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Every rational number is a real number. Justify your answer

As we know, real numbers are the collection all the numbers such as natural and whole numbers, rational and irrational numbers. Since, we can... View Article

A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red? (ii) not red?

(i) Number of red balls = 3 Total number of balls = 3+5 = 8 Probability of getting red ball = 3/8 (ii) Probability of getting non-red balls = 5/8... View Article

6C2 how will we solve this?

6C2 = 6!/[2!.(6-2)!] = (6x5x4!)/(2x4!) = (6x5)/2 = 15... View Article

If three coins are tossed simultaneously, then find the probability of getting at least two heads.

If three coins are tossed, then the possible outcomes will be: (HHH), (HHT), (HTH), (THH), (TTT), (TTH), (THT),(HTT) Total outcomes = 8 Number... View Article

Integration of sin^7 x dx.

∫sin7 xdx We can write as: = ∫sin6x sinx dx = ∫(sin2x)3 sinx dx Since, sin2x = 1 - cos2x Thus, ∫(1−cos2x)3 sinxdx... View Article

Express 256 as a power of 4.

Given, the number is 256. By prime factorisation of 256, we get; 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 256 = 4 x 4 x 4 x 4 256 = 44... View Article

If both (x + 2) and (2x + 1) are factors of ax2 + 2x + b, then the value of a – b is?

Given, (x + 2) and (2x + 1) are factors of ax2 + 2x + b Now putting x = -2, in he equation. a(-2)2 + 2 (-2) + b = 0 4a - 4 + b = 0 4a - b = 4... View Article

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Diameter of the hemisphere is equal to edge of the cube Thus, diameter = side of cube = l Surface area of solid = Area of cube + Curved Surface... View Article

Represent 1/3 on the number line.

1/3 can be represented in the number line by dividing the space between 0 and 1 into three equal parts. Thus, 1/3, 2/3 and 3/3 (=1) are the... View Article

Write 343 in exponential form.

By prime factorization, we know; 343 = 7 × 7 × 7 = 7³ Thus, the exponential form of 343 is 7³.... View Article

Find multiplicative inverse of (1 + i).

Given, 1+i is a complex number. The multiplicative inverse of 1+i is 1/1+i. 1/(1+i) = (1-i)/(12 - i2) = (1-i)/(2) Since, i2 = -1 = 1/2... View Article

Is 10824 divisible by 11?

Given, 10824 is the number. Using the divisibility rule of 11. Sum of odd digits = 1 + 8 + 4 = 13 Sum of even digits = 0 + 2 = 2 Difference =... View Article

In which table 49 comes?

Factors of 49 are 1, 7 and 49. Therefore, 49 comes in the table of 1, 7 and 49.... View Article

Find the square root of 5625 by prime factorization method.

The prime factorisation of 5625 is: 5625 = 5×5×5×5×3×3 Taking the square root on both sides. =25×3 =75... View Article

The numerator of a fraction is 3 less than its denominator if 2 is added to both the numerator and denominator, then the sum of new fraction and the original fraction is 29/20. Find the original fraction.

Let the fraction be (x-3)/x As per the given condition, if 2 is added to both numerator and denominator, then; (x-3+2)/(x+2) = (x-1)/(x+2) Now,... View Article

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