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Cyber Crime Volunteer Program

The Union Home Ministry has launched a Cyber Crime Volunteers Concept as a measure to fight cybercrime. In this article, you can read all about... View Article

30 Apr 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 30th April 2021. Important news and views to... View Article

UPSC 2021: Weekly GK and Current Affairs Quiz May 01 – May 07

UPSC 2021: Weekly GK and Current Affairs Quiz May 01 - May 07 with Multiple Choice Questions and answers for IAS Exam Preparation other... View Article

National Climate Vulnerability Assessment Report

The Department of Science and Technology released the National Climate Vulnerability Assessment Report 2019-20 on April 17, 2021. It is a part... View Article

30 Apr 2021: UPSC Exam Comprehensive News Analysis

CNA 30th April 2021:- Download PDF HereTABLE OF CONTENTS A. GS 1 Related B. GS 2 Related HEALTH 1. ‘Childhood vaccinations must not be delayed’... View Article

29 Apr 2021: PIB Summary & Analysis

April 29th, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. A simple and fast solution to the Oxygen crisis 2. MACS 1407 1. A simple and... View Article

29 Apr 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 29th April 2021. Important news and views to... View Article

World Cities Culture Forum (WCCF)

Culture has been acknowledged as one of the key features by city leaders for thriving urban centres. The World Cities Culture Forum (WCCF)... View Article

Operation Gibraltar

Operation Gibraltar was code name for a military operation launched by the Pakistani military in the Indian administered part of Kashmir. The... View Article

Gist of Yojana March 2021 Issue: Union Budget 2021-22

Yojana Magazine is an important source of material for the UPSC exam. The monthly magazine provides details of major government schemes and... View Article

Operation Polo

Operation Polo was the code name for the police action against the Princely State of Hyderabad in September 1948 by the newly Independent... View Article

The distance between the foci of the conic 7x² – 9y² = 63 is equal to

1) 8 2) 4 3) 3 4) 7 5) 12 Solution: (1) 8 7x2 - 9y2 = 63 (x2 / 9) - (y2 / 7) = 1 is the equation of the hyperbola. a2 = 9, b2 = 7 a = 3, b... View Article

If t₁ and t₂ are the parameters of the end points of a focal chord for the parabola y² = 4ax, then which one is correct

1) t1 t2 = 1 2) t1 / t2 = 1 3) t1 t2 = - 1 4) t1 + t2 = 1 Solution: (3) t1 t2 = - 1 It is a fact that t1 t2 = - 1.... View Article

The eccentricity of the hyperbola with latusrectum 12 and semi – conjugate axis 2√3 is

1) 3 2) √3 / 2 3) 2√3 4) 2 Solution: (4) 2 Latus rectum = 2b2 / a = 12 and semi conjugate axis b = 2√3 2b2 / a = 12 2 * [(2√3)2 / a] = 12 a... View Article

The length of the latusrectum of the ellipse 16x² + 25y² = 400 is

1) 5/6 units 2) 32/5 units 3) 16/5 units 4) 5/32 units Solution: (2) 32/5 units 16x2 + 25y2 = 400 (16x2 / 400) + (25y2 / 400) = 1 x2 / 25 +... View Article

The sum of the reciprocals of the focal distance of a focal chord PQ of y² = 4ax is

1) 1/a 2) a 3) 2a 4) 1/2a Solution: (1) 1 / a The latus rectum with ends (a, 2a), (a, -2a). The sum of reciprocals of focal distances is (1... View Article

The straight lines y = ± x intersect the parabola y² = 8x in points P and Q, then length of PQ is

1) 4 2) 4√2 3) 8 4) 16 Solution: (4) 16 y2 = 8x y2 = ± 8y y (y ± 8) = 0 Length of PQ = √(16)2 + 02 = 16... View Article

If the centre, one of the foci and semi – major axis of an ellipse are (0, 0), (0, 3) and 5, then its equation is

1) x2 / 16 + y2 / 25 = 1 2) x2 / 25 + y2 / 16 = 1 3) x2 / 9 + y2 / 25 = 1 4) None of these Solution: (1) x2 / 16 + y2 / 25 = 1 c2 = b2 - a2... View Article

If (x, y) are any point on the parabola y² = 4x. Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then, the locus of P is

1) x2 = y 2) y2 = 2xy 3) y2 = x 4) x2 = 2y Solution: (3) y2 = x h = [x + 1] / 4, k = [y + 0] / 4 x = 4h, y = 4k Given that y2 = 4x (4k)2 = 4... View Article

The equation y² + 4x + 4y + k = 0 represents a parabola whose latusrectum is

1) 1 2) 2 3) 3 4) 4 Solution: (4) 4 y2 + 4x + 4y + k = 0 (y + 2)2 = - 4 [x + [- 4 + k] / 4]] Latus rectum = 4 Tangent at (1, 7) to the parabola.... View Article