For the following pairs of observations (1, 10), (2, 9), (3, 9), (4, 8), (5, 6), (6, 12), (7, 4), (8, 3), (9, 13), (10, 1), then Cov (x, y) =
1) 1.05 2) 2.45 3) – 4.45 4) – 4.9 Solution: (3) – 4.45 Here x {bar} = 5.5, y... View Article
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If var (x) = 21 / 4 and var (y) = 21 and r = 1, then standard error of y is
1) 0 2) 1/2 3) 1/4 4) 1 Solution: (1) 0 Sy = y √1 – r2 = y √1... View Article
The coefficients of correlation between the heights (in inches) of fathers and sons from the following data will be: Heights of fathers (x) 65 66 67 68 69 70 71. Heights of sons (y) 67 68 66 69 72 72 69
1) 0.60 2) – 0.60 3) – 0.67 4) 0.67 Solution: (4) 0.67 Mean of x = 68, Mean of... View Article
Karl Pearson’s coefficient of rank correlation between the ranks obtained by ten students in Mathematics and Chemistry in a class test as given below is: Rank in Mathematics 1 2 3 4 5 6 7 8 9 10. Rank in Chemistry 3 10 5 1 2 9 4 8 7 6
1) 0.224 2) 0.204 3) 0.240 4) None of these Solution: (1) 0.224 Since, ∑d2 = 128 ⍴ = 1... View Article
If 2 random variables x and y of a bivariate distribution are connected by the relationship 3x + 2y = 4, then correlation coefficient rxy =
1) 1 2) –1 3) 2/3 4) –2/3 Solution: (2) –1 Here, y = (- 3 / 2) x +... View Article
For the given data, the calculation corresponding to all value of pairs (x, y) is following ∑ (x – x {bar})2 = 36, ∑ (x – y {bar})2 = 25, ∑ (x – x {bar}) ∑ (y – y {bar}) = 2. Then the Karl Pearson’s correlation coefficient is
1) 0.2 2) 0.5 3) 0.66 4) 0.33 Solution: (3) 0.66 rxy = 20 / √(36) (25) = 2 /... View Article
If a, b, h, k are constants, while U and V are U = [X – a] / h, V = [Y – b] / k, then
1) Cov (X, Y) = Cov (U, V) 2) Cov (X, Y) = hk Cov (U, V) 3) Cov (X,... View Article
Covariance (x, y) between x and y if ∑x = 15, ∑y = 40, ∑xy = 110, n = 5 is
1) 22 2) 2 3) –2 4) None of these Solution: (3) –2 It is given that ∑x = 15,... View Article
If r is the correlation coefficient between two variables, then
1) r ≥ 1 2) r ≤ 1 3) |r| ≤ 1 4) |r| ≥ 1 Solution: (3) |r| ≤... View Article
If Var (x) = 8.25, Var (y) = 33.96 and Cov (x, y) = 10.2, then the correlation coefficient is
1) 0.89 2) –0.98 3) 0.61 4) –0.16 Solution: (3) 0.61 rxy = covariance (x, y) / (√var (x), var... View Article
Three forces P, Q, R act along the sides BC, CA, AB of triangle ABC, taken in order. If their resultant passes through the incentre of ∆ABC, then
1) P + Q + R = 0 2) (P / a) + (Q / b) + (R / c)... View Article
Two like parallel forces P and 3P act on a rigid body at points A and B respectively. If the forces are interchanged in position, the resultant will be displaced through a distance of
1) (1 / 2) AB 2) (1 / 3) AB 3) (1 / 4) AB 4) (3 / 4) AB... View Article
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Like parallel forces act at the vertices A, B and C of a triangle ABC and are proportional to the lengths BC, AC and AB respectively. The centre of the forces is at the
1) Centroid 2) Circum-centre 3) Incentre 4) None of these Solution: (3) Incentre Let λa, λb, λc be the forces... View Article
If the resultant of two forces of magnitude P and 2P is perpendicular to P, then the angle between the forces is
1) 2π/ 3 2) 3π/ 4 3) 4π/5 4) 5π/6 Solution: (1) 2π/ 3 Let the angle between the forces... View Article
