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Math Test 7 Close Subjective Test (i) The question paper contains two sections, section A and section B. (ii) Each question carries 10 marks Section A (i) Section A carries 40 marks. (ii) This section contains four questions. All the questions are compulsory. Question 1(a) ( 3.0 marks) Mrs. Singh has an account in a certain cooperative bank. The following table shows the entries on her passbook. Date Particulars Withdrawal (in Rs) Deposit (in Rs) Balance (in Rs) Jan, 1 09 B/F - - 5600 Jan, 20 To cheque 1500 - 4100 Feb, 14 To cash 1000 - 3100 March, 6 By cheque - 3500 6600 March, 19 To cheque 5400 - 1200 April, 05 By cheque - 2300 3500 April, 10 By cash - 1000 4500 April, 28 To cheque 2000 - 2500 April 30 By cheque - 500 3000 May 14 By cash - 1200 4200 June, 20 To cheque 2800 - 1400 Mrs. Singh earns Rs 63.75 as interest at the end of June 09, where the interest is compounded annually. Find the rate of interest paid by the bank in her savings bank account. Question 1(b) ( 3.0 marks) In a culture, the initial count of bacteria was 90000. It is observed that the count of bacteria is increasing at a constant rate. If the count of bacteria after 3 hours is 119790, then at what rate is the unit of bacteria increasing? Question 1(c) ( 4.0 marks) Question 2(a) ( 4.0 marks) Two lines 2x + 5y + 3 = 0 and x 4y + 14 = 0 are intersected by a third line at the points ( a, b) and (a, 2a) respectively. What is the equation of third line? Question 2(b) ( 3.0 marks) In the given figure, RQ and PS are perpendicular to the line PQ. The lengths of the sides PO and OQ are 15 cm and 5 cm respectively. If the area of ROQ is 7.5 cm2, then find the area of POS. Question 2(c) ( 3.0 marks) (i) If , then find the values of a and b. Question 3(a) ( 3.0 marks) The hypotenuse and one side of a right-angled triangle are 25 cm and 7 cm respectively. A circle is inscribed in it. Find the area of the remaining portion of the triangle. [Use = 3.14] Question 3(b) ( 3.0 marks) PQ and RS are two parallel chords of a circle such that PQ = 30 cm and RS = 16 cm. If the chords are on the opposite sides of the centre and the distance between them is 23 cm, then find the radius of the circle. Question 3(c) ( 4.0 marks) The radius and height of a cone are reduced by 20%. Find the percentage reduced by or increased by in surface area. Question 4(a) ( 3.0 marks) If sin A + cos A = p and sec A + cosec A = q, then prove that q (p2 1) = 2p Question 4(b) ( 3.0 marks) (i) Prove that: (ii) If mean, median, and mode of the given data are 11x + 5, 12x 6, and 9x + 22, then find the value of x. Question 4(c) ( 4.0 marks) (i) Find the value of: (ii) When a die is thrown, what is the probability of getting: (I) An odd number (II) A number which is a multiple of 3 Section B (i) Section B also carries 40 marks. (ii) This section contains seven questions. Answer any four questions. Question 5(a) ( 3.0 marks) Daman took a loan of Rs 27000 for years from a bank. The bank charged him an interest at the rate of 8% per annum compounded half yearly. Find the amount which Daman will have to repay. Question 5(b) ( 4.0 marks) A shopkeeper marks an article 20% above its cost price. He sells the article at Rs 6804 after a discount of 10% and sales tax of 5%. How much did the article cost the shopkeeper? Question 5(c) ( 3.0 marks) Ms. Amina has a recurring deposit account in a certain nationalised bank. She deposits a certain fixed amount of money per month for 4 years at the rate of 10% per annum. If she gets Rs 46240 on maturity, then find the monthly instalment. Question 6(a) ( 3.0 marks) Using the long division method, determine the remainder when the polynomial 4x5 + 2x4 x3 + 4x2 7 is divided by (x 1). Question 6(b) ( 4.0 marks) (i) A ray of light is sent along the line x + y = 3. The x-axis acts as a mirror and the ray is reflected. What is the equation of the reflected ray? (ii) What is the solution set of the system of linear inequalities, 3x + 5 < x 9 and 2x 1 (x + 34)? Question 