D5E DEF E'F' EF http://jsuniltutorial.weebly.com/mathematics.html Page 2 of 6 D1, D 2, D 3, . are points at equal distances on ray DX and D3E' D5E and E'F' EF. 6 cm 10 cm P Draw tangents to a circle of radius 6 cm from a point P at a distance of 10 cm from its centre. OR IA 9 L In the figure, DE F is equilateral having side 5 cm. What will be the side of DEF, where D1, D2, D3, 10 2 2 The diameter and height of a cylinder and a cone are equal. Find the volume of each also, find the ratio of their volume. TU T / SECTION-C 11 20 3 Question numbers 11 to 20 carry 3 marks each. 6x2 7x 10 0 11 3 3 AP 30 n 2 3n th Find the sum of the first 30 terms of an AP whose n term is 2 3n. 13 UN 12 IL Find the roots of the equation 6x2 7x 10 0 by the method of completing squares. P QR PR AQ BR AQ AB B JS A Q In the figure, QR is a tangent at Q to a circle, whose centre is P. PR AQ, where AQ is a chord through A, an end point of the diameter AB. Prove that BR is tangent at B. http://jsuniltutorial.weebly.com/mathematics.html Page 3 of 6 3 14 3 60 15 OR IA L 30 50 m The angle of elevation of the top of a hill from the foot of a tower is 60 and the angle of elevation of the top of the tower from the foot of the hill is 30 . If the tower is 50 m high, find the height of the hill. 3 3 Two fair dice are rolled simultaneously. What is the probability that the sum of the numbers obtained is a multiple of 3 ? 16 TU T (7, 9) 3 (10, 10) The coordinates of one end point of a diameter of a circle are (7, 9). If the coordinates of the centre are (10, 10), find the coordinates of the other end point of the diameter. 18 (x, y) (a b, a b) ( a b, a b) If the point (x, y) is equidistant from ( a b, a b), prove that x a 0. 30 the points x a 0 (a b, a b) 3 and 3 8 IL 17 19 UN Area of a sector of a circle with angle 30 is 8 square units. Find the area of the circle. Also, find the radius of this circle. 1628 cm2 37 cm 3 20 JS 22/7 The sum of the radius of the base and height of a solid cylinder is 37 cm. The total surface area of the solid cylinder is 1628 cm2. It is melted to form a sphere, find the volume of the sphere. (Take 22/7). 22176 m2 ` 50 The area of a circular playground is 22176 m2. Find the cost of fencing this ground at the rate of ` 50 per metre. http://jsuniltutorial.weebly.com/mathematics.html Page 4 of 6 3 / SECTION-D 21 31 4 Question numbers 21 to 31 carry 4 marks each. 21 x2 kx 64 0 k x2 8x k 0 4 Find the positive value of k for which x2 kx 64 0 and x2 8x k 0 will have real roots. a, b, c, d e A.P. a 4b 6c 4d e 0 If the numbers a, b, c, d and e are in an A.P. then prove that a 4b 6c 4d e 0 23 x 4 1 1 1 a b x a b 1 1 1 1 Solve for x : a b x a b x O 24 O' 3 cm 1 x OR IA L 22 4 cm P 4 Q 4 25 1 3 AB 6.2 cm, BC 5.4 cm TU T OP O'P, PQ Two circles with centres O and O' of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles. Find the length of the common chord PQ. 4 PQR ABC AC 4 cm IL Construct PQR ABC in which AB=6.2 cm, BC=5.4 cm and AC=4 cm, using scale factor 50 m 30 UN 26 1 . 3 4 60 27 JS There are two temples, one on each bank of a river, just opposite to each other. One temple is 50 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30 and 60 respectively. Find the width of the river and the height of the other temple. 1, 3 (A) 4 4 (B) (C) (D) 3 Three digit numbers are made using the digits 1, 3 and 4 (without repetition of digits). If a number among them is selected at random, what is the probability that the number will (A) be even ? (B) be odd ? http://jsuniltutorial.weebly.com/mathematics.html Page 5 of 6 (C) 28 end with zero ? (D) be a multiple of 3 ? (1, 7), (4, 2), ( 1, 1) ( 4, 4) Show that the points (1, 7), (4, 2), ( 1, 1) and ( 4, 4) are the vertices of a square. Also, find the area of this square. 12 29 4 2 cm 4 4 cm 14 cm L 50 OR IA ? A manufacturer involves twelve children in colouring pen stands all over excluding base which are in the shape of a cylinder made of wood of thickness 2 cm. The inner radius of the cylinder is 4 cm and its height is 14 cm. Find the area they had to paint if 50 pen stands were given to them for painting. What type of social problem is depicted in the question nad measure you will suggest to abolish it ? 21 m TU T 70 m 52 m 30 4 A horse is placed for grazing inside a rectangular field 70 m by 52 m and is tethered to one corner by a rope 21 m long. On how much area it cannot graze ? 2048 cm3 3 31 2 cm 3 IL 6 The volume of a solid iron sphere is 2048 cm3. This sphere is melted and eight rings of iron 3 2 cm and thickness 3 cm are made. Find the internal radius of each 3 -o0o0o0o- JS ring. UN plates of external radii 6 3 cm http://jsuniltutorial.weebly.com/mathematics.html Page 6 of 6 4

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