What is the definition of Ethics?
To define Ethics, “it is the branch of philosophy that involves a systematic study of human actions from the point... View Article
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UPSC Toppers’ Optional Subjects
IAS Toppers have focussed on the importance of a strategic plan for UPSC prelims and mains preparation over the years.... View Article
UPSC 2023
UPSC CSE Interview 2022 Update: The first phase of the interviews was held from on 30th January 2023 to 10th... View Article
Gist of EPW October Week 4, 2021
The Economic and Political Weekly (EPW) is an important source of study material for IAS, especially for the current affairs... View Article
The denominator of a fraction is 1 less than twice its numerator. If 1 is added to numerator and denominator respectively, the ratio of numerator to denominator is 3: 5. Find the fraction.
Solution: Let x be the numerator of the fraction and y be the denominator. Then y = 2x – 1 ... View Article
Find the LCM of the numbers 180, 72, and 252.
Solution: Find the factors of the given numbers. 180 = 2× 2 × 3 × 3 × 5 72 =... View Article
Express as power notation 512.
Solution: 512 = 2×2×2×2× 2×2×2×2×2 = 29 Hence 512 can be written as 29.
One side of an equilateral triangle measures 8 cm. Find its area using Heron’s formula. What is its altitude?
Solution: By heron’s formula, the area of a triangle = √(s(s-a)(s-b)(s-c)) Where s = (a+b+c)/2 Given side = 8 So... View Article
Find dy/dx if y = sec-1[1/(2x2 – 1)].
(a) 1/√(1 – x2) (b) -2/√(1 – x2) (c) 1/(1+x2) (d) none of these Solution: Given y = sec-1[1/(2x2 –... View Article
The diagonal of a rectangle is thrice its smaller side. Find the ratio of its sides.
(A) √2:1 (B) 2√2:1 (C) 3:2 (D) √3:1 Solution: Let x be the smaller side and y be the longer... View Article
Differentiate, tan-1 (cos x + sin x)/(cos x – sin x) with respect to x.
(a) 1 (b) 0 (c) 1/2 (d) π/4 Solution: Let y = tan-1 (cos x + sin x)/(cos x –... View Article
25 degree celcius is equal to?
(A) 77 Fahrenheit (B) 85 Fahrenheit (C) 100 Fahrenheit (D) 120 Fahrenheit Solution: The formula to convert Celsius to Fahrenheit... View Article
Solve the following equations. 3x – 2(2x-5) = 2(x+3)-8. Also, verify.
Solution: Given 3x – 2(2x-5) = 2(x+3)-8 …(i) 3x – 4x + 10 = 2x + 6 – 8 -x... View Article
Find the missing term. 11, 10, __, 100, 1001, 1000, 10001.
(a) 101 (b) 91 (c) 100 (d) 81 Solution: By observing the pattern, we can see that the second number... View Article
What is the next number in the sequence 100, 52, 28, 16, 10, __
(a) 5 (b) 6 (c) 7 (d) 8 Solution: Given 100, 52, 28, 16, 10, __ (100)/2 + 2 =... View Article
On children’s day sweets were to be equally distributed among 175 students in a school. Actually on that day 35 children were absent and therefore each child got 4 sweet extra. How many sweets were available in all for distribution?
(a) 2750 (b) 2800 (c) 2672 (d) 2675 Solution: Number of children = 175 Let x be the total number... View Article
PAN stands for
Answer: Permanent Account Number abbreviated as PAN is a unique 10-digit alphanumeric number issued by the Indian Income Tax Department... View Article
If a cone and a sphere have equal radii and equal volumes, what is the ratio of the diameter of the sphere to the height of the cone?
(A) 1:1 (B) 1:2 (C) 2:1 (D) 3:2 Solution: Given that a cone and a sphere have equal radii and... View Article
In the given question, select the related number from the given alternatives. 3265 : 4376 : : 4673 : ?
(a) 2154 (b) 5487 (c) 3562 (d) 5784 Solution: Given 3265 : 4376 : : 4673 : ? While... View Article
Factorise x4 – 625.
Solution: Use identity a2 – b2 = (a+b) (a-b) x4 – 625 = (x2)2 – 252 = (x2)2 – (25)2... View Article
