Correct Answer: 6 cm

Solution : The total volume of the 24 solid hemispheres is equal to the volume of the cylinder.
The volume of the cylinder = $\pi r^2h$
Volume of the cylinder (height $h$, radius $r$) = $\pi(12)^2 × 24 = 144 × 24\pi$
Since the 24 solid

Correct Answer: Tanjore

Solution : The Correct Answer is Tanjore

Vijayalaya laid the foundation of the Chola Empire. He overthrew the Pallavas within the eighth century, took over the Tanjore kingdom, and paved the way for the establishment of the potent Chola kingdom. Under the Chola rulers, who ruled supremely

Correct Answer: 65 degree

Solution :
Given, ${O}$ is the orthocenter of this triangle, $\angle {K}=55$ degree and $\angle \mathrm{KOL}=120$ degree. 
In quadrilateral ${JMON}$,
$\angle KJL + 90^\circ + 90^\circ + \angle MON = 360^\circ$
⇒ $\angle KJL + 90^\circ + 90^\circ + 120^\circ = 360^\circ$
⇒ $\angle KJL =

Correct Answer: Rs. 1986

Solution : Principal, $P$ = Rs. 6000
Time, $t$ = 18 months = 1.5 years
Rate, $R$ = 20% per annum
Amount = $P(1+\frac{R}{100})^{nt}$, where $n$ is the number of times the interest is compounded per year
= $6000(1+\frac{\frac{20}{2}}{100})^{2 \times 1.5}$
= $6000 \times 1.10^3$
=

Correct Answer: 40%

Solution : Cost price of 24 bananas = Rs. 30
Selling price of 15 bananas at (Rs. 12 per dozen) = 12 + 3 = Rs. 15
Selling price of remaining 9 bananas at (Rs. 4 per dozen)
= Rs. $\frac{4}{12}$ × 9 = Rs. 3
Total

Correct Answer: Helium

Solution : The correct option is Helium.

Nobel gases are generally inert. Despite this, these gases are also odourless and colourless. Several noble gases form a group in the Periodic table. Helium is a noble gas.

Correct Answer: Birbal

Solution : The correct option is Birbal.

Birbal was the only Hindu courtier of Akbar who accepted Din-i-Ilahi. He was regarded for his wit, knowledge, and devotion to the emperor and was one of the Nine Jewels (Navaratnas) in Akbar's court. 

Correct Answer: 40

Solution : Cost price of 44 items = Selling price of $x$ items
Profit = 10%
Profit percentage = $\frac{\text{(Selling price – Cost price)}}{\text{Cost price}} \times 100$
$⇒ 10 =\frac{(44 - x)}{x} \times 100$
$⇒ x = 40$
Hence, the correct answer is 40.

Correct Answer: proportionate increase in consumption is less than a proportionate increase in income.

Solution : The correct answer is a proportionate increase in consumption is less than a proportionate increase in income.

According to the Psychological Law of Consumption, when income rises, consumption rises as well, although at

Correct Answer: $4 \sqrt{3}$

Solution : Given: $x^3=270+y^3$ and $x=(6+y)$
Putting the value of the $x=(6+y)$, we have:
⇒ $(6)^{3}+y^{3}+3×6×y(6+y)=270+y^{3}$
⇒ $216+y^{3}+18y(6+y)=270+y^{3}$
⇒ $108y+18y^{2}–54=0$
⇒ $y^{2}+6y–3=0$
The given quadratic equation is $y^{2}+6y-3=0$. 
$y = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$
⇒ $y = \frac{-6 \pm \sqrt{6^{2}-4(1)(-3)}}{2(1)}$
⇒ $y = \frac{-6 \pm \sqrt{48}}{2}$
⇒