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Name : ___________________________________ Grade : X Div : Roll No : Subject : Mathematics Date : 04/01/2021 Duration : 2 Hrs 30 Min Maximum Marks: 80 No of sides : 5 First Preliminary Examination Answers 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 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. ______________________________________________________________________________ Section A is compulsory. Attempt any four questions from section B. The intended marks for questions or parts of question are in brackets [ ].Mathematical tables will be provided. ______________________________________________________________________________ Section A (All questions are compulsory) Question 1 a Find the mean for the following: x f 10 2 [3] 11 7 12 9 13 6 14 1 b When divided by (x-3), the polynomials x3 px2 + x + 6 and 2x3 x2 (p+3) x 6 leave the same remainder. Find the value of p. [3] c In the given figure, AT is a tangent. ABC = 112 , BAT =38 . Find . ADC and CAB. [4] D C B T A 1 Question 2 a b Zara deposited Rs 400 per month for 3 years in a bank s recurring deposit account. If the bank pays interest at the rate of 11% p.a. , find the amount she gets on maturity. [3] A building has 8 cylindrical pillars of radius 0.5 m and height 6.3m. If these pillars are to be painted at the rate of Rs 15 per m2, what will be the cost of painting all [3] of them? ( = c Question 3 a b c Question 4 a 22 7 ) If x R, solve the following inequation and represent it on the number line: 3x 3 27 2x 3x + 7 [4] Write the 17th term of the AP , whose first 2 terms are -2 and 3. [3] + 1 Prove that : = +1 1+ [3] A manufacturer sells a wet grinder to a wholesaler for Rs 2500. The wholesaler sells it to a retailer at a profit of Rs 500 and the retailer sells it to a customer at a profit of Rs 800. If the rate of GST charged is 12% and all sales are intra-state, find (i) the amount of GST received from the wholesaler by the State Government. (ii) the amount of GST received from the retailer by the Central Government. (iii) the price paid by the customer for the wet grinder. [4] Find the median of the following: [3] x f 34 5 32 11 35 2 31 8 33 12 b Given a line segment AB joining the points A(-4,6) and B(8,-3). Find : (i) the ratio in which AB is divided by y-axis, (ii) the co-ordinates of the point of intersection. c Given [ (i) (ii) 2 3 1 7 ]X=[ ]. 6 4 Write the order of matrix X. Find the matrix X. 2 30 3 [3] [4] Section B (Attempt any 4 out of 7) Question5 a Find the equation of a line passing through the point (-2,3) and having the x-intercept of 4 units. [3] b A bag contains 6 green, 7 red and 3 white balls. A ball is chosen without looking into the bag. Find the probability that the ball is (i) red (ii) not white (iii) white or green. [3] c From the top of a church spire which is 96m high, the angles of depression of two cars on the road on the same side of the church are x and y where tan x = [4] 3 4 1 and tan y = . Find the distance between the cars. 3 Question 6 a Find two consecutive positive even numbers, the sum of whose squares is 452. [3] b In the given circle, O is the centre, PQR = 49 and QRS = 21 . Find OPS. [3] P Q S R c (i) (ii) (iii) (iv) Plot the points A(4,6) and B(1,3) on the graph paper. These two points are the vertices of figure ABCD which is symmetrical about lines x = 4 and y = 3. Complete the figure on the graph. Write down the co-ordinates of C and D. Give a geometrical name for the figure. Find its area 3 [4] Question 7 a b 5 11 ] 9 5] If X + Y= [ and X Y = [ , find the matrices X and Y 10 4 2 14 [3] In the given figure, PQR = 85 and QRP = 60 . Find SQR + SRQ. [3] P Q S R c Question 8 a If 3 +1 + +1 = 4, use properties of proportion and solve for x. 3 +1 +1 [4] A cylindrical jug of radius 8cm and height 10cm is filled with orange juice. It is then poured into small conical cups of radius 2cm and height 6cm. Find the number of cups that can be filled. [3] b 10 years ago , Amina s age was square of her sister s age. Eleven years hence, she will be 6 years older than her sister, Find their present ages. [3] c Solve and give your answer correct to 3 significant figures 5x ( x + 2 ) = 3 [4] Find the image of the following points as directed. (without using graph paper) (i) Point A(4,5) reflected in the line x = 6. (ii) Point B(-3,2) reflected in the line x = -5. (iii) Point C(3,6) reflected in the line y = -2. [3] b Prove that (2x 1) is a factor of 2x3 + x2 13x + 6 and hence factorise the given polynomial. [3] c Draw a histogram for the following data and estimate the mode. Marks 10-19 20-29 30-39 40-49 50-59 No. of 6 9 16 13 4 students [4] Question 9 a 4 Question 10 a Eric deposits Rs 500 every month in a recurring deposit scheme and receives Rs 1 16,550 at the end of 2 years. Calculate the rate of interest given by the bank. 2 [3] b Solve 3x 2 = 3 + 10 . [3] c In ABC, PQ BC. If AP: PB =2:3, find (i) the length of PQ if BC = 7.5cm. (ii) the area of APQ : area of ABC. (iii) the area of APQ : area of PBCQ. [4] A P Q B Question 11 a b C Solve the following inequation. Represent the solution set on the number line. 2 1 -2 - 1 , x N. 3 2 6 [4] The following table shows a record from a hospital of 84 number of casualties due to accidents of different age groups. Age(in 5-15 15-25 25-35 35-45 45-55 55-65 65-75 years) No. of 6 10 15 13 25 8 7 casualties Taking a scale of 2cm = 10 years on one axis and 2cm = 10 casualties on the other. Draw an ogive and estimate : (i) the median. (ii) the lower quartile. (iii) the upper quartile. (iv) the number of casualties above age 57 years. [6] 5
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