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1st Pre-Board Examination 2020-21 GRADE 10 SUBJECT: - MATHEMATICS Date : 27-11-2020 Time : Two and half hours Reading Time : 09:00-09:15 am Maximum Marks : 80 Writing Time : 09:15-11:45 am Uploading Time : 11:45-12:15 pm 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. You will be allowed to scan and upload during the last 30 minutes. _______________________________________________________________________________ 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. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical table can be used from textbook. ----------------------------------------------------------------------------------------------------------------------------- ----------- SECTION A (40 Marks) (Attempt All Questions) Question 1 a) Find the value of 'k' for which x = 4 is a solution of the quadratic equation, (k +2)x2 (5k + 2)x - 4 = 0. Hence, find the other root of the equation. [3] b) Solve the following inequation and represent the solution set on the number line. 5 -36< 1 6 4 3 5 2 6 , x R. [3] c) Find the amount of bill for the intra-state transaction if the rate of GST = 12%. Quantity (No. of items) MRP of each item (Rs.) Discount % 20 225 40 30 350 30 15 300 20 30 250 40 [4] Question 2 a) Mr. Matthew gets Rs. 83,100 at the end of 3 years at the rate of 10 % per annum in a Recurring Deposit Account. Find his monthly instalment. [3] b) Find the values of x, y and z if : [ 3 2 3 6 ].[ ] =[ 0 8 12 c) In the figure given, O is the centre of the circle. DAE =70 . Find giving suitable reasons, i) BCD , ii) BOD , iii) OBD. 15 ] 30 [3] [4] Question 3 a) Use properties of proportion to solve for x : + 5 + 16 + 5 16 7 =3. [3] b) Using Remainder Theorem, factorise : 3x3 + 2x2 - 23x - 30 completely. [3] c) The median of the observations 11, 12, 14, (x 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of x and hence find the mean. [4] Question 4 a) Find sum of all natural numbers which are multiples of 8 between 250 and 1000. [3] b) Point P divides the joining of line segment A(2, 5) and B(7, 15) in the ratio 2 : 3. i) Find the coordinates of point P. ii) Find the equation of a line with gradient 5 3 and passing through P. c) The following table gives the daily wages of workers in a factory: Wages (in Rs.) 45-50 50-55 55-60 60-65 65-70 No. of workers 5 8 Calculate their mean by short cut method. 30 25 14 [3] [4] 70-75 75-80 12 6 SECTION B (40 Marks) (Attempt Any 4 Questions) Question 5 a) Prove that : 1 + cos 1 2 = ( 1)2 [3] b) The line segment joining A(4, 7) and B(-6, -2) is intercepted by the Y-axis at the point K. Write down the abscissa of the point K. Hence, find the ratio in which K divides AB. Also, find the co-ordinates of the point K. [3] c) Use graph paper to answer the question. Take 2 cm = 2 units on both the axes. i) Plot the points A (8, -4) and B (6, 2). ii) Reflect points A and B in the line x = 4. Write their co-ordinates. iii) Give geometrical name of the figure ABB A . iv) Find area of the figure so formed. [4] Question 6 a) There were 50 questions in an examination paper numbered from 1 to 50. Write down the probability that the number of question chosen will : i) contain more than one digit. ii) contain atleast one of the digit as 3. iii) ends in 5. b) In the following figure, PQ is the tangent to the circle at A. DB is the diameter and O is the centre of the circle. If ADB = 30 and CBD= 60 , calculate : i) QAB, ii) PAD iii) CDB. [3] [3] c) The mean of the frequency distribution is 61.5 and sum of all the frequencies is 40. Find the values of a and b . Class Mark Frequency 0-20 4 20-40 a 40-60 10 60-80 b 80-100 7 [4] 100-120 5 Question 7 a) A (-2, 7), B (-1, 0) and D (3, 4) are the vertices of a parallelogram ABCD. Find the co-ordinates of vertex C. b) If a, b, c and d are in proportion, prove that : 11 + 15 11 + 15 3 2 5 2 = 3 2 5 2 [3] [3] c) A man stands 15 m away from a flagpole. He observes that angle of elevation of top of the pole is 30 and angle of depression of the bottom of pole is 12 . Calculate the height of the pole. [4] Question 8 a) Prove that : b) If A = [ 2 5 cosec A + 1 cosec A 1 = (sec A + tan A)2 3 0 4 1 ], B=[ ] and C = [ 7 1 7 1 [3] 0 ] . Find : BC + A2 10C. 4 [3] c) A passenger train takes 2 hours 30 min more than an express train for a journey of 600 km. The speed of the express train is 8 km/hr more than the passenger train. Find the speed of the passenger train. [4] Question 9 a) In the figure given, O is the centre of the circle. ABC = 100 , ACD = 40 . CT is the tangent to the circle at C. Find : i) ADC , ii) DCT. [3] b) Solve the equation 4x2 - 7x + 2 = 0 and give answer correct to 2 significant figures. [3] c) A circus tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 60 m and the height of the cylindrical part is 30 m. If the diameter of the base is 80 m, find the quantity of canvas required to make the tent. Allow 10% extra for fold and stitching. Give your answer to the nearest m2. [Take = 3.14] [4] Question 10 a) In an A.P, 6th term is half of the 4th term and the 3rd term is 15. How many terms are needed to give a sum is 66 ? [3] b) Kabir opened a recurring deposit account with Axis Bank for a period of 2 yrs. If the bank pays interest at the rate of 8% p. a. and the monthly instalment is Rs. 5,000. Find : i) interest earned in 2 years. ii) maturity value. [3] c) In the given figure, AB and DE are perpendiculars to BC. i) Prove that : ABC ~ DEC. ii) If AB = 15 cm, DE = 10 cm, AC = 30 cm, calculate DC. iii) Find ( ABC) ( DEC). [4] Question 11 a) A retailer buys an article from a wholesaler for Rs 50,000. He marks the price of an article 20% above his cost price and sells it to a consumer at 10% discount on the marked price. If the sales are intra-state and the rate of GST is 12%, find: i) The marked price of an article. ii) The amount which the consumer pays for an article. iii) The amount of tax (under GST) paid by the retailer to the Central Government. [4] b) The weights of 160 applicants for the Army are given below : Weight (in kg) 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 No. of applicants 6 8 16 24 40 36 22 8 Draw an ogive for the given distribution on a graph paper. Use scale : On X-axis : 2 cm = 5 kg and on Y-axis : 2cm = 20 applicants. Use the ogive to estimate : i) the median weight. ii) lower quartile. iii) number of applicants rejected weighing less than 60 kg and more than 80 kg. iv) percentage of applicants rejected. - : ALL THE BEST : - [6]
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