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Cess tax in India

An earmarked tax that is collected for a specific purpose and which must be spent only for that specific purpose and not any other... View Article

22 Oct 2021: UPSC Exam Comprehensive News Analysis

Oct 22nd, 2021, CNA:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related POLITY AND GOVERNANCE 1. SC says farmers have right to... View Article

203rd-anniversary-of-the-bhima-koregaon-battle

Bhima Koregaon is a small village located in present-day Pune District of Maharashtra. The Battle of Bhima Koregaon has an important place in the... View Article

Gist of Kurukshetra September 2021 Issue: Rural Marketing

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

21 Oct 2021: PIB Summary & Analysis

TABLE OF CONTENTS 1. Vaccination milestone 2. Police Commemoration Day 3. PM Gati Shakti National Master Plan (NMP) Yojana Gist... View Article

21 Oct 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 21st Oct 2021. Important news and views to boost... View Article

The differential coefficient of log tan x is

Solution: Let y = log tan x dy/dx = (1/tan x)sec2x = (cos x / sin x)/cos2x = 1/cos x sin x = 2/sin 2x = 2 cosec 2x... View Article

Show that 3 tan^-1x = tan^-1(3x-x³)/(1-3x²)

Solution: We know that tan-1A + tan-1B = tan-1(A+B)/(1-AB) LHS = 3 tan-1x = tan-1x + tan-1x + tan-1x = tan-1(2x/(1-x2)) + tan-1x =... View Article

Factorise the following expressions. (i) 7x – 42

(i) 7x - 42 (ii) 6p-12q (iii) 7a2 + 14a (iv) -16z + 20z3 (v) 20l2m + 30alm (vi) 5x2y - 15xy2 (vii) 10a2 - 15b2 + 20c2 (viii) -4a2 +... View Article

Fabina borrows Rs. 12500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same period at 10% per annum, compounded annually. Who pays more interest and by how much?

Solution: Case 1: Fabina - simple interest Principal, P = 12500 Rate of interest, r = 12% Number of years, n = 3 Simple interest, I = Pnr =... View Article

tan² θ − sec² θ is equal to

(a) 1 (b) -1 (c) 0 (d) none of these Solution: tan2 θ − sec2 θ = (sin2 θ/cos2 θ) - (1/cos2 θ) =... View Article

Write additive inverse of 2/8 and 6/5.

Solution: To find the additive inverse of a number, we have to change the sign of the number. When we add a number and its additive inverse, the... View Article

4 men and 6 women can finish work in 8 days while 3 men and 7 women can do that same work in 10 days. In how many days will 10 women do the same work.

Solution: Let work done by 1 man in a day = x Work done by 1 woman in a day = y 4x + 6y = 1/8 3x + 7y = 1/10 Solving above equations, we get... View Article

The mean of 100 items was found to be 64. Later on, it was discovered that two items were misread as 26 and 9 instead of 36 and 90 respectively. The correct mean is

Solution: Mean = sum of observations/number of observations Given mean of 100 items = 64 Sum of observations = 6400 Sum of misread items =... View Article

Two numbers a and b are selected successively without replacement in that order from the integers 1 to 10. The probability that a/b is an integer, is

(a) 17 /45 (b) 1/5 (c) 17/90 (d) 8/45 Solution: Total numbers of elementary events are: 10 ×9 = 90 (numbers are of... View Article

Solve 9x/(7- 6x) = 15

Solution: 9x/(7- 6x) = 15 Cross multiply 9x = 15(7-6x) 9x = 105 - 90 x 99x = 105 x = 105/99 = 35/33 Hence the value of x is 35/33.... View Article

A solid cylinder of radius r and height h is placed over another cylinder of the same height and radius. The total surface area of the shape so formed is:

(a) 4πrh (b) 4πrh + 2πr2 (c) πrh + πr2 (d) none of these. Solution: Here height of cylinder = 2h Radius = r TSA of cylinder... View Article