Correct Answer: 32

Solution : Given, $8 a^3+27 b^3=16$ and $2 a+3 b=4$
Consider $8 a^3+27 b^3=16$
⇒ $(2a)^3+(3b)^3=16$
⇒ $(2a+3b)(4a^2-6ab+9b^2)=16$
⇒ $(4)(4a^2-6ab+9b^2)=16$
⇒ $4a^2-6ab+9b^2=4$ ......(1)
Now, consider $2a+3b=4$
Squaring both sides, we get,
⇒ $(2a+3b)^2=4^2$
⇒ $4a^2+12ab+9b^2=16$ ......(2)
Solving (1) and (2), we get,
$18 ab=12$
⇒ $ab=\frac{2}{3}$
And,

Correct Answer:

Solution : As per the mirror image properties, closer things appear closer 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 AB). So, the left side of the reflected image will appear

Correct Answer: Art classes for children were being taken by a ten-year-old girl.

Solution : The correct choice is the fourth option.

Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active voice becomes

Correct Answer: $\sqrt[6]{25}<\sqrt[3]{9}<\sqrt[4]{20}$

Solution : Given: The numbers are $\sqrt[3]{9}$, $\sqrt[4]{20}$, $\sqrt[6]{25}$.
LCM of 3, 4, and 6 = 12
$⇒ \sqrt[3]{9}=9^{\frac{1}{3}}=9^{\frac{4}{12}}=\sqrt[12]{6561}$
$⇒ \sqrt[4]{20}=20^{\frac{1}{4}}=20^{\frac{3}{12}}=\sqrt[12]{8000}$
$⇒ \sqrt[6]{25}=25^{\frac{1}{6}}=25^{\frac{2}{12}}=\sqrt[12]{625}$
By comparing these values, we get:
$\sqrt[12]{625}<\sqrt[12]{6561}<\sqrt[12]{8000}$
$⇒\sqrt[6]{25}<\sqrt[3]{9}<\sqrt[4]{20}$
Hence, the correct answer is $\sqrt[6]{25}<\sqrt[3]{9}<\sqrt[4]{20}$.

Correct Answer: sawdust is a poor conductor of heat

Solution : The correct answer is sawdust is a poor conductor of heat.

Heat conducts poorly through the sawdust. Heat is insulated by the air that is present in sawdust's tiny pores. This air prevents heat from the environment from reaching

Correct Answer: Undersea Waves

Solution : The correct answer is Undersea waves.

Tsunami are high energy tidal waves which originate under the sea because of undersea volcanic eruption. Tsunami waves are not visible in ocean water but when they strike continental shelf their height goes on increasing, having a dangerous

Correct Answer: 48%

Solution : The average production of fertilisers by country Z in 2017, 2018 and 2020
= $\frac{330+360+420}{3}$
= $\frac{1110}{3}$
= $370$
The average production of fertilisers by country X in 2018 and 2020
= $\frac{240+260}{2}$
= $\frac{500}{2}$
= $250$
Required percentage = $\frac{370-250}{250}\times100=\frac{120}{250}\times 100= 48\%$
Hence, the

Correct Answer: Rs. 920

Solution : Given: A trader marks his goods in such a way that after allowing a discount of 10%, he gains 15% and his cost price is Rs. 720.
Let the marked price = 100 units
Discount = 10%
So, the selling price = (100 –

Correct Answer: (A), (B), (D), (C)

Solution : Given:

(A) Necrology

(B) Necromancy

(C) Necropolis

(D) Necrophilia

Start from Necrology because l comes before m

Necrology

Now, write Necromancy because m comes before p

Necromancy

Now, write Necrophilia because h comes before o

Necrophilia

Correct Answer: BEJQZ

Solution : Let's check the option–

First option: ADGJM
A + 3 = D; D + 3 = G; G + 3 = J; J + 3 = M 
This option does not follow the given pattern.

Second option: BEJQZ
B + 3 = E; E +