Correct Answer: 0

Solution : Given: $a+b=1$ (equation 1)
We know that the algebraic identities are $(a-b)^2=a^2+b^2-2ab$, $(a^3+b^3)=(a+b)(a^2-ab+b^2)$ and $(a^2-b^2)=(a+b)(a-b)$.
So, $a^4+b^4-2a^2b^2-a^3-b^3+ab$
$=(a^2-b^2)^2-(a^3+b^3)+ab$
$=(a+b)^2(a-b)^2-(a+b)(a^2-ab+b^2)+ab$
Substituting the value from equation 1 in the above expression we get,
$a^4+b^4-2a^2b^2-a^3-b^3+ab=(a-b)^2-a^2+ab-b^2+ab$
$=(a-b)^2-(a^2-2ab+b^2)$
$=(a-b)^2-(a-b)^2=0$
Hence, the correct answer is 0.

Correct Answer:

Solution : Males encompass both brothers and fathers, thus their circles will be contained within the larger circle of males. Additionally, there may be overlap as a brother can also be a father, and a father can also be a brother.
Therefore, the Venn diagram will be as

Correct Answer: pa hz

Solution : Given:
1. travel for fun is coded as dv pa vi
2. fun will begin  is coded as cr dv em
3. will travel today is coded as vi cr hz

By comparing all the three coded sentences, we find that –
In sentences

Correct Answer:

Solution : As per mirror image properties, closer things appear closer to the mirror in reflection.
According to the information provided, if the mirror is placed on the right side of the figure, the right of the reflected image will appear as the left, and the left will

Correct Answer: By Law

Solution : The Correct Answer is-  by law

Liberty is defined as the law-abiding exercise of one's freedom without obstructing the rights of others. The removal of freedom is a form of punishment.  It can, however, be limited by law or restricted in specific situations where

Correct Answer: H₂SO₄

Solution : The correct option is Sulphuric acid.

Sulphur is mostly used in the production of sulphuric acid (H2SO4). Sulpuric acid is one of the most commonly used industrial chemicals in the world, with uses ranging from metallurgy to petroleum refining, battery production, water

Correct Answer: I

Solution : Given:

First option: I ; Vowel

Second option: N ; Consonant

Third option: W ; Consonant

Fourth option: H ; Consonant

Here, only I is vowel.

Hence, first option is correct.

Correct Answer: 338

Solution : Given:
242, 288, ?, 392, 450

Multiply the square of the consecutive natural numbers (starting from 11) by 2 to get the terms given in the series.
(11)² × 2 = 121 × 2 = 242
(12)² × 2 = 144 × 2

Correct Answer: Rain water

Solution : The correct answer is Rain Water.

Rainwater is formed by the condensation of water in the presence of the sun. Water evaporates from water bodies on earth. The impurities in water are removed during the vaporization process, and then that water falls directly on

Correct Answer: 729

Solution : Given: $\left ( \frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right )=0$
⇒ $xy + yz+zx = 0$
Given: $x+y+z = 9$
We know, $x^{3}+y^{3}+z^{3}-3xyz = \left ( x+y+z \right )\left ( x^{2}+y^{2}+z^{2}-xy-yz-zx \right )$
⇒ $x^{3}+y^{3}+z^{3}-3xyz = \left ( x+y+z \right )\left (\left ( x+y+z \right )^{2}-3\left ( xy+yz+zx \right