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DONBOSCO SCHOOL, SILIGURI PRE-BOARD EXAMINATION 2020 21 CLASS: X SUBJECT- MATHEMATICS (SET B) TIME: 2 HRS F.M: 80 NOTE: DROP ANSERWERSHEET IN WHATSAPP LINK IN PDF FORMAT ONLY Answer to this paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is spent in reading the question paper. The time given at the head of this paper is the time allowed for writing the answer. SECTION-A Answer all the questions from this part___________ Question 1: a) Using componendo and dividendo, find the value of , given 3 +4+ 3 5 3 +4 3 5 =9 [3] b) Find the value of k if on dividing 4 3 2 2 + + 5 by 2 + 1, leaves a remainder -10 c) Find x and y if: 3 [ 6 5 6 ] [ 4 0 3 2 ] =3 [ ] 4 0 6 [3] [4] Question 2: a) Mr. deep deposits Rs 1600 per month in a cumulative deposit account for 18 months. If he gets Rs 31080 at the time of maturity, what is the rate of interest per annum? [3] b) Use graph paper for this question. (1,1), (5,1), (4,2) and (2,2) are the vertices of a quadrilateral. Name the quadrilateral ABCD. , , and are reflected in the origin onto , , and respectively. Locate , , and on the graph sheet and write their coordinates. Are , , and collinear? [3] c) A two digit number is such that the product of its digit is 12. When 36 is added to this number, the digits interchange their places. Find the number. [4] Question 3: a) Find the solution set of , which satisfy the inequation. 1 1 1 2 2 2 5 3 3 2, . Graph the solution set on the number line. [4] [ 3] 2 b) A cone of height 24 cm has a curved surface are 550 cm .Find its volume. (Take = 22 7 ) [3] c) Prove the identity: sin 1+ + 1+ = 2 [4] Question 4: a) In an auditorium, seats are arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by 10, then total number of seats increased by 300. Find: 1. The number of rows in the original arrangement. 2. The number of seats in the auditorium after re-arrangement. [3] th b) Find the 16 term of A.P. in 7, 11, 15, 19, ..Also find the sum of 6 terms. [3] c) Find the mean from the following distribution using short-cut method: [4] ( ) 40-50 2 . 50-60 8 60-70 12 70-80 14 80-90 8 90-100 6 SECTION-B Answer any 4 questions from this part Question 5: a) In the adjoining figure, PQ=RQ, = 72 , and are tangents to the circle with the centre P O. Calculate the values of: [3] C 1. 2. 0 R Q b) Find the equation of the line passing through the point (0, 2) and the point of intersection of the lines 4 + 3 = 1 and 3 3 9 = 0. [3] c) The distribution given below shows the marks obtained by 25 students in an aptitude test. Find the mean, median and mode of the distribution. [4] 6 7 8 9 10 5 9 6 4 2 1 . 3 Question 6: a) If + = + = + 1 , show that each ratio is equal to or 1 2 [3] b) A dealer in Calcutta buys some goods worth Rs 6000. If the rate of GST is 18percent,find how much will the dealer pay for the goods bought? [3] c) Solve for x: 2( + 2)2 = x + 4. [4] Question 7: a) = { : 11 5 > 7 + 3, }and = { : 18 9 15 12 , } Find the solution set of x and represent it on a number line. b) Solve for : 1 2 + 3 4 [3] 1 = 3 , 2,4. (3) 3 c) Two coins are tossed simultaneously. Find probability of getting 1. atleast one tail 2. Exactly two tails. [4] Question 8: a) The angles of elevation of the top of a tower from two points P and Q at distances of and respectively from the base and in the same straight line with it are complementary. Prove that the height of the tower is [3] b) Find the value of for which the lines 2 + 3 7 = 0 and 4 12 = 0 are perpendicular to each other. [3] c) A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10km/hr and as such it takes two hours longer to cover the total distance. Assuming the uniform speed to be km/hr, form an equation and solve it to evaluate . [4] Question 9: A a) In the below figure, and : = 5: 4, Find: 1. : 2. : 3. Area of :Area of E D O B C [4] b) The heights of 100 students are given below: ( ) 140-145 145-150 150-155 155-160 160-165 165-170 170-175 12 18 22 26 10 4 . 8 c) Draw an ogive of the given distribution using graph sheet. [6] Take 1cm= 10kg on one axis and 1cm= 5 workers along the other axis. Use a graph to estimate the followings: The median height and the number of students whose height is less than 148cm.
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