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Find the odd one out from the given alternatives?

(A) 97 (B) 233 (C) 437 (D) 599 Solution: In the given options, 97, 233 and 599 are prime numbers. 437 is not a prime number. Hence... View Article

If the cost of 2 pencils and 3 erasers is Rs. 9 and the cost of 4 pencils and 6 erasers is Rs. 18. Find the cost of each pencil and each eraser.

Solution: Let x be the cost of a pencil and y be the cost of eraser. Then 2x + 3y = 9…(i) 4x + 6y = 18 …(ii) We can see that... View Article

(x³ – 1) can be factorised as: where ω is one of the cube roots of unity.

(a) (x-1) (x - ω) (x + ω2) (b) (x-1) (x - ω) (x - ω2) (c) (x-1) (x + ω) (x + ω2) (d) (x-1) (x + ω)... View Article

Factorize 8x³+ 36x²y + 54xy²+ 27y³.

Solution: 8x3 + 36x2y + 54xy2 + 27y3 = (2x)3 + 3(2x)2(3y) + 3(2x)(3y)2 + (3y)3 Use identity (a+b)3 = a3 + 3a2b + 3ab2 + b3 Here we get a = 2x... View Article

The antilog of 5/6 to the base 64 is

Solution: The antilog of a number is the inverse technique of finding the logarithm of the same number. If x is the logarithm of a number y with... View Article

All the three face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting : (i) a black face card (ii) a queen (iii) a black card.

Solution: Total number of cards = 52 Given that 3 face cards of spades are removed. Remaining number of cards = 52 - 3 = 49... View Article

What is the square of the number 89?

Solution: We know 89 = 100 -11 Use (a-b)2 = a2 - 2ab + b2 892 = (100 - 11)2 = 10000 - 2200 + 121 = 7921 Hence the square of 89 is 7921.... View Article

The cost price of 12 candles is equal to the selling price of 15 candles. Find the loss percent?

Solution: Cost price of 12 candles = selling price of 15 candles. Let C.P of 12 candles be x. Then C.P of 1 candle = x/12 SP of 15 candles =... View Article

If 1, x, y, z, 2 are in geometric progression, the xyz =

(a) 2√2 (b) 4 (c) 8 (d) None of this Solution: Given 1, x, y, z, 2 are in GP. Let a be the first term of GP and r be the common... View Article

Sunita travelled 15 km 268 m by bus, 7 km 7m by car and 500 m on foot in order to reach her school. How far is her school from her residence?

Solution: Distance travelled by bus = 15 km 268 m = 15268 m Distance travelled by car = 7 km 7m = 7007 m Distance travelled on foot = 500 m... View Article

If HCF(a, 8) = 4, LCM(a, 8) = 24 then find the value of a.

Solution: We know HCF × LCM = product of given numbers 4×24 = 8a a = 4×24/8 a = 12 Hence the value of a is 12.... View Article

Look at this series: 21, 9, 21, 11, 21, 13, . . .What number should come next?

(a) 14 (b) 15 (c) 21 (d) 23 Solution: In this alternating repetition series, the random number 21 is repeated. The second number increases... View Article

Solve the following sets of simultaneous equations. 2x+3y+4 = 0; x-5y = 11

Solution: Given 2x + 3y + 4 = 0 2x + 3y = -4 …(i) x - 5y = 11 …(ii) Multiply (ii) by 2 2x - 10y = 22 …(iii) (i)... View Article

Prove that cos A/(1 + sin A) = [cot (A/2) – 1]/[cot (A/2) +1]

Solution: LHS = cos A/(1 + sin A) = [2 cos2(A/2) - 1]/(1 + 2 sin (A/2) cos (A/2)) = [cos2(A/2) + cos2(A/2) - 1]/[sin2(A/2) + cos2(A/2) +... View Article

Using prime factorisation, find the HCF and LCM of 23, 31. Verify that HCF × LCM = product of given numbers.

Solution: Given numbers are 23 and 31. These are prime numbers. The LCM of two or more prime numbers is equal to their product. LCM of 23 and... View Article

If sin θ = 7/25, find the values of cos θ and tan θ.

Solution:We know sin θ = opposite side/hypotenuse Given sin θ = 7/25 cos θ = √(1 - sin2 θ) = √(1 -... View Article

Find the sum of the first 8 multiples of 3.

Solution: The first 8 multiples of 3 are 3, 6, 9, …. 8 terms This is an AP with a = 3, common difference d = 3 Number of terms, n = 8... View Article

AIR Spotlight – Celebrating Clean and Eco-friendly Deepawali

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

08 Nov 2021: UPSC Exam Comprehensive News Analysis

Nov 8th, 2021, CNA:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related POLITY AND GOVERNANCE 1. Haryana law on local hiring... View Article

07 Nov 2021: PIB Summary & Analysis

TABLE OF CONTENTS 1. PM to lay foundation stone of dedicated walkways for ‘Palkhi’ 2. Vice President calls for promotion of agro-based... View Article