MAHESH TUTORIALS I.C.S.E.

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1 MAHESH TUTORIALS I.C.S.E. GRADE - X ( ) Exam No. : MT/ICSE/SEMI PRELIM - I - SET - B 005 Value Added Tax, Banking, Shares and Dividend, Matrices, Reflection, Section and Mid-Point Formula, Equation of a Line, Similarity, Loci, Cylinder, Cone and Sphere, Graphical Representation, Measures of Central Tendency, Probability MATHEMATICS (2 and half hours) Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first l5 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. Attempt all questions from Section A and any four 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. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. SECTION I (40 Marks) Attempt all questions from this Section. Question 1 (a) Mrs. Mathew opened a Recurring Deposit Account in a certain bank and deposited ` 640 per month for 4½ years. Find the maturity value of this account, if the bank pays interest at the rate of 12% per year. [3] Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is : (i) a multiple of 4 or 6. (ii) a multiple of 3 and 5. (iii) a multiple of 3 or 5. [3] ( 2, 4), (4, 8), (10, 7) and (11, 5) are the vertices of a quadrilateral. Show that the quadrilateral, obtained on joining the mid-points of its sides, is a parallelogram. [4] This Paper consists of 5 printed pages Copyright reserved.

2 Question 2 (a) A cylinder has a diameter of 20 cm. The area of curved surface is 100 cm 2. Find : (i) the height of the cylinder correct to one decimal place. (ii) the volume of the cylinder correct to one decimal place. [3] If A = 1 1 a b and A2 = I; find a and b. [3] An article is marked at ` 500. The wholesaler sells it to a retailer at 20% discount and charges sales tax on the remaining price at 12.5%. The retailer, in turn, sells the article to a customer at its marked price and charges sales tax at the same rate. Calculate : (i) the price paid by the customer. (ii) the amount of VAT paid by the retailer. [4] Question 3 (a) In what ratio does the point (1, a) divide the join of ( 1, 4) and (4, 1)? Also find the value of a. [3] The point P(a, b) is first reflected in origin and then reflected in the y-axis to P. If P has co-ordinates (4, 6); evaluate a and b. [3] Divide ` 50,760 into two parts such that if one part is invested in 8% ` 100 shares at 8% discount and the other in 9% ` 100 shares at 8% premium, the annual incomes from both the investments are equal. [4] Question 4 (a) The mean of the following distribution is 62.8 and the sum of all the frequencies is 50. Find the missing frequencies f 1 and f 2. Class : Frequency : 5 f 1 10 f [3] A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed. [3] The following figure shows a triangle PQR in which XY is parallel to QR. If PX : XQ = 1 : 3 and QR = 9 cm, find the length of XY. Further, if area of PXY = x cm 2 ; find the area of : (i) triangle PQR (ii) trapezium XQRY [4]

3 SECTION II (40 Marks) Attempt any four questions from this Section. Question 5 (a) The line passing through ( 4, 2) and (2, 3) is perpendicular to the line passing through (a, 5) and (2, 1) find a. [3] Rajat buys ` 80 shares at 30% premium in a company paying 18% dividend. Find : (i) (ii) the market value of 150 shares. Rajat s annual income from these shares. (iii) Rajat s percentage return from the investment. [3] Construct a triangle ABC, with AB = 7 cm, BC = 8 cm P and ABC = 60º. Locate by construction the point P such that : X Y (i) P is equidistant from B and C. (ii) P is equidistant from AB and BC. (iii) Measure and record the length of PB. Q R [4] Question 6 A (a) In the given figure, AB and DE are perpendiculars to BC. If AB = 9 cm, DE = 3 cm, AC = 24 cm. Calculate : AD 9 cm? 24 cm D 3 cm [3] B C E A(5, x), B( 4, 3) and C(y, 2) are the vertices of the triangle ABC whose centroid is the origin. Calculate the values of x and y. [3] Given : 1 4. X =. Write down : 10 (i) the order of matrix X. (ii) the matrix X. [4] Question 7 (a) Four identical circles are drawn inside a square paper of side 14 cm. This paper is kept horizonal on a table top and a very small die is dropped on the paper. If the die falls on the paper, find the probability that it will fall and land on the shaded region. Leave your answer as a fraction. [3]

4 The internal and external diameters of a hollow hemispherical vessel are 21 cm and 28 cm respectively. Find : volume of material of the vessel. [3] The maturity value of a R.D. Account is ` 16,176. If the monthly instalment is ` 400 and the rate of interest is 8%; find the time (period) of this R.D. Account. [4] Question 8 (a) Let A = , B = 1 0 Find A2 + AB + B 2. [3] A man invests ` 3,072 in a company paying 5% per annum, when its ` 10 share can be bought for `16 each. Find : i) his annual income; ii) his percentage income on his investment. [3] P(4, 2) and Q( 1, 5) are the vertices of parallelogram PQRS and ( 3, 2) are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of R and S. [4] Question 9 (a) A triangle LMN has been reduced by scale factor 0.8 to the triangle L M N. Calculate: (i) the length of M N, if MN = 8 cm. (ii) the length of LM, if L M = 5.4 cm. [3] David opened a Recurring Deposit Account in a bank and deposited ` 300 per month for two years. If he received ` 7,725 at the time of maturity, find the rate of interest per annum. [3] Find the mode of the following frequency distribution : Class Frequency [4] Question 10 (a) Find the equation of a line passing through the point (2, 3) and having the x-intercept of 4 units. [3] A shopkeeper buys 15 identical articles for ` 840 and pays sales-tax at the rate of 8%. He sells 6 of these articles at ` 65 each and charges sales-tax at the same rate. Calculate the VAT paid by the shopkeeper against the sale of these six articles. [3]

5 From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm 24 cm is drilled out. Find the surface 42 cm area of remaining solid. [4] 20 cm 7 cm 30 cm Question 11 (a) (a) The point P ( 4, 3) is reflected about the line x = 0 to get the image Q. Find the co-ordinates of Q. The point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R. Name the figure PQR. (d) Find the area of figure PQR. [4] The following distribution represents the height of 160 students of a school. Height (in cm) No. of students Height (in cm) No. of students Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, determine : (i) the median height (ii) the interquartile range (iii) the number of students whose height is above 172 cm. [6] All the Best

MATHEMATICS. (Two hours and a half) Answers to this Paper must be written on the paper provided separately.

MATHEMATICS. (Two hours and a half) Answers to this Paper must be written on the paper provided separately. MATHEMATICS (Two hours and a half) 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