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SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE(W) Class Subject Exam Date Marks Time X MATHS Prelims 30 01 21 80 2 hrs No. of printed sides 5 General Instructions: 1. Attempt all questions from section A 2. Attempt any 4 complete questions from section B 3. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer 4. Omission of essential working will result in loss of marks 5. Use Graph sheets and logarithmic tables wherever required. SECTION A (40 marks) (Attempt all questions from this section) Question 1 A) On dividing ( 3 + 8 2 4 + 10) by ( + 1), we get ( 3) as remainder. Find the value of . [3] B) Solve the following inequation , and represent the solution set on the number line. 1 2 2 3 2 5 1 , 6 [3] C) Mrs. Meera invests Rs.500 every month in a cumulative time deposit scheme for 3 years at an interest rate of 8% per annum. (i) Find the total interest that she will earn at the end of the period. (ii) Find the maturity value of the deposit. [4] Question 2 A) Solve the following equation and give your answer correct to three significant figures. 2 3 9 = 0 [3] 1 B) Prove that 1+ cot2 1+ = . [3] 4 1 ] and 2 = 6 , where I is an identity matrix of order 2 x 2 , Find the 1 2 value of m. [4] C) If A = [ Question 3 A) The 8 term of an AP is ( 6) and its 12th term is ( 14). Find its : (i) First term (ii) Common difference (iii) 16th term [3] B) The cost of washing machine for a wholesaler is Rs 10000. He sells it to a retailer for Rs 11000 and retailer sells it to a customer for Rs 12,200. If the rate of GST is 12%. Find: (i) the amount of GST deposited with the Government by Retailer (ii) Price paid by the customer for the washing machine inclusive of tax. [3] C) is a diameter of the given circle with centre O and . If = 65 , find: (i) (ii) (iii) [4] Question 4 A) Cards numbered 1,2, 3, , 35 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 24 iii. multiple of 7 [3] 2 B) Find the number of coins 1.2 cm in radius and 2 mm thick, to be melted to form a right circular cylinder of height 12 cm and diameter 6 cm. [3] C) Draw a histogram for the given data using graph paper and hence estimate the mode. Take 2cm= Rs.100 on one axis and 2cm= 2 students on the other axis. Pocket money(Rs.) No. of students [4] 200-300 300-400 400-500 500-600 600-700 700 -800 800-900 6 18 15 10 22 12 8 Section B (40 marks) (Attempt any four complete questions from this section) Question 5 2 A) Let X be a matrix such that 2AX = B where A = [ 0 (i)Write the order of matrix X (ii) Find X 3 ] 2 8 B=[ ] 8 [3] B) Find the set of values of k for which the equation ( 5) + = 0 has equal roots. [3] C) The volume of a right circular cone is 9856 3 d the area of the base is 616 2 .Find (i) Radius of the cone (ii) Height of the cone (iii) Slant height of the cone [4] Question 6 A) The age of a father is twice the square of the age of his son. Eight years hence, the age of father will be 4 years more than 3 times the age of the son. Find their present ages. Frame an equation in x and solve it. [4] B) Scores obtained by 120 shooters in a shooting competition are given below Scores 0-10 No. of 5 Shooters 10-20 10 20-30 18 30-40 23 40-50 26 50-60 19 60-70 11 70-80 8 Use a graph paper to draw an ogive for the given distribution taking 2 cm= 10 scores on one axis and 2cm = 20 shooters on the other axis. Use the ogive to estimate : (i) Median (ii) Lower Quartile (iii) the number of students who obtained more than 60 scores. [6] 3 Question 7 A) The first and last term of an Arithmetic Progression are 17 and 350 respectively. If the common difference is 9, Find the number of terms. Also find the sum of its terms. [3] B) If a, b, c are in continued proportion, Prove that : = (3 2 + 5 + 7 2 ): (3 2 + 5 + 7 2 ) [3] C) In , such that LP= 2 cm and PM=6 cm, MN= 20 cm (i) Find PQ (ii) Find [4] Question 8 A) Prove that tan sec +sec = 2 tan 2 2 1 [3] B) The line segment joining the points A (2, 3)and B(3,4) cuts the axis at P. Find the ratio in which P divides the line segment AB. Also find the coordinates of P. C) Calculate mean ( to the nearest rupees) for the following distribution Wages per day 50 60 70 80 90 100 (Rs) Number of 2 4 8 12 10 6 Workers [3] [4] 110 8 Question 9 A) The intercepts made by a straight line on the axes are -3 and 2 units respectively. Find (i) The gradient of the line (ii) The equation of the line [3] 4 B) The tangent PQ touches the given circle at A and is parallel to the chord BC. (i) If = 85 , (ii) If AB = 2.4 cm , Find AC [3] C) A pole of height 5 m is fixed on the top of a tower. The angle of elevation of the top of the pole as observed from a point A on the ground is 60 and the angle of depression of the point A from the top of the tower is 45 . Find the height of the tower. [4] Question 10 A ) The mid points of the line joining (2m,4) and ( 2, 2n ) is ( 1, 2m+1). Find the values of m and n. [3] B ) In the adjoining figure , are two triangles where BA and AF:AC=5:8 (i) Prove that ~ (ii) Find AD if CE=6 cm. [3] C) Use a graph paper for this question. Plot the points A (4,6) and B(1,3) on the graph paper. These two points are the vertices of a figure ABCD such that A(4,6) is reflected in y=3 and point C is obtained and B (1,3) is reflected along = 4 and point D is obtained . Write the coordinates of C and D and give a geometrical name of the figure and find its area. [4] Question 11 A) Let P (5,0) and Q (-2,2) and R (3,4) be the vertices of the . Find the equation of the median through P. Also find the coordinates of the centroid. [3] B) Use factor theorem to factorise the given polynomial completely 4 3 + 4 2 9 9 C) If = 8 + , find the value of +4 4 + +4 4 [3] [4] ***** 5
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