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ICSE Prelims 2016 : Mathematics (Narbheram Hansraj English School (NHES), Jamshedpur)

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Narbheram Hansraj English School (NHES), Jamshedpur

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NARBHERAM HANSRAJ ENGLISH SCHOOL BISTUPUR, JAMSHEDPUR FIRST ASSESSMENT SECOND UNIT TEST 2015-16 MATHEMATICS STD. 10(ABCD) F.M.80 Time 2 Hrs SECTION A (Compulsory) QI. a) b) c) d) e) e) f) g) h) Daily wages No of workers i) Prove that ( Cosec A Sin A ) (Sec A - Cos A) Sec2A = TanA [3] 5 y y Simplify :- 10 1 = =3 =5 1 Y R 3 3 3 2 graph the solution set on the number line ? [3] ...2 0 ...0 1 Given A = B = [4] Calculate = 3, 1 = 2, 3 i) 3A -2 B ii) A2 BA The value of a flat worth Rs.50,00,00 is depreciating at the rate of 8% p.a in how many years will its value be reduced to Rs.389344 [3] Using Quadratic formula solve : [3] 1 2 4 = = x =1 x = 2 x = 4 A manufacturer sold a fridge to a wholesaler for Rs.14,000. The wholesaler sold it to a trader at a profit of Rs.2500. If the trader sold it to the customer at a profit of Rs.3000. Find [4] i) Total VAT collected by the State Govt. at the rate of 6%. ii) Amount paid by the customer for the fridge. A sum of money lent out at C.I at a certain rate per annum doubles itself in 5 years. Find in how many years will the money become eight times of itself at the same rate of interest p.a. [3] Water flows through a circular pipe of diameter 2cm at the rate of 6m/sec into a cylindrical tank of radius 60cm. By how much will the level of water rice in 30min ? [3] Calculate the mean daily wage of a worker from the following table. 40-45 2 45-50 3 50-55 7 55-60 12 [4] 60-65 6 Manish deposits Rs.2000 per month in a recurring deposit account for 1 years at 8% Per annum. Find the amount he will receive at the time of maturity. [3] j) Without using tables find the value of [3] Co sec2 67 0 = tan 2 230 tan 2 37 0 tan 2 53 = = Sec 2 200 = Cot 2 700 Sec 2 37 0 Sec 2 53 k) Mr. Mishra opened a saving s Bank Account at S.B.I on 1st April, 2007. The entries of one year as shown in his pass book are given below :[4] Date Particulars Withdrawals Deposits Balance (in Rs.) (in Rs.) (in Rs.) 1st April,2007 By cash 8,550.00 8,550.00 12th April,2007 To self 1,200.00 7,350 24th April,2007 By cash 4,550.00 11,900.00 8th July,2007 By cheque 1,500.00 13,400.00 th 10 Sept.,2007 By cheque 3,500.00 16,900.00 17th Sept.,2007 To cheque 2,500.00 14,400.00 th 11 Oct.,2007 By cash 800.00 15,200.00 6th Jan.,2007 To self 2,000.00 13,200.00 th 9 March,2007 By cheque 950.00 14,150.00 If the bank pays interest at the rate of 5% p.a., find the interest paid on 1st April, 2008. Give your answer correct to the nearest rupee. p.t.o. STD.10 ABCD : 2 : SECTION B (Attempt any four) Q2. a) A farmer wants to divide Rs.390300 between his two daughters who are 16 yrs and 18 yrs old respectively in such a way that the sum invested at the rate of 4% per annum. Compounded annually will give the same amount to each, when they attain the age of 21 yrs. How should he divide the sum. [3] b) Marks No of Stu. c) Draw a histogram from the following frequency distribution and find the mode from the graph. [4] 50-60 4 60-70 8 70-80 14 80-90 19 In the adjoining figure AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15cm find the distance MN between the two chords of the length 24cm and 18cm respectively [3] A B C Q3. a) b) c) 90-100 5 D Use graph paper for the question. The points P ?(1,2) , Q (3,4) and R (6,1) are the vertices of PQR. i) Write down the co-ordinates of P1, Q1 and R1, if P1, Q1 R1 is the image of PQR, when reflected in the origin. ii) Write down the co-ordinates of P , Q and R , if P Q R is the image of PQR, when reflected in the x axis. iii) Mention the special name of the quadrilateral QRR Q and find its area [3] ...2 1 7 Given X = write the order of the matrix X (ii) the matrix X. 6 = 3, 4 In the given figure, ABCD is a parallelogram and AP : PB = 3 : 5. Calculate i) area ( PBN) : area (trapezium APND) ii) PN : BC and area ( PMN) : area ( BMC) D C N M [3] [4] Q4. a) A P B With out using trigonometric labels, show that CosqSinq = [3] SinqCos (90 = q )Cosq CosqSin(90 = q ) Sinq = is equal to zero. Sec(900 = q ) Co sec(900 = q ) b) A shop keeper sells an article of the listed price of Rs.1500 and the rate of VAT is 12% at each stage of sale. If the shopkeeper pays a VAT of Rs.36 to the Govt, what was the amount of inclusive of tax at which the shopkeeper purchased the article from the wholesaler ? [3] c) Five years ago, a women s age was the square of her son s age. Ten years hence her age will be twice that of her sons age. Find i) the age of the son five years ago ii) the present age of the woman [4] Cont d .3 STD.10 ABCD Q5. a) : 3 : Given below are the entries in a Saving Bank A/c passbook. Date Particulars Feb. 8 Feb 18 April 12 June 15 July 8 B/F To self By cash To self By cash Withdrawals (in Rs.) 4000 5000 - Deposits (in Rs.) 2230 6000 [4] Balance (in Rs.) 8500 - Calculate the interest for six months from February to July at 6% p.a. Q6. b) The difference between the outer and the inner surfaces of a circular cylinder 14cm long is 88cm. Find the outer and the inner radii of the cylinder given that the volume of the metal is 176 cm3. [3] c) Prove that :- a) In the given figure, an equilateral ABC is inscribed in a circle of radius 4cm and centre at point O. Find the area of the shaded portion. [3] A CotA = Co sec A =1 1 = CosA = CotA = Co sec A = 1 SinA B b) Class Interval Frequency [3] C The mean of the following distribution is Rs.18 find the value of P. [4] 11 13 13 15 15 - 17 17 - 19 19 - 21 21 - 23 23 25 3 6 9 13 P 5 4 Q7. c) The model of a building is constructed with the scale factor 1:30. If the height of the model is 80cm (a). Find the actual height of the building in meters (b). If the actual volume of a tank at the top of the building is 27m3. Find the volume of the tank on the top of the model ? [3] a) AB and CD are two parallel chords of a circle of length 10cm and 4cm respectively. If the chords lie on the same side of the centre and the distance between them is 3cm find the diameter of the circle. [4] b) Rs.480 is divided equally among x children. If the number of children were 20 more then each would have got Rs.12 less find x. [3] c) Solve the following in equation and graph the solution on the number line. 4 x = 19 = 3x 2 =2 = = x x R 5 5 ****** [3]

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