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Pong Dam Lake Wildlife Sanctuary

Pong Dam Lake Wildlife Sanctuary, located in Himachal Pradesh, India, is an important staging site for migratory species such as waterfowl and... View Article

Sixth Schedule of Indian Constitution

The Sixth Schedule of Indian Constitution contains provisions related to the Administration of Tribal Areas in the States of Assam, Meghalaya,... View Article

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 of view of its rightfulness or... View Article

UPSC Toppers’ Optional Subjects

IAS Toppers have focussed on the importance of a strategic plan for UPSC prelims and mains preparation over the years. Considering that the marks... View Article

UPSC 2023

UPSC CSE Interview 2022 Update: The first phase of the interviews was held from on 30th January 2023 to 10th March 2023 for a total of1026... 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 segment. In this... 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 2x - y = 1 …(i) Adding 1 to numerator... 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 = 2 × 2 × 2 × 3 × 3... 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.... View Article

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 s =... 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 - 1)]. Put x = cos θ... 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 side. The diagonal of the... 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 - sin x) = tan-1 (1 + tan x)/(1 - tan x) = tan-1 (tan... 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 is given by... 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 - 2x = -2 - 10 -3x = -12 x = -12/-3 x = 4 Substitute 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 is obtained by subtracting 1 from first... 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 = 52 (52/2) + 2 = 28 (28/2) + 2 = 16 (16/2) + 2 = 10 (10/2)... 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 of sweets. So the number of sweets per... 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 to... 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 equal volumes. Let r be the radius of cone... View Article