Formatting page ...
SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE. Class 10 Subject Exam Date Mathematics Prelims 25 01 21 Marks Time Total No. of Printed sides 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 x3 - px2 + x + 6 and 2x3 - x2 - (p + 3) x - 6 are divided by (x - 3) , the remainder is same . Find the value of p. [3] B) Solve the inequation and represent the solution set on the number line 8 7 2(2 ) , [3] 1 C) Madhuri deposits Rs 800 every month for 22 years in a recurring deposit scheme. The interest earned is Rs 2790. Calculate the rate of interest and maturity value of the investment. [4] Question 2 A) Solve the quadratic equation and give your answer to correct 3 significant figures . 2 5 + 5 = 0 B) Prove the identity : C) If A =[ 2 2 2 4 6 ] , B = [ 4 3 5 [3] = 2 [3] 2] and PA = B , Find: i. The order of matrix P ii. The matrix P [4] Question 3 A) An AP consists of 60 terms . If the first and the last terms are 6 and 124 respectively , find the 27th term. [3] B) In the figure , AB is parallel to DC, BCE = 800 and BAC= 250 Find : i. CAD ii. CBD iii. ADC [3] C) The printed price of an air conditioner is Rs 40000.The wholesaler allows a discount of 10% on the marked price to the shopkeeper. The shopkeeper sells it to the customer at a discount of 5% on the marked price . If the rate of GST charged is 28% , find : i. GST paid by the shopkeeper to the government ii. The total amount paid by the customer inclusive of tax [4] Question 4 A) Odd numbered cards 1,3,5,7,9, , 27,29 were shuffled and put in a box . If a card is picked up from this box , what is the probability that the number on the card is i. a prime number ii. factor of 21 iii. multiple of 5 [3] B) Hot coffee from a cylindrical jug 15 cm deep and radius 16cm is poured into cylindrical glasses 4 cm in diameter and 8cm deep. How many such glasses can be filled ? [3] C) Draw a histogram to represent the following data and determine the mode. Pocket money (in Rs) 150-200 No.of students 2 200-250 9 250-300 10 300-350 6 350-400 2 [4] SECTION B (40 marks) (Attempt any four complete questions from this section) Question 5 A) The midpoint of the line segment joining P (2a ,6) and Q (8, b) is (3, 4a-1) . Find the values of a and b. [3] B) In the given figure , ABC = 900 and AB=5.7cm BD=3.8cm and CD=5.4cm. Prove: i. BDA ~ CDB ii. hence find BC [3] C) Plot the points P(6,3) and Q(3,0) on the graph paper. Reflect P in x axis to get P 1. write the co-ordinates of P1. O is the origin .Give the geometrical name of POP1Q. Find the area of the geometrical figure POP1Q . [4] Question 6 A) Prove the identity: 1 +1 = secA - tanA [3] B) Calculate the ratio in which the line joining A (-4,2) and B (3,6) is divided by the point P(x,3). Also find x. [3] C) Calculate the mean for the following distribution . Marks 0 10 No. of 3 students 10 20 8 20 30 12 30 40 14 [4] 40 50 10 50 60 6 60 70 5 Question 7 A) Find the equation of a line through (-6,7) and with the x -intercept of 5 units. 70 80 2 [3] B) In the circle with centre O , AT and BT are tangents . If ATB =700 , Find : i. AOB ii. APB iii. AQB [3] C) From the top of a tower 60m high the angles of depression of the top and bottom of a building are observed to be 300 and 600 respectively. Find the height of the building and the distance between them . [4] Question 8 A) Find the sum of all natural numbers less than 300 which are divisible by 5. B) If a,b,c and d are in proportion , prove that : + + = 2 + 2 2 + 2 C) In ABC, PQ II 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 trapezium PBCQ [3] [3] [4] Question 9 A) Some members of a club decided to go for a picnic and hired a bus for Rs 6000 . If 5 more members had joined , it would have cost each one Rs 40 less for the bus. How many members went for the picnic? [4] B) The weight of 60 workers is given below: Weight 50-60 60-70 70-80 80-90 90-100 100-110 110-120 (in kg) No. of 4 7 11 14 6 15 3 workers Draw an ogive for the given distribution using a graph sheet. Take 2cm = 10kg on one axis and 2cm = 10 workers along the other axis. Use the graph to estimate the following: i. the upper quartile ii. lower quartile iii. If weighing 95kg and above is considered as over-weight, find the number of workers who are over-weight. [6] Question 10 A) M and N are two points on the x axis and y axis respectively. P(3,2) divides the line segment MN in the ratio 2:3, Find : i. the co-ordinates of M and N ii. slope of line MN B) Using factor theorem, factorise the polynomial 2x3 + x2 -13x + 6 completely . C) If +5+ 16 +5 16 = 7 3 , Prove that x = 20 [3] [3] [4] Question 11 1 3 2 1 A) If A = [ ] = [ ] 2 5 = 5 . Find the matrix C ,where C is a 3 4 3 2 2 by 2 matrix. [3] B) Find the value of k for which the equation has equal roots: 2 + 4 + ( 2 + 2) = 0 [3] C) A conical tent is to accommodate 77 persons . Each Person must have 16m 3of air to breathe. Given the radius of the tent as 7 m , find the height of the tent and also its curved surface area . [4] ********************************
|
