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Half -Yearly Examination -2020-21 Class X Mathematics SECTION A (40 Marks) Attempt all questions from this Section TT:2 Hrs MM:80 Question 1 (a) Find the value of k if 4x3 2x2 + x + 5 leaves remainder -10 when divided by 2x + 1. (b) Amit deposits Rs.1600 per month in a bank for 18 months in a recurring deposit account. If he gets Rs. 31,080 at the time of maturity, what is the rate of interest per annum? (c) Construct a regular hexagon of side 4cm. Construct a circle circumscribing the hexagon. [3] [3] [4] Question 2 (a) Solve the following inequation and represent your solution on the real number line: (b) (c) 5 x 3x 3 x, x [3] Find the 16th term of the A.P. 7, 11, 15, 19 . Find the sum of the first 6 terms. [3] In the given figure CE is a tangent to the circle at point C. ABCD is a cyclic quadrilateral. If ABC = 930 and DCE = 350 Find:(i) Question 3 (a) (b) (c) ADC (ii) CAD (iii) ACD [4] Prove the following identity Find x and y if : [3] - = For what value of k will the following quadratic equation: ( + 1)2 4 2 + 9 = 0 have real and equal roots? Solve the equations. [3] [4] Question 4 (a) A box consists of 4 red, 5 black and 6 white balls. One ball is drawn out at random. Find the probability that the ball drawn is: (i) black (ii) red or white [3] (b) Calculate the median and mode for the following distribution: Weight (in kg) 35 47 52 56 60 No. of students 4 3 5 3 2 [3] (c) A solid cylinder of radius 7 cm and height 14 cm is melted and recast into solid spheres each of radius 3.5 cm. Find the number of spheres formed. [4]
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