Correct Answer: 2

Solution : Given:
The sum of squares of two numbers = 12
Product of the numbers = 4
Let the numbers be $a$ and $b$.
⇒ $a^2+b^2=12$ and $ab = 4$
We know, $(a-b)^2=a^2+b^2-2ab$
⇒ $(a-b)^2=12-2\times4$
⇒ $(a-b)^2=12-8$
⇒ $(a-b)^2=4$
⇒ $a-b=\sqrt4=2$
Hence, the correct answer is

Correct Answer: ABCD

Solution : The correct choice is the fourth option.

A. Isabel saw a strange rabbit running through the bushes. (Introducing the initial action or event)
B. Following it, she found a door, which she opened with the help of keys. (Continuation of the action initiated

Correct Answer: 60

Solution : The correct answer is 60.

The Real Estate Regulatory Authority (RERA) is a governing organization that serves as a quick dispute resolution mechanism and is established by the Real Estate Act of 2017 in each state to regulate the real estate industry. Under this Act

Correct Answer: DGCIPB

Solution : Given:
ANSWER is coded as APPWGO

Follow the pattern to obtain the code –

Thus, ANSWER is coded as APPWGO.
Similarly, follow the same pattern for DEFINE –

So, DEFINE is coded as DGCIPB. Hence, the first option is correct.

Correct Answer: 1

Solution : $A+\frac{1}{A}=-1$ ⇒ $A^2+A+1=0$
Now,
$A^3-1^3 = (A-1) (A^2+A+1)$ 
⇒$A^3-1 = (A-1)\times 0$ 
⇒$A^3-1 =0$ 
⇒$A^3=1$
So, $\frac{{A}^6+{A}^3-1}{{~A}^9+{A}^3-1}$
$=\frac{{(A^3)}^2+{A}^3-1}{{(A^3)}^3+{A}^3-1}$
$=\frac{1^2+1-1}{1^3+1-1}$
$= 1$
Hence, the correct answer is 1.

Correct Answer: Balaghat

Solution : The correct option is Balaghat.

The Balaghat district in Madhya Pradesh is a leading producer of copper in India. It is home to the Malanjkhand copper deposit, which is one of the largest copper deposits in the country. The Malanjkhand Copper Project, operated by

Correct Answer: 10

Solution : Let the rate be $r$.
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
So, interest from B = $\frac{10000×3×r}{100}=300r$
Also, interest from C = $\frac{6000×4×r}{100}=240r$
According to the question,
⇒ $300r+240r = 5400$
⇒ $540r = 5400$
$\therefore r =10\%$
Hence, the correct

Correct Answer: $\frac{1}{2}(x+y+z)$

Solution : By polynomial identity
$x^3+y^3+z^3−3xyz = (x+y+z)(x^2+y^2+z^2−xy−yz−zx)$ 
= $\frac{1}{2}(x+y+z)(2x^2+2y^2+2z^2−2xy−2yz−2zx)$
= $\frac{1}{2}(x+y+z)(x^2−2xy+y^2+y^2−2yz+z^2+z^2−2xz+x^2)$
= $\frac{1}{2}[(x+y+z)(x−y)^2+(y−z)^2+(z−x)^2]$
$\therefore \frac{x^3+y^3+z^3-3 x y z}{(x-y)^2+(y-z)^2+(z-x)^2}$ = $\frac{\frac{1}{2}[(x+y+z)(x−y)^2+(y−z)^2+(z−x)^2]}{(x-y)^2+(y-z)^2+(z-x)^2}$ = $\frac{1}{2}(x+y+z)$
Hence, the correct answer is $\frac{1}{2}(x+y+z)$.

Correct Answer: 3

Solution : The error lies in the third part of the sentence because 'is it' should be replaced with 'it is' in order to follow parallelism in case of correlative conjunction neither......nor.

Therefore, the correct sentence should be "Acceptance is not about allowing everything to occur or

Correct Answer:

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