Correct Answer: 3

Solution : $a+b+c=0$
$a^3+b^3+c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$
⇒ $a^3+b^3+c^3 - 3abc = 0$
⇒ $a^3+b^3+c^3 = 3abc$
⇒ $\frac{a^3+b^3+c^3}{abc} = 3$
⇒ $\frac{a^2}{bc} + \frac{b^2}{ac} + \frac{c^2}{ab} = 3$
Hence, the correct answer is 3.

Correct Answer: 10

Solution : Given number = 785$x$3678$y$ is divisible by 72, then the number must be divisible by 8 and 9.
785$x$3678$y$ is divisible by 8 if the last digit three-digit 78y is divisible by 8.
78$y$ is divisible by 8 if $y$ = 4
785$x$36784 is divisible

Correct Answer: incident

Solution : The correct choice is the third option.

Incident means an event or occurrence. This is the correct answer, as it fits the context of the sentence, describing that the demonstration occurred without any noteworthy events or occurrences.

The meanings of the other options are as

Correct Answer: 25

Solution : Let's check the given options –
First option: 25 is not divisible by 3.
Second option: 15; 15 ÷ 3 = 5 (It is divisible by 3)
Third option: 18; 18 ÷ 3 = 6 (It is divisible by 3)
Fourth option: 21; 21 ÷

Correct Answer: 5

Solution : Taking dice positions 1 and 2 with 3 as a common face,

Moving clockwise from the common face with 3,

Pairs of opposite numbers –

So, the face opposite to the face containing 1 is 5. Hence, the second option is correct.

Correct Answer: Kerala

Solution : The correct option is Kerala.

The first non-Congress government in India was formed in the state of Kerala. The 1957 Kerala Legislative Assembly election resulted in the formation of the first democratically elected communist government in the world, led by the Communist Party of

Correct Answer:

Solution : As per the mirror image properties, closer things appear close to the mirror in the reflection.
So, according to the above property and the information provided, the mirror is placed on the right side of the figure (on line AB). So, the left side of the

Correct Answer: Oxygen

Solution : The correct option is Oxygen.

Oxygen is said to be colourless in its elemental state. Composed of two linked oxygen atoms, oxygen gas (O₂) is typically colourless and transparent. We inhale oxygen when we breathe, and the air we breathe looks colourless to

Correct Answer: BDHIUV

Solution : Given:
SLOW : MPTX :: CAUGHT : ?

Arrange letters in alphabetical order and then add 1 in the positional value of SLOW, to obtain the required code –
SLOW→LOSW
L + 1 = M, O + 1 = P, S + 1 = T,

Correct Answer: 198

Solution : Given,
$x^4+\frac{1}{x^4}=1154$
Adding 2 on both sides,
$x^4+\frac1{x^4}+2=1154+2$
⇒ $(x^2)^2+(\frac1{x^2})^2+2\times x^2\times\frac1{x^2}=1156$
We know, $a^2+b^2+2ab=(a+b)^2$
⇒ $(x^2+\frac{1}{x^2})^2=1156$
⇒ $x^2+\frac{1}{x^2}=\sqrt{1156}$
⇒ $x^2+\frac{1}{x^2}=34$
Again, adding 2 on both sides,
⇒ $x^2+\frac{1}{x^2}+2=34+2$
⇒ $(x+\frac{1}{x})^2=36$
⇒ $x+\frac{1}{x}=6$
We know, $a^3+b^3=(a+b)(a^2-ab+b^2)$
⇒ $x^3+\frac{1}{x^3}=(x+\frac1x)(x^2-x\times\frac1x+\frac1{x^2})$
$= (x+\frac1x)(x^2+\frac1{x^2}-1)$
$= 6 × (34 – 1)