Archives

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)... View Article

Write a square – b square formula.

The formula for a square - b square is given as:a2 - b2 = (a - b)(a + b)... View Article

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 ∆BCD... 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.... View Article

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 cube is 9261.... 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 × 17HCF of 170 and 238 = 2 × 17 = 34... 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 in different three ways as given below.1. The... 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 00, the number will be divisible by 4.Given... 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 × 33 × 51 × 71... 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 × (22/7)... 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 cmCentral angle = θ = 90°Area of... View Article

ABCD is a rectangle, AC and BD are diagonals. Prove that diagonals are equal.

Given: Rectangle ABCD such that AC and BD are diagonals. To prove: AC = BD Proof: We know that the opposite sides of rectangle are equal. AB... View Article

What are the points on the x-axis whose perpendicular distance from the line x/3 + y/4 = 1 is 4 units?

Given equation of line: x/3 + y/4 = 14x + 3y = 124x + 3y - 12 = 0And the point on the x-axis will be (x, 0).We know that the distance of a point... View Article

If three different coins are tossed together, what is the probability of getting two heads?

Three different coins are tossed together.Total outcomes = {(HHH), (THH), (HTH), (HHT), (TTT), (TTH), (THT), (HTT)}i.e. n(S) = 8Let E be the... View Article

Find the sets A and B if A/B = {1, 5, 7, 8}, B/A = {2, 10} and A ∩ B = {3, 6, 9}. Are they unique?

Given,A/B = {1, 5, 7, 8}B/A = {2, 10}A ∩ B = {3, 6, 9}Thus, A = (A/B) U (A ∩ B)= {1, 5, 7, 8} U {3, 6, 9}= {1, 3, 5, 6, 7, 8, 9}B = (B/A)... View Article

In the given figure, ∆OBA ~ ∆ODC, ∠BOC = 125° and ∠CDO = 70°. Find teh value of ∠OAB.

Figure: Solution:Given,∆OBA ~ ∆ODC Thus, ∠ODC = ∠OBA = 70° {corresponding angles of similar triangles)AOC is a straight line.∠AOB... View Article

Find the derivative of (3x^2 + 5)sin x.

Let y = (3x2 + 5)sin x Differentiating with respect to x on both sides, dy/dx = (d/dx) [(3x2 + 5) sin x] Using the product rule of... View Article

In triangle ABC, prove that cos(A/2) + cos(B/2) + cos(C/2) = 4. cos(π – A)/4. cos(π – B)/4. cos(π – C)/4.

In triangle ABC,A + B + C = πFrom this we can write the following:π - A = B + Cπ - B = A + Cπ - C = A + BNow, consider the RHS,=... View Article

ABC is an equilateral triangle with each side of length 2p. If AD ⊥ BC, find the value of AD.

Given,ABC is an equilateral triangle with each side of length 2p.That means, AB = BC = CA = 2pAlso, AD ⊥ BCAs we know, in an equilateral... View Article

Prove that (sin θ – cos θ + 1)/(sin θ + cos θ – 1) = 1/(sec θ – tan θ).

LHS = (sin θ - cos θ + 1)/(sin θ + cos θ - 1) Dividing the numerator and denominator by cos θ, = [(sin θ/cos θ) - (cos θ/cos θ) + (1/cos θ)] /... View Article