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If m is the cube root of n, then n is (a) m3 (b) √m (c) m/3 (d) 3√m

The correct answer is (a) m3 Explanation 3√n = m n = m3 Let us consider an example 63= 216 216 is a perfect cube Hence 3√216=6... View Article

A perfect square number having n digits where n is even will have square root with (a) n + 1 digit (b) n/2 digit (c) n/3 digit (d) (n + 1)/2 digit

The correct answer is (b) n/2 digit Explanation Let us consider an example 36 is a perfect square and it has 2 digits Here n=2... View Article

If m is the square of a natural number n, then n is (a) the square of m (b) greater than m (c) equal to m (d) √m

The correct answer is (d) √m Explanation Given that m is the square of a natural number n Hence n2 = m Then, => n = √m... View Article

3√1000 is equal to (a) 10 (b) 100 (c) 1 (d) none of these

The correct answer is (a) 10 Explanation = 3√1000 = 3√(10 × 10 × 10) = 3√(103) = 10... View Article

Which of the following numbers is not a perfect cube? (a) 216 (b) 567 (c) 125 (d) 343

The correct answer is (b) 567 Explanation 216 = 6 × 6 × 6 567 = 9 × 9 × 7 125 = 5 × 5 × 5 343 = 7... View Article

A perfect square can never have the following digit in its ones place. (a) 1 (b) 8 (c) 0 (d) 6

The correct answer is (b) 8 Explanation From the properties of square we know that a number with 2, 3, 7 or 8 at unit’s place should... View Article

Which among 43², 67², 52², 59² would end with digit 1? (a) 43² (b) 67² (c) 52² (d) 59²

The correct answer is (d) 592 Explanation From the properties of square we know that if a number ends with 1 or 9, then its square will... View Article

AIR Spotlight – Development Works in Aspirational Districts

AIR Spotlight is an insightful program featured daily on the All India Radio Newsonair. In this program, many eminent panellists discuss issues... View Article

05 Oct 2021: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 5th Oct 2021. Important news and views to boost... View Article

IAS Topper 2020 [AIR 35] – Aparna Ramesh

Aparna Ramesh, a daughter of a civil servant, and an architect & urban planner by profession, topped the UPSC CSE Exam 2020 in her second... View Article

IAS Topper 2020 [AIR 51] – Nisha Grewal

Nisha Grewal is from Bhiwani’s Bamla village in Haryana. She cleared UPSC-CSE 2020 and secured AIR 51 in her 1st attempt. Nisha Grewal’s family... View Article

The next two numbers in the number pattern 1, 4, 9, 16, 25 … are (a)35, 48 (b) 36, 49 (c) 36, 48 (d) 35,49

The correct answer is (b) 36, 49 Explanation The numbers given in the question are perfect square numbers. 12 = 1 22 = 4... View Article

The hypotenuse of a right triangle with its legs of lengths 3x × 4x is (a) 5x (b) 7x (c) 16x (d) 25x

The correct answer is (a) 5x Explanation From the concpet of Pythagoras theorem, we know that = a = √(b2 + c2) Where... View Article

Which of the following numbers is a perfect cube? (a) 243 (b) 216 (c) 392 (d) 8640

The correct answer is (b) 216 Explanation A perfect cube can always be expressed as the product of triplets of prime factors. 216 = 6 × 6... View Article

The sum of first n odd natural numbers is (a) 2n + 1 (b) n² (c) n² – 1 (d) n² + 1

The correct answer is (b) n2 Explanation The sum of first n odd natural numbers are given by 1,3,5,7,9…… (2n – 1)... View Article

The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is (a) 81 (b) 64 (c) 49 (d) 36

The correct answer is (b) 64 Explanation = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64... View Article

If one member of a Pythagorean triplet is 2m, then the other two members are (a) m, m² + 1 (b) m² + 1, m² – 1 (c) m², m² – 1 (d) m², m + 1

The correct answer is (b) m2 + 1, m2 – 1 Explanation We know that general form of Pythagorean triplet is (2m, m²-1,... View Article

Which letter best represents the location of √25 on a number line? (a) A (b) B (c) C (d) D

The correct answer is (c) C Explanation √25 = 5 × 5 = 52 = 25... View Article

A square board has an area of 144 square units. How long is each side of the board? (a) 11 units (b) 12 units (c) 13 units (d) 14 units

The correct answer is (b) 12 units Explanation We know that area of square = Side × Side side2= 144 side=√144 = 12 units... View Article

The one’s digit of the cube of 23 is (a) 6 (b) 7 (c) 3 (d) 9

The correct answer is (b) 7 Explanation The one’s digit of cube 23 23 × 23 × 23 = 12,167 So, one’s digit is 7... View Article