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09 Jun 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 9th Jun 2021. Important news and views to boost... View Article

Lancang-Mekong Cooperation

The Lancang-Mekong Cooperation Mechanism is a multilateral format for cooperation among members on the Lancang-Mekong River. Multilateral... View Article

If P(3, 4, 5), Q(4, 6, 3), R(-1, 2, 4), S(1, 0, 5) then the projection of RS on PQ is

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

If x coordinates of a point P of the line joining the points Q(2, 2, 1) and R(5, 2, -2) is 4, then the z-co-ordinates of P is

1) -2 2) -1 3) 1 4) 2 Solution: (2) -1... View Article

The distance between the points (1, 4, 5) and (2, 2, 3) is

1) 5 2) 4 3) 3 4) 2 Solution: (3) 3 S = √(2 - 1)2 + (2 - 4)2 + (3 - 5)2 = 3... View Article

If O is the origin and OP = 3 with direction ratios -1, 2, -2, then co-ordinates of P are

1) (1, 2, 2) 2) (-1, 2, -2) 3) (-3, 6, -9) 4) (-1/3, 2/3, -2/3) Solution: (2) (-1, 2, -2)... View Article

The plane XOZ divides the join of (1, – 1, 5) and (2, 3, 4) in the ratio λ : 1, then λ is

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

The points A(5, – 1, 1); B(7, – 4, 7); C(1, – 6,10) and D(-1, – 3, 4) are vertices of a

1) Square 2) Rhombus 3) Rectangle 4) None of these Solution: (2) Rhombus AB = BC = CD = DA = 7 AB . BC ≠ 0 ABCD is not a square... View Article

If a line makes α, β, γ, δ angles with four diagonals of a cube, then cos² α + cos² β + cos² γ + cos² δ =

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

If a line makes angles α, β, γ with the co-ordinate axis, then

1) cos 2α + cos 2β + cos 2γ - 1 = 0 2) cos 2α + cos 2β + cos 2γ - 2 = 0 3) cos 2α + cos 2β + cos 2γ + 1= 0 4) cos 2α + cos 2β + cos 2γ + 2... View Article

The points (5, – 4, 2), (4, – 3, 1), (7, – 6, 4) and (8, – 7, 5) are the vertices of

1) A rectangle 2) A square 3) A parallelogram 4) None of these Solution: (4) None of these... View Article

The projection of the line segment joining the points (-1, 0, 3) and (2, 5, 1) on the line whose direction ratios are 6, 2, 3 is

1) 10 / 7 2) 22 / 7 3) 18 / 7 4) None of these Solution: (2) 22 / 7... View Article

The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to (1, -1, 2) and (2, 1, -1) are

1) - 1 / √35, 5 / √35, 3 / √35 2) 13 / √35, - 1 / √35, 1 / √35 3) 2 / √3, 5 / √3, 7 / √3 4) 3 / √35, 5 / √35, 7 / √35 Solution: (1) - 1 /... View Article

The coordinates of the point in which the line joining the points (3, 5, – 7) and (-2, 1, 8) is intersected by the plane yz are given by

1) (0, 13 / 5, 2) 2) (0, - 13 / 5, - 2) 3) (0, - 13 / 5, 2 / 5) 4) (0, 13 / 5, 2 / 5) Solution: (1) (0, 13 / 5, 2)... View Article

A line AB in three-dimensional space makes angle 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals

1) 30° 2) 45° 3) 60° 4) 75° Solution: (3) 60°... View Article

If a line makes angles ɑ, β, , with four diagonals of a cube, then the value of sin² ɑ + sin² β + sin² + sin² is

1) 4 / 3 2) 1 3) 8 / 3 4) 7 / 3 Solution: (3) 8 / 3... View Article

Points (-2, 4, 7), (3, – 6, – 8) and (1, – 2, – 2) are

1) Collinear 2) Vertices of an equilateral triangle 3) Vertices of an isosceles triangle 4) None of the above Solution: (1) Collinear... View Article

M	T	W	T	F	S	S
	1	2	3	4	5	6
7	8	9	10	11	12	13
14	15	16	17	18	19	20
21	22	23	24	25	26	27
28	29	30