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GOKULDHAM HIGH SCHOOL & JUNIOR COLLEGE SECOND PRELIMINARY EXAMINATION 2019-2020 STD: X DATE:13.01.2020 MAX. MARKS: 80 TIME: 2 hrs.30 min. ________________________________________________________________ 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 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 loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. SECTION A (40 Marks) Attempt all questions from this Section. Question 1 (a) Mr. Gupta has a recurring deposit account of Rs. 500 per month at 6.5% per annum. If he gets Rs.812.50 as interest at the time of maturity, find the total time for which the account was held. (b) Solve the following inequation and write the solution set: 4 4 5 2 ( + 1 ) < , x R 3 4 3 6 Represent the solution set on a real number line. (c ) The point Q ( 3, k ) divides the line segment joining the points P(9, 4 ) and R(-9 , 7 ). Find : (i) The ratio in which point Q divides the join of points P and R. (ii) The value of k . (iii) Slope of a line parallel to PR. This paper consists of 7 printed pages [3] [3] [4] STD X 2 _ MATHEMATICS Question 2 (a) A jar contains some marbles of blue , green or white colour. The green and white marbles together are 36 in number. The probability of selecting a blue marble is green marble is 4 9 1 3 and the probability of selecting a . How many marbles are there of each colour? [3] (b) Prove that 1 + ( tan )2 cosec A ( secA tan A) = 2 tan A [3] (c ) (i) Find the nature of roots of the following quadratic equation without solving it: (2x + 3 ) ( x - 2 ) + 2 = 0 (ii) Solve the above quadratic equation. Give answer correct to three significant figures. [4] Question 3 (a) If A =[ 3 1 4 2 6 2 ] , B = [ ] , C = [ ] and D = [ ] , find 5 4 1 2 AB + 2C 4 D. (b) The sum of the radius of the base and height of a solid cylinder is 37m. If the total surface area of the solid cylinder is 1628 m2, find (i) radius of its base. (ii) surface area of a sphere with the same radius.[ Use = 22/7] (c ) In the given figure, O is the centre of the circle. ADE is a straight line. E BDE = 140 and ABC = 80 . D Find: A 140 O (i) BDC (ii) BOC 80 (iii) BAC C B (iv) DBC [3] [3] [4] STD X 3 MATHEMATICS Question 4 (a) A shopkeeper buys an article whose printed price is Rs 5000 from a wholesaler at a discount of 10% and sells it to the consumer at the printed price. If the sales are intra-state and the rate of GST is 12 %, find (i) The amount of tax (under GST) paid by the shopkeeper to the State Government. (ii) The amount of tax (under GST) received by the Central Government. (iii) The amount which the consumer pays for the article inclusive of GST. [3] (b) In an arithmetic progression, the first term is 8, nth term is 33 and the sum of first n terms is 123. Find n and the common difference. [3] (c ) Use graph paper for this question. [Use scale: on x-axis 2 cm = Rs.10, on y-axis 2cm = 4students.] In a class, the weekly pocket money of students is as follows: Weekly pocket 40-50 50-60 60-70 70-80 80-90 90-100 money (Rs.) Number 2 8 10 14 8 6 of students (i) Draw a histogram and hence estimate the modal pocket money. (ii) State the modal class. [4] SECTION B (40 Marks) Attempt any four questions from this Section. Question 5 (a) If A =[ 1 1 0 ], find m such that A2 = 8A + mI. 7 [3] STD X (b) 4 MATHEMATICS In the given figure ,O is the centre and QR is the diameter of the circle .The tangent at P meets QR produced at S. Find: T (i) (ii) TPQ, if PQR = 28 , Length of PS , if QS = 16 cm and Q QR = 12 cm. P 28 O R (c ) Use graph paper for this question. [Use scale: on both axes 2 cm = 1 unit] Plot A (4,4) , B ( 4 , - 4), C (0, - 4 ) and D (0, 4 ) ,vertices of a rectangle. (i) Reflect A in y-axis to A' and reflect A' in x-axis to A''. Plot and write co-ordinates of A' and A''. (ii) Name a single transformation which reflects B to A'. (iii) State the geometric name of the figure AA'A''B. (iv) Write