Correct Answer: 15,626

Solution : $(\frac{5}{b}+5 b)(\frac{25}{b^{2}}-25+25 b^2)$
This equation is in the form of $(x+y)(x^{2}–xy+y^{2})$
We know $x^{3}+y^{3}=(x+y)(x^{2}–xy+y^{2})$
So, $x = \frac{5}{b}$ and $y = 5b$
Putting the value of $b = 5$ we get,
$x^{3}+y^{3} = (\frac{5}{5})^{3} + (5\times 5)^{3}$
Or, $x^{3}+y^{3}= 1+15625 = 15626$
Hence, the correct

Correct Answer: Kesavananda Bharati Case, 1973

Solution : The correct answer is Kesavananda Bharati Case, 1973.

In the historic decision of Kesavananda Bharati v. State of Kerala, the Supreme Court of India established the notion of the "Basic Structure" of the Constitution. The date of this momentous ruling

Correct Answer: (27, 33, 40)

Solution : Given:
(82, 35, 78); (18, 27, 30)

In the given sets, divide the sum of the first two numbers by 3 and then multiply by 2 to get the third number.
(82, 35, 78)→{(82 + 35) ÷ 3} × 2 = {117 ÷

Correct Answer: 255.0548 cm²

Solution : Given: Steel is used to make a hemispherical bowl that is 0.37 cm thick.
The bowl's inner radius is 6 cm.
According to the formula,
⇒ Outer radius = 6 + 0.37 = 6.37 cm
$\therefore$ Curved surface area = 2 × 227

Correct Answer:

Solution : The correct answer is decreases.

According to centrifugal acceleration formulae, as angular speed increases, the net acceleration due to gravity decreases. As a result, the weight will reduce.
Alternatively, as the rotational speed of earth increases, the gravity at equator decreases and as a result the

Correct Answer: Disguised

Solution : The correct choice is the third option.

In the given sentence, the word concealed is used to convey the idea that truth cannot be hidden or kept secret from anyone. Among the options, disguised is the most suitable choice, as it implies altering the

Correct Answer: P – Q × R

Solution : Given:
X – Y means that X is the mother of Y.
X × Y means that X is the father of Y.
X ÷ Y means that X is the sister of Y.

Now, let's check the options –
First

Correct Answer: avail yourself of

Solution : The correct choice is the second option.

Avail yourself of is the correct idiomatic usage, which means to take advantage of. This helps convey the intended meaning that one should try to take advantage of every situation that comes one's way.

Therefore,

Correct Answer: $8 x^2(x+5)^2(x-1)$

Solution : Consider, $(8 x^3+80 x^2+200 x)$
Taking $8x$ as common, we get,
$=8x(x^2+10x+25)$
$=8x(x^2+5x+5x+25)$
$=8x(x(x+5)+5(x+5))$
$=8x(x+5)^2$
Now consider, $(4 x^4+16 x^3-20 x^2)$
Taking $4x^2$ as common, we get,
$=4x^2(x^2 + 4x-5)$
$=4x^2(x^2-x+5x-5)$
$=4x^2(x(x-1)+5(x-1))$
$=4x^2(x-1)(x+5)$
$\therefore$ LCM $=8x^2(x+5)^2(x-1)$
Hence, the correct answer is $8x^2(x+5)^2(x-1)$.

Correct Answer: $72^\circ$

Solution : From the pie chart provided:
Total production = 220 + 240 + 180 + 160 + 200 = 1000
Production in Kerala = 200
Central angle = $\frac{\text{Production in kerala}}{\text{Total production}}\times 360^\circ$
= $\frac{200}{1000}\times 360^\circ$
= $72^\circ$
Hence, the correct answer is $72^\circ$.