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DELHI PUBLIC SCHOOL NEWTOWN SESSION 2021 22 PRE BOARD EXAMINATION (SEMESTER 2) CLASS: X SUBJECT: MATHEMATICS FULL MARKS: 40 TIME: 1 HOURS Answers to this Paper must be written on a paper provided separately. You will not be allowed to write during the first 10 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions from Section A and any three questions from Section B. The intended marks for questions or parts of questions are given in brackets [ ]. This paper contains 5 printed pages. SECTION A (Attempt all questions from this section) Question1 Choose the correct answers to the questions from the given options. (Do not copy the question, Write the correct answer only.) [10] (i) Find the reflection of the point P (-2, 8) in the point M (4, -2) a) (15, 2) b) (10, -12) c) (5, 2) d) (-1, -2) (ii) In the given figure < = . BD is a diameter of the circle. The value of < is: A D B C E 1 a) 1480 b) 1080 c) 960 d) 540 (iii) The ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are 7.5 cm and 3.5 cm is: a) 21: 15 b) 22 : 15 c) 19 : 11 d) 19 : 9 (iv) The third vertex of a triangle, if two of its vertices are at (-3, 1) and (0, -2) and the centroid is at the origin is: a) (2, 1) b) (-3, 1) c) (1, 4) d) (3, 1) (v) If cos A + cos A = 1, then sin2 A + sin4 A = a) 6 b) -5 c) 1 d) -4 (vi) If 35 is removed from the data: 30, 34, 35, 36, 37, 38, 39,40, then the median increases by: a) 2 b) 1.5 c) 1 d) 0.5 (vii) The equation of the line passing through the point (-2, 3) and having x- intercept 4 units is: a) x + 2y +4 = 0 b) x + 2y - 4 = 0 c) x - 2y +4 = 0 d) x - 2y - 4 = 0 (viii) If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is: a) r3 b) r3 c) 3 r3 d) 9 r3 (ix) For the following distribution, CLASS 0-5 6 -11 12-17 18-23 24-29 FREQUENCY 13 10 15 8 11 The upper limit of the median class is: a) 17 b) 17.5 c) 18 d) 18.5 (x) Three coins are tossed simultaneously. The probability of getting at least two heads is: (a) 1 (b) (c) (d) 2 SECTION B (Attempt any three questions from this section) Question 2 (i) If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram taken in order, find the value of p. [2] (ii) Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is less than or equal to 10? [2] (iii) In the figure given, O is the centre of a circle. Also, PQ = QR = RS and < PTS = 750 Calculate: (a) < POS T (b) < QOR (c) < PQR S O P Q R [3] (iv) From a point P on the ground the angle of elevation of the top of a 10m tall building is 300. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 450. Find the length of the flag staff and the distance of the building from the point P to the nearest metre. [use = 1.732] [3] Question 3 (i) If AB and CD are two chords which when produced meet at P and if AP = CP, show that AB = CD. [2] (ii) The circumference of the base of a cylindrical vessel is 132cm and its height is 25cm. How many litres of water can it hold? [2] (iii) Prove the following identity: ( )( ) [3] = A 3 (iv) A survey regarding height (in cm) of 60 boys belonging to Class 10 of a school was conducted. The following data was recorded: Height (in cm) 135 -140 140-145 145-150 150-155 155-160 160-165 165-170 4 8 20 14 7 6 1 No. of boys Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = height of 10 cm along x-axis and 2 cm = 10 boys on y-axis). Use your ogive to estimate the median height. [3] Question 4 (i) If the lines mx + ny + 5 = 0 and 2x + 3y +6 = 0 are perpendicular to each other, find the relation between m and n. [2] (ii) If 7 is the mean of 5, 3, 0.5, 4.5, b, 8.5, 9.5 find the value of b. [2] (iii) A hollow cylindrical pipe is 21 dm long. If its outer and inner diameters are of 10 cm and 6 cm respectively, find the volume of the copper used in making the pipe. [Use = ] [3] (iv) Use graph paper for this question. The coordinates of a point A under reflection in origin is B (-2, 5), find the reflection of the point A under the line x = 4, name it C. Also find the reflection of C under X-axis and name it D. Join the points BACD and name the figure. [3] Question 5 (i) In the given figure angle ACB= 30 , Prove that AB is equal to the radius of the circumcircle of , whose centre is O. 4 [2] (ii) Prove that 2cos2 cos4 + sin4 = 1 [2] (iii)Find the equation of the line passing through (-3, 2) and parallel to the line 2x + 3y +4 = 0 [3] (iv) Draw a histogram to represent the following data and from the histogram find the mode. [3] Class interval Frequency 0 10 5 10 20 11 20 30 19 30 40 21 40 50 16 50 60 10 60 70 8 70 80 6 80 90 3 90 - 100 1 Question 6 (i) From a pack of 52 cards find the probability of (a) getting a red king (b) not getting an Ace. [2] (ii) Find the value of p, where given that the line = x p passes through the point ( 4, 4). [2] (iii) A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 and from the same point, the angle of elevation of the top of the pedestal is 45 . Find the height of the pedestal. Give the answer corrected up to 2 decimal places. [ = 1.732] [3] (iv) The daily expenditure of 100 families are given below. Calculate f 1 and f2 if the mean daily expenditure is 188. [3] Expenditure 140-160 (in ) Number of 5 families 160-180 180-200 200-220 220-240 25 f1 f2 5 5
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