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Question : The ratio of the curved surface area of two cones is 1 : 4 and the ratio of slant height of the two cones is 2 : 1. What is the ratio of the radius of the two cones?
Option 1: 1 : 2
Option 2: 1 : 4
Option 3: 1 : 8
Option 4: 1 : 1
Correct Answer: 1 : 8
Solution : The curved surface area of a cone $ = \pi rl$ where \(r\) is the radius and \(l\) is the slant height of the cone. Given that the ratio of the curved surface areas of two cones = 1 : 4 $⇒\frac{\pi r_1
Question : If $\tanθ + \cotθ = 2$, $\theta$ is an acute angle, then find the value of $2 \tan^{25}θ + 3 \cot^{20}θ + 5 \tan^{30}θ \cot^{15}θ$.
Option 1: 8
Option 2: 6
Option 3: 10
Option 4: 12
Correct Answer: 10
Solution : Given: The value of the trigonometric equation is $\tanθ + \cotθ = 2$ where $θ$ is an acute angle. $\tanθ + \cotθ = 2$ ⇒ $\tan 45^{\circ} + \cot45^{\circ} = 2$ ⇒ $\theta = 45^{\circ}$ The value of the trigonometric expression $2 \tan^{25}45^{\circ} + 3
Question : Directions: Which of the following numbers will replace the question mark (?) and complete the given number series? 2, 12, 144, 2592, ?
Option 1: 62108
Option 2: 62208
Option 3: 62204
Option 4: 63408
Correct Answer: 62208
Solution : Given: 2, 12, 144, 2592, ?
The pattern is as follows –
So, 62208 is the missing number of the series. Hence, the second option is correct.
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the following sets. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed.) (4, 9, 16) (25, 36, 49)
Option 1: (49, 64, 81)
Option 2: (1, 16, 49)
Option 3: (36, 81, 49)
Option 4: (49, 36, 81)
Correct Answer: (49, 64, 81)
Solution : Given: (4, 9, 16); (25, 36, 49)
The given numbers are squares of consecutive natural numbers – ⇒ (4, 9, 16)→22 = 4; (2 + 1)2 = 32 = 9; (3 + 1)2 = 42 = 16 ⇒
Question : Which organic compound has a pleasant almond aroma that is commonly used to impart almond flavour to chocolate and baked goods?
Option 1: Manzanate
Option 2: Benzaldehyde
Option 3: Ethyl maltol
Option 4: Isoamyl acetate
Correct Answer: Benzaldehyde
Solution : The correct option is Benzaldehyde.
Benzaldehyde is an organic compound with the chemical formula C7H6O. This colourless liquid possesses a distinctive almond-like fragrance and flavour. It is celebrated for its sweet, nutty and delightful almond scent and taste. Benzaldehyde serves
Question : Directions: In a certain code language, SETTLE is coded as DLSTDS. What is the code for STRUCK in that code language?
Option 1: JCTRST
Option 2: JCTRSS
Option 3: JCTSRS
Option 4: JTCRSS
Correct Answer: JCTRSS
Solution : Given: SETTLE is coded as DLSTDS.
Subtract 1 from the place value of the second, fourth, and sixth letters of SETTLE and the remaining letters will remain the same and then reverse the order of the letters as shown to obtain the code –
Thus,
Question : Which of the following is an example of contact force?
Option 1: Electrostatic force
Option 2: Muscular force
Option 3: Gravitational force
Option 4: Magnetic force
Correct Answer: Muscular force
Solution : The correct answer is Muscular force.
Contact force is the force generated when two things come into contact with each other. Here, non-contact forces such as gravitational, magnetic, and electrostatic can act at a distance without making physical contact with the object. On
Question : Identify an organism that exhibits metagenesis.
Option 1: Obelia
Option 2: Spongilla
Option 3: Sycon
Option 4: Euspongia
Correct Answer: Obelia
Solution : The correct option is Obelia.
Obelia is a type of hydrozoan, and its life cycle involves alternating between a sexually reproducing medusa stage and an asexually reproducing polyp stage. Metagenesis is a phenomenon in the life cycle of certain organisms where they undergo the
Question : Select the correct passive form of the given sentence.
He drank a lot of coffee before the marathon.
Option 1: A lot of coffee was drunk by him before the marathon.
Option 2: A lot of coffee is drunk by him before the marathon.
Option 3: A lot of coffee was drunken by him before the marathon.
Option 4: A lot of coffee had been drunk by him before the marathon.
Correct Answer: A lot of coffee was drunk by him before the marathon.
Solution : The first option is the correct answer.
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
Question : Improve the underlined part of the sentence. Choose 'No improvement' as an answer if the sentence is grammatically correct. His father was few proud of his power over the horse.
Option 1: No improvement
Option 2: much proudest
Option 3: very proud
Option 4: very proudly
Correct Answer: very proud
Solution : The correct answer is the third option.
The underlined part of the sentence is improved by adding the word "very" to convey a stronger degree of pride. The addition of "very" enhances the intensity of the pride his father feels. This modification results in
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