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18 Mar 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 17th March 2021. Important news and views to... View Article

Global Multidimensional Poverty Index 2021-22

The Global MPI stands for Multidimensional Poverty Index that is released by Oxford Poverty and Human Development Initiative (OPHI). The idea... View Article

Indra Exercise – Facts for UPSC

Exercise Indra is a bilateral exercise between the militaries of India and Russia. In September 2020, both countries launched the 11th edition of... View Article

What is Bird Diverter?

Latest Context: Bird Diverters came in the news after the Great Indian Bustard, the critically endangered species in India started falling dead... View Article

The lines joining the origin to the points of intersection of the line y = mx + c and the circle x² + y² = a² will be mutually perpendicular, if

1) a2 (m2 + 1) = c2 2) a2 (m2 – 1) = c2 3) a2 (m2 + 1) = 2c2 4) a2 (m2 – 1) = 2c2 Solution: Given equation of line is y = mx + c ..(i)... View Article

If one of the lines of the pair ax² + 2hxy + by² = 0 bisects the angle between positive directions of the axes, then a,b,h satisfy the relation

1) a + b = 2|h| 2) a + b = -2h 3) a – b = 2|h| 4) (a – b)2 = 4h2 Solution: Given ax2 + 2hxy + by2 = 0 ..(i) One of the lines... View Article

The angle between the pair of straight lines y² sin²θ – xy sin²θ + x²(cos²θ – 1) = 1, is

1) π/2 2) π/3 3) π/4 4) none of these Solution: Given equation of pair of straight lines y2 sin2θ - xy sin2θ + x2(cos2θ - 1) = 1 => y2... View Article

The area (in square units) of the quadrilateral formed by the two pairs of lines l² x² – m² y² – n(lx + my) = 0 and l² x² – m² y² + n(lx – my) = 0

1) n2/2|lm| 2) n2/|lm| 3) n/2|lm| 4) n2/4|lm| Solution: Given l2 x2 - m2 y2 - n(lx + my) = 0 …(i) => (lx + my)(lx - my - n) = 0 =>... View Article

Area of the triangle formed by the lines y² – 9xy + 18x² = 0 and y = 9 is

1) 27/4 sq. units 2) 27 sq. units 3) 27/2 sq. units 4) None of these Solution: Given y = 9 ..(i) y2 - 9xy + 18x2 = 0 => y2 - 6xy - 3xy +... View Article

The equations to a pair of opposite sides of a parallelogram are x² – 5x + 6 = 0 and y² – 6y + 5 = 0. The equations to its diagonals are

1) x + 4y = 13 and y = 4x – 7 2) 4x + y = 13 and 4y = x – 7 3) 4x + y = 13 and y = 4x – 7 4) y – 4x = 13 and y + 4x = 7 Solution:... View Article

The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point (a, b) is

1) x2 + y2 - ax - by = 0 2) x2 + y2 + ax + by = 0 3) x2 + y2 - 2ax - 2by = 0 4) None of these Solution: Equation of line passing... View Article

If the portion of the line lx + my = 1 falling inside the circle x² + y² = a² subtends an angle of 45⁰ at the origin, then

1) 4[(a2(l2+m2) - 1)] = a2(l2 + m2) 2) 4[(a2(l2+m2) - 1)] = a2(l2 + m2) - 2 3) 4[(a2(l2+m2) - 1)] = [a2(l2 + m2) - 2]2 4) none of these... View Article

The image of the pair of lines represented by ax² + 2hxy + by² = 0 by the line mirror y = 0 is

1) ax2 – 2hxy – by2 = 0 2) bx2 – 2hxy – ay2 = 0 3) bx2 + 2hxy + ay2 = 0 4) ax2 – 2hxy + by2 = 0 Solution: Given ax2 + 2hxy + by2 =... View Article

If the pair of lines ax² + 2hxy + by² + 2gx + 2fy + c = 0 intersect on the y-axis, then

1) 2fgh = bg2 + ch2 2) bg2 ≠ ch2 3) abc = 2fgh 4) None of these Solution: Given ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 ..(i) This represents... View Article

The lines p(p² + 1) x – y + q = 0 and (p² + 1)² x + (p² + 1)y + 2q = 0 are perpendicular to a common line for

1) No value of p 2) Exactly one value of p 3) Exactly two values of p 4) More than two values of p Solution: Given lines are p(p2... View Article

The area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals

1) |(m + n)|/(m - n)2 2) 2/|(m + n)| 3) 1/|(m + n)| 4) 1/|(m - n)| Solution: Let the lines be OB: y = mx …(i) CA: y = mx + 1 …(ii) OC: y =... View Article

The diagonals of the parallelogram whose sides are lx + my + n = 0, lx + my + n’ = 0, mx + ly + n = 0, mx + ly + n’ = 0 include an angle

1) π/2 2) π/4 3) π/3 4) none of these Solution: Given sides of parallelogram are lx + my + n = 0 ..(i) lx + my + n’ = 0 ..(ii) mx + ly + n =... View Article

Equation of one of the sides of an isosceles right-angled triangle whose hypotenuse is 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2), will be

1) x – 7y + 12 = 0 2) 7x + y – 12 = 0 3) x – 7y + 16 = 0 4) 7x + y + 16 = 0 Solution: Given equation of the hypotenuse is 3x + 4y = 4 Slope... View Article

Coordinates of the vertices of a quadrilateral are (2, -1), (0, 2), (2, 3) and (4, 0). The angle between its diagonals will be

1) 900 2) 00 3) tan-1(2) 4) tan-1(1/2) Solution: Let A(2, -1), B(0, 2), C(2, 3) and D(4, 0) be the vertices of a quadrilateral. Slope of... View Article

For the straight lines given by the equation (2 + k)x + (1 + k)y = 5 + 7k, for different values of k which of the following statements is true

1) Lines are parallel 2) Lines pass through the point (–2, 9) 3) Lines pass through the point (2, –9) 4) None of these Solution:... View Article

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