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... View Article
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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... 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) Download the... 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... 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... 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 =... 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... 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,... 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)... 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... 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... 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... 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... 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... 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 =... View Article
Solve for 1/(x-1)(x-2) + 1/(x-3)(x-2) = 2/3, x ≠ 1, 2, 3.
Solution: Given 1/(x-1)(x-2) + 1/(x-3)(x-2) = 2/3 [(x-3) + (x-1)]/(x-1)(x-2)(x-3) = 2/3 3[(x-3) + (x-1)] = 2(x-1)(x-2)(x-3) 3(2x – 4)... View Article
Which of the following is a pair of co-primes?
(a) (14, 35) (b) (18, 25) (c) (31, 93) (d) (32, 62) Solution: A set of numbers or integers which... View Article
Check which of the following are solutions of an equation x – 2y = 4.
(a) (0, 2) (b) (2, 0) (c) (4, 0) (d) (√2, 4√2) Solution: Given equation is x – 2y =... View Article
The difference between two positive integers is 30. The ratio of these integers is 2:5. Find the integers.
Solution: Given that the ratio of the integers is 2:5. Let 2x be the first integer and 5x be the... View Article
Period of cos x is
(a) 2π (b) π (c) π/4 (d) none of these Solution: The period of cos x is 2π. The period... View Article
