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What is the integral of sin^4 (x) dx?

Assume that, I = ∫ sin4x dx Now, reduce sin4x dx to integrate the function. I = ∫ (sin2x)2 dx... View Article

What is transitive relations. Give an example

In set theory, a transitive relation is a binary relation. If a relation R on set A is said to... View Article

Three men paint a house in 20 days. How many days do 30 men take to do the same?

Given that, 3 men paint a house in 20 days. Now, we have to find the number of days, when... View Article

Out of 80 students 45%, students passed in Mathematics and 60% students passed in English. If 35% students failed in both the subjects, how many students passed in both the subjects?

Given that the total number of students = 80 45% students passed in Mathematics = (45/100)80 = 36 students passed... View Article

A dice is rolled twice. Find the probability that 5 will not come up either time.

If a die is rolled twice, the total number of outcomes is 36. S = {(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) (2,1)(2,2)(2,3)(2,4)(2,5)(2,6) (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) (5,1)(5,2)(5,3)(5,4)(5,5)(5,6)... View Article

Write a square – b square formula.

The formula for a square – b square is given as:a2 – b2 = (a – b)(a + b)

Prove that angles opposite to equal sides of an isosceles triangle are equal.

Given:An isosceles triangle ABC where AC = BC.To prove: ∠CAB = ∠CBA.Construction:CD, the bisector of ∠ACB. Proof:Now in ∆ACD and... View Article

1 trillion is how many billion?

Billion = 1,000,000,000Ten billion – 10,000,000,000Hundred billion – 100,000,000,000Trillion – 1,000,000,000,000That means, 1 trillion is 1000 billion.

What is the value of 21 cube?

21 cube can be written as (21)3.(21)3 = 21 × 21 × 21(21)3 = 9261Therefore, the value of the 21... View Article

Find the HCF of 170 and 238 using prime factorization of 170 and 238.

The prime factorization of 170 = 2 × 5 × 17 The prime factorization of 238 = 2 × 7... View Article

Write any three different forms of the formula (a + b)^2.

We know that,(a + b)2 = a2 +b2 + 2abIn mathematics, the algebraic identity (a + b)2 can be defined... View Article

Use the divisibility rule to check the divisibility of 23457 by 4.

The divisibility rule of 4 states that if the last two digits of the number is divisible by 4 or... View Article

What is the prime factorization of 3780?

Prime factorization of 3780 = 2 x 2 x 3 x 3 x 3 x 5 x 7= 22 ×... View Article

If r = 7 cm and θ = 60°, then find the perimeter of the minor sector.

Given,r = 7 cmθ = 60°Perimeter of the minor sector = 2r + (θ/360°) 2πr= 2(7) + (60°/360°) × 2... View Article

A chord of a circle of radius 10 cm subtends a right angle at the centre, then the area of the minor segment is (a) 78.5 (b) 28.5 (c) 50 (d) 128.5

Correct answer: (b) 28.5Solution:Let O be the centre of the circle.OA = OB = radius Given,OA = OB = 10... View Article

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