6(c) ( 3.0 marks) In a class of 90 students, if 26% of boys and 35% of girls got first class, then the total number of first class students is less than 30% of total students. If 25% of boys and 50% of girls got first class, then more than of the total students got first class. What will be the number of girls in the class? Question 7(a) ( 3.0 marks) In the given figure, a circle is shown which touches the sides of the quadrilateral WXYZ. If the lengths of the opposite sides WX and YZ are 15 cm and 18 cm respectively, then find the perimeter of the quadrilateral WXYZ. Question 7(b) ( 4.0 marks) Suppose that a circle is given to you without its centre and a point P outside it is given to you as shown in the following figure. How will you construct the tangents to this circle? Question 7(c) ( 3.0 marks) Identify the line(s) of symmetry in the following figures. Justify your answer with reason. (i) (ii) (iii) Question 8(a) ( 3.0 marks) In the following figure, PT is a tangent and OPT = 30 . What is the area of OTP, if perimeter of OPT is cm. Question 8(b) ( 3.0 marks) Two rectangular cardboards of dimension 44 cm 22 cm are folded to form a cylinder. The first one is folded along the length and second one is folded along the breadth. Compare their (i) Lateral surface areas (ii) Volumes Question 8(c) ( 4.0 marks) A toy is in the shape as shown in the figure. The bottom of the toy has a hemispherical raised portion. The height of the entire toy is cm whereas the height of the conical shape is 6 cm. The bases of the hemisphere, cone, and cylinder are identical. Find the volume of the entire toy and its surface area, if the radius of base of hemisphere is 2.5 cm. Question 9(a) ( 3.0 marks) The angles of elevation of the top of a tower from two points, distant a and b from its base in the same straight line, are complementary. Show that the height of the tower is . Question 9(b) ( 3.0 marks) There are two malls of equal heights on a straight road exactly opposite to each other. The width of the road is 100 m. From a point somewhere lying in between them on the road, the angles of elevation of the top of the malls are 45 and 30 respectively. Find the heights of the malls and the distances of the point from these malls. Question 9(c) ( 4.0 marks) At the foot of a mountain, the elevation of its peak is 45 . After ascending 2 km towards the peak at an inclination of 30 , the elevation becomes 60 . Find the height of the mountain. Question 10(a) ( 4.0 marks) The following table represents the average daily earnings of 50 general stores in a market during a certain week. Find the mean daily earning of these stores by using step deviation method. Daily earning (in rupees) 1000 1500 1500 2000 2000 2500 2500 3000 3000 3500 Number of stores 20 10 9 6 5 Question 10(b) ( 6.0 marks) The following distribution gives the height of 100 students of a class. Height of students (in cm) 120 130 130 140 140 150 150 160 160 170 170 180 Number of students 5 15 25 30 20 5 Convert above frequency distribution into more than type distribution and find the median height of the students by drawing an ogive. Question 11(a) ( 3.0 marks) The line is perpendicular to the line joining the points (5, 9) and (17, 4). If k is an integer, then what is the value of k? Question 11(b) ( 3.0 marks) Mohit goes to school daily from Monday to Friday. He also attends school on odd Saturdays. If we select a day randomly out of two continuous weeks, what is the probability that he goes to school on that day? Question 11(c) ( 4.0 marks) State whether the following statements are correct or incorrect. Justify your answers. (i) When a die is rolled, it is equally likely that a multiple of 3 or a number greater than 4 will be obtained. (ii) When a ball is drawn at random from a bag containing 4 yellow and 3 black balls, it is equally likely that a yellow or a black ball will be drawn. (iii) When a coin is tossed, it is not equally likely that a head or a tail will occur.

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