equation of any one diagonal of the figure AA'A''B. S [3] [4] Question 6 (a) Ashok invests some amount of money in Rs. 25 shares, selling at Rs. 36 to obtain an income of Rs. 720. If the dividend declared is 12% ,find ; (i) The number of shares bought by Ashok. (ii) The investment by Ashok. (iii) The percentage return on his investment to the nearest whole number. [3] (b) Prove that 2 tan 1 + cot 1 tan = 1+ cosec . sec [3] STD X 5 MATHEMATICS (c ) The fourth, seventh and the last term of a geometric progression are 54, 1458 and 4374 respectively. Find (i) The common ratio (ii) The first term (iii) n ,the number of terms in this GP. (iv) sum of all terms for this G.P. [4] Question 7 (a) Model of a ship is made to scale 1:200. (i) If the length of the model is 500cm, calculate the length of the ship in meters. (ii) The area of the deck of the ship is 2, 00, 000 sq.m. Find the area of the deck of the model of the ship. (iii) Volume of the model is 0.3 m3. Calculate the volume of [3] the ship. (b) The sum of four numbers in A.P. is 32. The ratio of product of the second and third term to the product of first and fourth term is 15:7. Find the numbers. [3] (c) Construct a right angle triangle ABC in which AB = 4.5 cm, [4] BC = 6 cm and ABC = 90 . Construct the incircle of this triangle. Measure and state the length of the in-radius. Question 8 (a) In the given figure, AB is parallel to DE and BC is parallel to EF. (i) (ii) (iii) AD CF Prove that = . DG FG Prove that DFG ~ ACG. Find area ( DFG) : area(trapezium ACFD), if AD : DG = 4 : 3. G D F [3] E C A B (b) The points A( 7, 3) and C ( 0 , - 4 ) are the two opposite vertices of a rhombus ABCD. Find the equation of the diagonal BD. [3] STD X 6 MATHEMATICS (c ) What number should be added to the polynomial 3 3 + 2 2 19x so that ( x + 3) is a factor of the resulting polynomial? [4] Factorize the resulting polynomial completely. Question 9 (a) Solve for x using properties of proportion: 4 +1 2 2 (b) = 41 9 [3] Calculate the mean(correct to two decimal places) of the following data using step-deviation method: Class Frequency interval 0-10 6 10-20 8 20-30 10 30-40 2 [3] 40-50 4 (c ) From the top of a light house AB, 100 m high, the angle of depression of two ships C and D on the opposite sides of it are 38 and 45 respectively. Find the distance between the two ships to the [4] nearest meter. Question 10 (a) Find the value of p if 5 3 + 2 x 3 and 3 3 4 2 3x+p [3] have the same remainder when divided by(x 2). (b) Construct ABC = 60 with AB = BC = 6.5 cm. (i)Locate by construction , the loci of a point P which is equidistant from A, B and C. (ii)Locate by construction the locus of points which are always at PB distance away from the point P. (iii)Construct a cyclic quadrilateral ABCD such that D is equidistant from AB and BC. [3] STD X 7 MATHEMATICS (c ) A cylindrical container of diameter 12cm and height 15 cm is filled with ice-cream. The whole ice-cream is to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times radius of its base, find the radius of the ice-cream cone. [4] Question 11 (a) A train covers a distance of 600km at a certain speed. Had the speed been 20 km/hr more , the time taken to cover the distance would have been reduced by 5 hours. Write down an equation taking original speed of train to be x km/hr and solve it to find x . [4] (b) Use graph paper for this question. [ Scale:2 cm = 100 marks on one axis and 2cm = 20 students on the other axis] The frequency distribution of scores obtained by 160 candidates in an entrance test is as follows: Scores Number of students 400- 500 20 500-600 10 600-700 14 700-800 22 800-900 30 900-1000 30 1000-1100 20 1100-1200 14 Draw an ogive and hence, estimate: (i) The median score. (ii) The interquartile range of scores. (iii) Number of students who qualified the test, if 780 is the qualifying score. ********************* [6]
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