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Example of transitive relation

Solution: A relation R on set A is called a transitive relation if (a, b)∈R, (b, c)∈R => (a, c)∈R for all a, b, c ∈ A.... View Article

Lcm of 7, 8, 11, and 12.

Solution: Prime factorisation of 7 = 71 Prime factorisation of 8 = 2×2×2 = 23 Prime factorisation of 11 = 111 Prime... View Article

The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has

(a) one solution (b) two solutions (c) infinitely many solutions (d) no solution Solution: Given 5x - 15y = 8 3x - 9y =... View Article

Prove that √6 is an irrational number.

Solution: Assume that √6 is rational. So it can be represented as a fraction. Let the lowest terms representation be √6 = a/b,... View Article

The equation x log x = 3-x has at least one root in the interval

Solution: We will have to draw the graphs of functions y = x logx and y = 3-x. The solution of the equation: x log x = 3-x will be given by the... View Article

What is ⁿP_r formula?

Solution: In nPr, P denotes permutation. This formula gives the number of ways of selecting and arranging r objects from the given n... View Article

How to integrate xe^x?

Solution: We have to find out ∫xex dx. We can make use of integration by parts. Take x = u Let ex = v ∫uv dx = u∫v -... View Article

The maximum value of 3×3 determinant whose elements are 0, 1.

Solution: Let D = = 0 - 1(0-1) + 1(1-0) = 0+1+1 = 2 Hence, the largest value of a third-order determinant whose elements are 0 or 1 is 2.... View Article

Evaluate 1211.04 root

Solution: We find the square root of 1211.04 using the long division method. Step 1: Place a bar over every pair of digits starting from the... View Article

Suppose x₁ and x₂ are the point of maximum and the point of minimum respectively of the function f(x) = 2x³ – 9ax² + 12a²x + 1 respectively, (a>0) then for the equality x₁² = x₂ to be true the value of a must be

(a) 0 (b) 2 (c) 1 (d) 1/4 Solution: Given f(x) = 2x3 - 9ax2 + 12a2x + 1 f’(x) = 0 => 6x2 - 18ax + 12a2 = 0 => x2 - 3ax... View Article

Find the prime factorisation of 735.

Solution: Prime factorisation is a way of expressing a number as a product of its prime factors. We can write 735 = 3×5×7×7... View Article

In a city 40% of the adults are illiterate while 85% of the children are literate If the ratio of the adults to that of the children is 2:3 then what percent of the population is literate?

Assume that, the number of adults and children are 2x and 3x respectively. From the given information, Literate Population = (100-40)%... View Article

Is 12 O’clock in the afternoon AM or PM?

Answer: AM (Ante-Meridiem) is a Latin term, used to indicate a 12-hour clock system before Noon. Also signifies before midday. It is a unit of... View Article

What does proportional relationship mean in math?

In Mathematics, the proportional relationship is defined as the relationship between two variables in which their ratios are equivalent. In... View Article

Sachin walks 20 km towards North. He turns left and walks 40 km. He again turns left and walks 20 km. Finally he moves 20 km after turning to the left. How far is he from his starting position?

According to the given information, the path formed is as follows: Hence, the required distance = (40 - 20) km = 20 km Hence, Sachin is 20... View Article

A man of height 1.5m sees the top of a tree and the angle of elevation of the top at his eye is 60°. Find the height of the tree if the distance of the man from the tree is 36m.

Given that, The distance of the man from the tree is 36 m. I.e., BC = DE = 36 m The height of the man = 1.5 m I.e., BD = CE = 1.5 m From... View Article

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