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Question : If the area of the non-spherical portion of a solid hemisphere is 1,560 m2, then the total surface area of the hemisphere is:
Option 1: 6,240 m2
Option 2: 4,680 m2
Option 3: 5,140 m2
Option 4: 3,120 m2
Correct Answer: 4,680 m2
Solution : Given: The area of the non-spherical portion of a solid hemisphere is 1560 m2. So, $\pi r^2=1560$ --------------(1) The total surface area of the hemisphere = $3\pi r^2$ where $r$ is the radius. Substitute the value of $\pi r^2$ from the
Question : If $\frac{\cos \alpha}{\sin \beta} = 10$ and $\frac{\cos \alpha}{\cos \beta} = 11$, the value of $\cos ^2 \beta$ is:
Option 1: $\frac{121}{132}$
Option 2: $\frac{100}{221}$
Option 3: $\frac{88}{108}$
Option 4: $\frac{221}{121}$
Correct Answer: $\frac{100}{221}$
Solution : Given: $\frac{\cos \alpha}{\sin \beta} = 10$ and $\frac{\cos \alpha}{\cos \beta} = 11$ ⇒ ${\cos \alpha} = 10\ {\sin \beta}$ and ${\cos \alpha} = 11\ {\cos \beta}$ ⇒ $10\ {\sin \beta} = 11\ {\cos \beta}$ ⇒ $\frac{\sin \beta}{\cos \beta} = \frac{11}{10}$ ⇒ ${\tan \beta} = \frac{11}{10}$
Question : Which of the following green houses gases has the greatest heat trapping ability?
Option 1: Chlorofluro carbon
Option 2: Methane
Option 3: Carbon dioxide
Option 4: Nitrous oxide
Correct Answer: Carbon dioxide
Solution : The correct option is Carbon dioxide.
Carbon dioxide (CO2) has the highest potential to trap heat among greenhouse gases. It is a major contributor to the greenhouse effect, which causes the Earth's surface and atmosphere to warm. Other greenhouse gases, such as methane and
Question : Which among the following is an example of a micro-economic variable?
Option 1: National income
Option 2: Aggregate supply
Option 3: Employment
Option 4: Consumer's equilibrium
Correct Answer: Consumer's equilibrium
Solution : The correct answer is the Consumer's equilibrium.
Microeconomics is a branch of economics that focuses on individual economic agents, such as consumers and corporations, and their interactions within specific marketplaces. One of the important microeconomic variables is the consumer's equilibrium. It refers to the
Question : The largest number of four digits that is exactly divisible by 17 and 36 is:
Option 1: 7956
Option 2: 9180
Option 3: 9792
Option 4: 8568
Correct Answer: 9792
Solution :
LCM of 17 and 36 is 612. The largest four-digit number is 9999. To find the largest four-digit number divisible by 17 and 36 we have to divide the 9999 by 612 and subtract the remainder from 9999. When we divide the 9999 by 612,
Question : Directions: Which number will replace the question mark (?) in the given series? 55, 68, 81, 94, ?, 120
Option 1: 105
Option 2: 107
Option 3: 111
Option 4: 109
Correct Answer: 107
Solution : Given: 55, 68, 81, 94, ?, 120
Add 13 in each number to obtain the required code – 55 + 13 = 68; 68 + 13 = 81; 81 + 13 = 94; 94 + 13 = 107; 107 + 13 = 120
So, the
Question : Rohit buys an old bat for Rs. 1280 and spends Rs. 120 on its repair. If he sells it for Rs. 1050, then what is the loss percentage?
Option 1: 40 percent
Option 2: 25 percent
Option 3: 20 percent
Option 4: 30 percent
Correct Answer: 25 percent
Solution : The total cost of the bat including the repair = Rs. 1280 + Rs. 120 = Rs. 1400 If Rohit sells the bat for Rs. 1050, then his loss = Rs. 1400 – Rs. 1050 = Rs. 350 $\therefore$ The loss percentage = $\frac{\text{Loss}}{\text{
Question : In September 2021, the Pension Fund Regulatory and Development Authority (PFRDA) increased the entry age for the National Pension System (NPS) from____ to______.
Option 1: 60 to 65 years
Option 2: 65 to 70 years
Option 3: 62 to 65 years
Option 4: 62 to 70 years
Correct Answer: 65 to 70 years
Solution : The correct option is 65 to 70 years.
The Pension Fund Regulatory and Development Authority (PFRDA) is responsible for promoting and developing pension funds, protecting the interests of subscribers to pension funds, and ensuring the orderly growth of the pension sector
Question : Directions: Which of the following letters will replace the question mark (?) in the given series? T, Q, N, K, H, ?
Option 1: R
Option 2: E
Option 3: O
Option 4: P
Correct Answer: E
Solution : Given: T, Q, N, K, H, ?
Subtract 3 from the place value of each letter to get the next letter – T – 3 = Q; Q – 3 = N; N – 3 = K; K – 3 = H; H – 3
Question : If the radius of a hemispherical balloon increases from 4 cm to 7 cm as air is pumped into it, find the ratio of the surface area of the new balloon to its original.
Option 1: 16 : 21
Option 2: 49 : 16
Option 3: 20 : 49
Option 4: 21 : 12
Correct Answer: 49 : 16
Solution : The surface area of a hemisphere = $3 \pi r^2$ The radius of the balloon before pumping air, $r_1$ = 4 cm The radius of the balloon after pumping air, $r_2$ = 7 cm The surface area of the balloon before pumping air,
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