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What is the integral of int tan(2x) dx?

∫1/xdx=ln|x|+C u=cos(2x)⇒du=−2sin(2x)dx ∫tan(2x)dx=∫sin(2x)/cos(2x)dx =−12∫1/cos(2x)(−2sin(2x))dx... View Article

How do you factor completely x³ + y³ + z³ – 3xyz?

x3+y3+z3−3xyz=0 ⇒x3+y3+3x2y+3xy2+z3−3xyz−3x2y−3xy2=0 ⇒(x+y)3+z3−3xy(x+y+z)=0... View Article

26 Apr 2021: PIB Summary & Analysis

April 26th, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. Forest fires in Mizoram 2. DGFT ‘COVID-19 Helpdesk' 3. Project Dantak 1.... View Article

Remission of Duties and Taxes on Exported Products (RoDTEP) Scheme

The Remission of Duties and Taxes on Exported Products (RoDTEP) Scheme was announced in 2019 by the Government of India and it became effective... View Article

Battle of the Hydaspes

The Battle of Hydaspes was a decisive battle fought between the armies of Alexander the Great and the King Porus (also known as Poru, Paurava) in... View Article

Battle of Haifa

The Battle of Haifa was a decisive battle fought on 23 September 1918,, where the elements consisting mainly of Indian troops of the British Army... View Article

Chand Bibi

Chand Bibi was a ruler and military leader from the Deccan region known for the spirited defense of her realm during the Mughal invasions of... View Article

Gist of Kurukshetra April 2021 Issue: Folk Art and Culture

Kurukshetra Magazine is a vital source of study material for the UPSC IAS exam. It is a monthly magazine that gives information about important... View Article

26 Apr 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 26th April 2021. Important news and views to... View Article

Economy This Week (17th Apr to 23rd Apr 2021)

Economy is an important part of the UPSC prelims and mains exams; this series titled ‘Economy This Week’ has been initiated to address the need... View Article

CPTPP – Comprehensive and Progressive Agreement for Trans-Pacific Partnership

Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP)—a free trade agreement between Canada and 10 other countries in the... View Article

The polynomial (ax² + bx + c) (ax² – dx – c), ac ≠ 0 has

1) four real roots 2) at least two real roots 3) at most two real roots 4) no real roots Solution: (2) at least two real roots ac ≠ 0 ac... View Article

The coefficients of x in the quadratic equation x² + bx + c = 0 was taken as 17 in place of 13, its roots were found to be – 2 and -15. The correct roots of the original equation are

1) - 10, - 3 2) - 9, - 4 3) - 8, - 5 4) - 7, - 6 Solution: (1) - 10, - 3 The given equation is x2 + bx + c = 0 and b = 17 x2 + bx + c = 0... View Article

The solution set of the equation pqx² – (p + q)² x + (p + q)² = 0 is

1) {p / q, q / p} 2) {pq, p / q} 3) {q / p, pq} 4) {[p + q] / p, [p + q] / q} 5) {[p - q] / p, [p - q] / q} Solution: (4) {[p + q] / p, [p +... View Article

Let a, b be the solutions of x² + px + 1 = 0 and c, d be the solutions of x² + qx + 1 = 0. If (a – c) (b – c) and (a + d) (b + d) are the solutions of x² + αx + β = 0, then β equals

1) P + q 2) p - q 3) p2 + q2 4) q2 - p2 Solution: (4) q2 - p2 Since a + b = - p; ab = 1 and c + d = - q, cd = 1 It is given that (a - c) (b... View Article