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A horizontal force F is applied to a small object P of mass m on a smooth plane inclined to the horizon at an angle θ. If F is just enough to keep P in equilibrium, then F =

1) mg cos2 θ 2) mg sin2 θ 3) mg cosθ 4) mg tan θ Solution: (4) mg tan θ... View Article

Let R be the resultant of P and Q and if (P / 3) = (Q / 7) = (R / 5), then the angle between P and R is

1) cos-1 (11 / 14) 2) cos-1 (- 11 / 14) 3) 2π / 3 4) 5π / 6 Solution:... View Article

The resultant of two forces P and Q acting at an angle θ is equal to (2m + 1) √P² + Q², when they act at an angle 90 – θ, the resultant is (2m – 1) (√P² + Q²); then tan θ =

1) 1 / m 2) [m + 1] / [m – 1] 3) [m – 1] / [m + 1]... View Article

Three forces of magnitude 30, 60 and P acting at a point are in equilibrium. If the angle between the first two is 60°, the value of P is

1) 30 √7 2) 30 √3 3) 20 √6 4) 25 √2 Solution: (1) 30 √7 Since the forces are... View Article

The direction of three forces 1 N, 2 N and 3 N acting at a point are parallel to the sides of an equilateral triangle taken in order. The magnitude of their resultant is

1) (√3 / 2) N 2) 3 N 3) √3 N 4) (3 / 2) N Solution: (3) √3 N... View Article

The resultant of two force P N and 3 N is a force of 7 N.If the direction of 3N force were reversed, the resultant would be √19. N. The value of P is

1) 5 N 2) 6 N 3) 3 N 4) 4 N Solution: (1) 5 N 72 = P2 +... View Article

The greatest and least magnitude of the resultant of two forces of constant magnitude is F and G. When the forces act at an angle 2α, the resultant in magnitudes is equal to

1) √F2 cos2 ɑ + G2 sin2 ɑ 2) √F2 sin ɑ + G2 cos2 ɑ 3) √F2 + G2... View Article

The resultant of two equal forces is equal to either of these forces. The angle between them is

1) π / 4 2) π / 3 3) π / 2 4) 2π / 3 Solution: (4) 2π / 3 Let... View Article

A force is resolved into components P and Q equally inclined to it. Then,

1) P = 2Q 2) 2P = Q 3) P = Q 4) None of these Solution: (3) P =... View Article

The maximum resultant of two forces is P and the minimum resultant is Q, the two forces are at right angles, the resultant is

1) P + Q 2) P – Q 3) (1 / 2) √P2 + Q2 4) √[P2 + Q2] /... View Article

The resultant of two forces 3P and 2P is R, if the first force is doubled, the resultant is also doubled. The angle between the forces is

1) π / 3 2) 2π / 3 3) π / 6 4) 5π / 6 Solution: (2) 2π / 3... View Article

When the origin is changed, then the coefficient of correlation

1) becomes zero 2) varies 3) remains fixed 4) None of these Solution: (3) remains fixed The value of the... View Article

If there exists a linear statistical relationship between two variables x and y, then the regression coefficients of y on x is

1) cov (x, y) / 𝜎 x 𝜎y 2) cov (x, y) / 𝜎 y2 3) cov (x, y) /... View Article

If θ is the angle between two regression lines with correlation coefficient γ, then

1) sin θ ≥ 1- γ2 2) sin θ ≤ 1- γ2 3) sin θ ≤ γ2 + 1 4)... View Article

If the lines of regression are 3x + 12y = 19 and 3y + 9x = 46, then r_xy will be

1) 0.289 2) -0.289 3) 0.209 4) None of these Solution: (2) – 0.289 Assume that the line of regression... View Article

In a bivariate data, ∑x = 30, ∑y = 400, ∑x² = 196, ∑xy = 850 and n = 10. The regression coefficient of y on x is

1) -3.1 2) -3.2 3) -3.3 4) -3.4 Solution: (3) -3.3 byx = [∑xy – (1 / n) ∑ x... View Article

Angle between two lines of regression is given by

1) tan-1 [bxy – (1 / byx)] / [1 – (bxy / byx)] 2) tan-1 [byx . bxy – 1]... View Article

The correlation coefficient of two variables x and y are 0.8. The regression coefficient of y on x is 0.2, then the regression coefficient of x on y is

1) 3.2 2) -3.2 3) 4 4) 0.16 Solution: (1) 3.2 Given correlation coefficient (r) = 0.8 byx = 0.2... View Article

The two regression lines were found to be 4X – 5Y + 33 = 0 and 20X – 9Y – 107 = 0. Find the coefficient of correlation between X and Y.

1) 0.6 2) 0.16 3) 0.3 4) 0.7 Solution: (1) 0.6 4X – 5Y = -33 … (1) 20X –... View Article

Two numbers within the brackets denote the ranks of 10 students of a class in two subjects (1, 10), (2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (9, 2), (10, 1), then rank correlation coefficient is

1) 0 2) -1 3) 1 4) 0.5 Solution: (2) -1 On relating the difference of ranks between the pairs... View Article

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