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Question : The median of an equilateral triangle is $6\sqrt3$ cm. The area (in cm2) of the triangle is:
Option 1: $72$
Option 2: $108$
Option 3: $72\sqrt3$
Option 4: $36\sqrt3$
Correct Answer: $36\sqrt3$
Solution : Given: Median = AD = $6\sqrt3$ cm Let AB = BC = CA = $a$ cm So, $\frac{\sqrt3}{2}a$ = $6\sqrt3$ ⇒ $a$ = $12$ cm Now, the area of $\triangle$ABC = $\frac{\sqrt3}{4}×a^2$ = $\frac{\sqrt3}{4}×12×12$ = $36\sqrt3$ cm2 Hence, the correct answer is $36\sqrt3$.
Question : Directions: A series is given below with one term missing. Choose the correct alternative from the given ones that will complete the series. BDF, CFI, DHL, ?
Option 1: EJO
Option 2: GJM
Option 3: EML
Option 4: EMI
Correct Answer: EJO
Solution : Given: BDF, CFI, DHL, ?
In the given series, add 1, 2, and 3 to the place value of the letters of the previous term to obtain the next term – BDF→B + 1 = C; D + 2 = F; F + 3 =
Question : If the areas of two similar triangles are in the ratio 196 : 625, what would be the ratio of the corresponding sides?
Option 1: 14 : 25
Option 2: 13 : 20
Option 3: 14 : 20
Option 4: 13 : 25
Correct Answer: 14 : 25
Solution : Ratio of Areas = 196 : 625 If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. ⇒ Ratio of sides = $\sqrt{\text{area}{_1}}:\sqrt{\text{area}{_2}}=\sqrt{196}:\sqrt{625}= 14 : 25$ Hence,
Question : Directions: Rama is taller than Saho. Manoj is shorter than Dinesh. Dinesh is taller than Tara but shorter than Saho. Kailash is shorter than Tara but taller than Manoj. Tara is shorter than Saho. Who is the shortest?
Option 1: Dinesh
Option 2: Kailash
Option 3: Tara
Option 4: Manoj
Correct Answer: Manoj
Solution : Given: I. Rama is taller than Saho. Tara is shorter than Saho. Dinesh is taller than Tara but shorter than Saho. Rama > Saho > Dinesh > Tara II. Manoj is shorter than Dinesh. Kailash is shorter than Tara but taller than Manoj. Dinesh >
Question : Vihaan is twice as efficient as Mayur and can finish a piece of work in 14 days less than Mayur. In how many days Mayur can finish this work?
Option 1: 14 days
Option 2: 21 days
Option 3: 28 days
Option 4: 7 days
Correct Answer: 28 days
Solution : Let the time taken by Mayur to finish the work be $x$ days. Vihaan is twice as efficient as Mayur, he can finish the work = $\frac{x}{2}$ days According to the problem, $\frac{x}{2} = x - 14$ ⇒ $x = 2x - 28$ ⇒
Question : Directions: In the following question, select the related number from the given alternatives. 8 : 64 :: 27 : ?
Option 1: 64
Option 2: 81
Option 3: 212
Option 4: 125
Correct Answer: 125
Solution : Given: 8 : 64 :: 27 : ?
Like, 8 : 64→23 = 8; 43 = 64 Similarly, for 27 : ?→33 = 27; 53 = 125
So, 27 is related to 125. Hence, the fourth option is correct.
Question : The sum of all prime numbers between 58 and 68 is:
Option 1: 179
Option 2: 178
Option 3: 187
Option 4: 183
Correct Answer: 187
Solution : The prime numbers between 58 and 68 are 59, 61 and 67. 59 + 61 + 67 = 187. Hence, the correct answer is 187.
Question : The given sentence is in active voice. Change the voice of the sentence. Select the correct option from the sentences given in the options. I know he will play his guitar.
Option 1: His guitar will be played by him is something I know.
Option 2: It is known to me that his guitar would be played by him.
Option 3: It is known to me that his guitar will be played by him.
Option 4: His guitar will be played by him is know to me.
Correct Answer: It is known to me that his guitar will be played by him.
Solution : The correct choice is the third 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
Question : Select the most appropriate meaning of the given idiom. Long in the tooth
Option 1: The show has come to an end
Option 2: Be optimistic, even difficult times will lead to better days
Option 3: To be old, often too old to do something
Option 4: Killing of a certain ethnic or religious group on a massive scale
Correct Answer: To be old, often too old to do something
Solution : The third option is the correct choice.
This idiom, long in the tooth is often used to humorously or colloquially describe someone who is ageing or has been around for a long time, implying that they may
Question : Select the most appropriate meaning of the underlined idiom in the given sentence. His probation was extended because his performance was not up to the mark.
Option 1: lacking in maturity
Option 2: up to the required standard
Option 3: of the desired height
Option 4: more than expected
Correct Answer: up to the required standard
Solution : The correct choice is the second option.
Explanation: In the context provided, the phrase "not up to the mark" implies that the person's performance did not meet the required or expected standard. It means the performance fell short of the
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