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SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE. Class Sub. Exam Date Marks Time Total No. of Printed sides 10 MATHS Prelims 25 01 2021 80 2 hrs 4 Instructions: Attempt all questions from Section A and any four complete 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. Omission of essential working will result in the loss of marks. SECTION A (40 marks) (Attempt all questions from this section) Question 1 A) When two polynomials 2x3 ax2 3x 7 and ax3 3x2 8x 19 are divided by (x 3), the remainder is same. Find the value of a. [3] B) If (m 3), (2m + 1) and (4m + 3) are three consecutive terms of an AP, find the value of m. [3] C) If A = [ 3 1 ] , then find A2 5A + 7I where I is an identity matrix of order 2 x 2. 1 2 [4] Question 2 A) A manufacturer sells a refrigerator to a wholesaler for Rs 30000. The wholesaler sells it to a retailer at a profit of Rs 2000. The retailer sells it to a customer and makes a profit of Rs. 3000. If GST charged is 18%, find: i. The GST deposited by the wholesaler with government. ii. The total amount of GST received by the government on sale of refrigerator. iii. The amount paid by the customer for it. [3] B) Solve the following inequation and represent the solution set on the number line : 2 x 5 5 x + 4 12, x I [3] C) In the given figure, O is the centre of the circle and AB is the diameter. DAB = 52 , find : i) DCB ii) ABD iii) DEB 1 [4] Question 3 A) Prove that : sin 1 cos + sin 1+cos = 2 cosec A [3] B) If the curved surface area of a right circular cylinder is 3850 cm2 and the circumference of the base is 220 cm, find : i. the height of the cylinder ii. the volume of the cylinder [3] C) Sonia deposited Rs 200 per month for 3 years in a recurring deposit scheme. If she received Rs 8088 at the time of maturity of the account, find the i) interest earned in 3 years ii) rate of interest per annum. [4] Question 4 A) Some identical cards are numbered from 2 to 25 and well shuffled. When a card is drawn randomly, what is the probability that the card has: i. a prime number ii. a multiple of 5 or 10 iii. a perfect square number [3] B) Solve the following equation and give your answer correct to 2 decimal places. x2 6 x 18 = 0 [3] C) The following distribution represent the height of the students of a school : Height ( in cm) 145 150 150 155 155 160 160 165 165 170 No. of students 34 42 25 6 13 Draw a histogram for above data using graph paper and hence find the mode. [ 4 ] SECTION B (40 marks) (Attempt any four complete questions from this section) Question 5 A) In what ratio is the line joining the points ( 4 , 3 ) and ( 10 , 4 ) divided by the x axis? Also find the co-ordinates of the point of intersection. [3] B) Prove that : 2 ( +1)2 = 1 sin 1+sin [3] C) The mean marks obtained by students in a test is 23, where p is missing frequency. Find p . [4] Marks 0 10 10 20 20 30 30 40 40 50 No. of students 4 16 p 6 4 2 Question 6 A) In the given circle with centre O, AOC = 160 , ACD = 40 and CT is tangent to the circle at C. Find: i. ADC ii. DCT B) In ABC, A ( 3 , 5 ), B ( 7 , 8 ) and C ( 1 , 10 ). Find the equation of the median through A. [3] [3] C) A man observes the angle of elevation of the top of the building to be 30 . He walks towards it in horizontal line through its base. On covering 60 m, the angle of elevation changes to 60 . Find the height of the building to the nearest metre. [4] Question 7 A) In ABC ; P and Q are points on sides AB and AC respectively such that PQ BC. If AP : PB = 2 : 3, AQ = x + 1 and QC = x + 5, find the value of x. [3] B) Find the co-ordinates of the centroid of a triangle whose vertices are A( 5 , 6 ), B( 2 , 3 ), C( 6 , 15 ). Also find equation of line passing through point B and parallel to x- axis. [3] C) Use graph paper for this question. Plot P (2 , 4 ), Q ( 2 , 1 ) and R ( 5 , 0 ). Reflect P and Q in x-axis to get P and Q . i. Write co-ordinates of P and Q ii. Write geometrical name to figure PQQ P R iii. Find area of the figure so formed. [4] Question 8 A) 24 is the mean proportional between two numbers x and y and 192 is the third proportional to x and y. Find x and y. [3] B) Find the sum of 1 + ( 3 ) + ( 7 ) + ( 11 ) + - - - - - - + ( 315 ) [3] C) In the adjoining figure, P and Q are points on AB and AC respectively such that PQ BC. Prove: i. APQ ~ ABC ii. If AP : PB = 4 : 3, find PQ if BC = 21 cm iii. Find area APQ : area ABC [4] 3 Question 9 A) A plane travels a distance of 1600 km at an average speed of x km/hr. On the return journey, due to bad weather, as the speed was reduced by 40 km/hr, it took 1 hour 20 minutes more than onward journey. Find x. [4] B) The weight of 200 workers is given below: Weight 50 60 60 70 70 80 80 90 ( in kg) No. of 20 34 30 48 workers 90 100 100 110 110 120 32 20 16 Use graph paper to draw an ogive for the above distribution. Take 2 cm = 10 kg on one axis and 2 cm = 20 workers along the other axis. Use the ogive to estimate: i. Median ii. Lower Quartile iii. If weighing 95 kg and above is considered overweight, find the number of workers who are overweight. [6] Question 10 A) Show that (x 2) is a factor of x3 + 10x2 37x + 26. Hence factorise the given expression completely. [3] B) The equation of the line AB is 3y x = 12. Find the slope of line AB. If AB meets x-axis at point P, find co-ordinates of P. [3] C) Using properties of proportion, solve for x: 2 +1 + 3 = 4 2 +1 3 [4] Question 11 A) If x = 2 is a root of the equation (k 3) x2 k x 8 = 0, find the value of k. Also, find the other root of the equation. [3] B) If 2 [ 3 5 1 4 7 ]+[ ]=[ 10 0 1 0 ] find the value of x and y . 5 [3] C) The volume of a conical tent is 1232m3 and the area of the floor is 154m2. Calculate: i. radius of the base ii. height of the tent iii. length of canvas required to cover the tent if the width of canvas is 2m. 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