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http://www.icseguess.com/ Sample Paper Class X Subject Mathematics Question 1 SECTION A (a) If both ( x 2 ) and (x ) are factors of px2 + 5x + r , show that p = r.[3] (b) E and F are the points in the sides DC and AB respectively of the parralelogram ABCD. If the diagonal AC and segment EF intersect at G; Prove that AG . EG = FG . CG. [3] (c) The population of a town increases by 5% every year. What was the population in 2002,if in 2005 it was 1,85,000? [4] Question 2 (a) The point (x,y) is first reflected in the x axis and then reflected in the origin to P . If P has co-ordinate (-8,5);evaluate x and y . [3] (b) Two parallel tangents of a circle meet a third tangent at point P and Q.Prove that PQ subtends a right angle at a centre. [3] (c) Calculate the area and the perimeter of the remaining, after four quadrants each of radius 4 cm are cut from the four corners of a rectangle measures 18 cm by 10 cm. [4] Question 3 2 3 8 x = (a) Solve for x ad y , if 8 9 4 y [3] www.icseguess.com Other Educational Portals www.cbseguess.com | www.ignouguess.com | www.aipmtguess.com | www.aieee.com | www.niosguess.com | www.iitguess.com http://www.icseguess.com/ (b) Construct an isosceles right angled triangle having hypotenuse = 6.0 cm.Draw its lines of symmetry. [3] (c) Solve and graph ; 2x 3 < x + 2 3 x + 5 ; x R. [4] Question 4 (a) Without using trigonometric table show that Sin 42 sec 48 + cos 42 cosec 48 = 2 [3] (b) Mrs Mathew opened a Recurring Deposit Account in a certain bank and deposited Rs. 640 per month for four and half years. Find the maturity value of this account, if the bank pays interest at the rate of 12%per annum. [3] (c) The total number of observations in the following distributions table is 120 and their mean is 50. find the values of missing frequencies of f 1 and f2 [4] Class interval Frequency 0 - 20 17 20 40 f1 40 60 32 60 80 f2 80 - 100 19 SECTION B Question 5 (a) A hotel bill for a number of people for overnight stay is Rs. 4800 ; if there were 4 people more , the bill each person had to pay would have reduced by Rs. 200 . Find the number of people staying overnight. [3] (b) Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. www.icseguess.com Other Educational Portals www.cbseguess.com | www.ignouguess.com | www.aipmtguess.com | www.aieee.com | www.niosguess.com | www.iitguess.com http://www.icseguess.com/ Find how many marbles have been dropped in it if the water rises by 5.6 cm. [4] (c) Which is better investment : 12% at 120 or 8% at 90? (3) Question 6 (a) Through the mid point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting Diagonal AC in L and AD produced in E Prove that : EL = 2 BL [3] (b) The probability that two boys do not have the same birthday is 0.897. what is the probability that the two boys have the same birthday. [3] (c) Solve for x ; x4 10x2 + 9 = 0 [4] Question 7 (a) Two numbers are in the ratio 2:3. If 5 is added to each number, the ratio becomes 5 : 7. Find the numbers. [3] (b) Draw a circle of radius 4 cm. Draw two tangents to this circle so that the angle between the tangents is 60 . [3] (c) A man holds a saving Bank account in the state bank of India. A page of his pass book shows the following entries: Date May 1 May 6 May 11 June 4 June 9 Aug 12 Particular Balance B/F By Cheque By Cheque By cash To cheque By cheque Withdrawal Deposit 500 800 1300 1650 1350 Balance 3200 3700 4500 5800 4150 5500 Calculate the total interest earned by the man for the months of may to aug at the rate 6% per annum. [4] www.icseguess.com Other Educational Portals www.cbseguess.com | www.ignouguess.com | www.aipmtguess.com | www.aieee.com | www.niosguess.com | www.iitguess.com http://www.icseguess.com/ Question 8 (a) If tan + sin = m and tan - sin = n ; Show that m2 n2 = 4 mn . [3] (b) Two chords AB and CD of a circle intersect each other at P. Prove that sum of angle subtended by the arcs AC and BD at the center O is equal to twice the angle APC. [4] (c) If three vertices of a parallelogram are (a + b , a b) , (2a + b , 2a b) and (a b , a + b) . Find the fourth vertex. [3] Question 9 [3] (a) If y = 2x + 3 and 2y = px + 3 are parallel; find the value of p. (b) Find the equation of the line that is parallel to 2x + 5y 7 = 0 and passes through the mid point of the line segment joining the points (2,7) and (-4,1).[4] (c) Two dice are thrown at the same time. Find the probability that the sum of the two number appearing on the top of the dice is (i) 8 (ii) 13 (iii) less than or equal to 12. [3] Question 10 (a) Draw the histogram of the following frequency distribution and hence find the mode. [5] Marks No of students 10 8 20 22 30 28 40 20 50 5 (b) A shopkeeper sells an article to a consumer at the list price of Rs 2200. The rate of sales tax is 6%. The shopkeeper deposits a VAT of Rs 24 to the government. If the shopkeeper purchases the article from the wholesaler, then find the tax paid by the shopkeeper to the wholesaler . [5] www.icseguess.com Other Educational Portals www.cbseguess.com | www.ignouguess.com | www.aipmtguess.com | www.aieee.com | www.niosguess.com | www.iitguess.com http://www.icseguess.com/ Question 11 a. The angle of the elevation of the top of the tower from two points on the ground at at distances a and b from the base of the tower and the same straight line with it are complementary. Prove that the height of the tower is ab metre. [5] b. A vessel is in the form of inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to rim. When lead shots each of which is a sphere of radius 0.5 cm are dropped into the vessel, one- fourth of the water flows out. Find the number of lead [5] shots dropped in the vessel. Paper Submitted By: Name: NITIN SHARMA Email: nsnitins1@gmail.com Phone No. 9415073329 www.icseguess.com Other Educational Portals www.cbseguess.com | www.ignouguess.com | www.aipmtguess.com | www.aieee.com | www.niosguess.com | www.iitguess.com
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