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Question 1.The means of two samples of sizes 60 and 120 respectively are 35.4 and 30.9 and the standard deviations are 4 and 5. Obtain the standard deviation of the sample of size 180 obtained by combining the two samples.Solution: Question 2.For certain data, the following information is available. Obtain the combined standard deviation.Solution: Question … Read more

Question 1.Find variance and S.D. for the following set of numbers.7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 2, 6Solution:Given data:7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 2, 6The tabulated form of the above data is Calculation of … Read more

Question 1.Find a range of the following data:19, 27, 15, 21, 33, 45, 7, 12, 20, 26Solution:Here, largest value (L) = 45, smallest value (S) = 7∴ Range = L – S = 45 – 7 = 38 Question 2.Find range of the following data:575, 609, 335, 280, 729, 544, 852, 427, 967, 250Solution:Here, largest … Read more

(I) Select the correct option from the given alternatives. Question 1. Question 2.The length of latus rectum of the parabola  – 4x – 8y + 12 = 0 is ________(A) 4(B) 6(C) 8(D) 10Answer:(C) 8Hint:Given equation of parabola is Question 3.If the focus of the parabola is (0, -3), its directrix is y = 3, … Read more

Question 1.Find the length of the transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices, and the length of the latus rectum of the hyperbolae. ⇒ b = 4 and a = 5Length of transverse axis = 2b = 2(4) = 8Length of conjugate axis = 2a = 2(5) … Read more

Question 1.Find the(i) lengths of the principal axes(ii) co-ordinates of the foci(iii) equations of directrices(iv) length of the latus rectum(v) distance between foci(vi) distance between directrices of the ellipse: a = 5 and b = 3Since a > b,X-axis is the major axis and Y-axis is the minor axis. (i) Length of major axis = … Read more

Question 1.Find co-ordinates of focus, equation of directrix, length of latus rectum and the co-ordinates of end points of latus rectum of the parabola: (ii) Given equation of the parabola is  = -20x.Comparing this equation with  = -4ax, we get⇒ 4a = 20⇒ a = 5Co-ordinates of focus are S(-a, 0), i.e., S(-5, 0)Equation of … Read more

(I) Choose the correct alternative. Question 1.Equation of a circle which passes through (3, 6) and touches the axes is Question 2.If the lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 sq. units, then find the equation of the circle. Question 3.Find … Read more

Question 1. Question 2. Question 4.7x – 3y – 1 = 0, which is same as the given line.The line 7x – 3y – 1 = 0 touches the given circle at (1, 2). Question 5.

Question 1. Question 2. Question 3.Find the equation of the circle passing through the points (5, 7), (6, 6), and (2, -2).Solution:Let C(h, k) be the centre of the required circle.Since the required circle passes through points A(5, 7), B(6, 6), and D(2, -2),CA = CB = CD = radiusSubstituting k = 3 in (i), … Read more