Correct Answer: $1$

Solution : If $A + B + C = 90°$, then $\tan A\tan B + \tan B\tan C + \tan C\tan A = 1$
Now, 27 + 34 + 29 = 90°
So, $\tan 27^{\circ} \tan 34^{\circ} + \tan 34^{\circ} \tan 29^{\circ} + \tan 29^{\circ} \tan 27^{\circ}=1$
Hence, the correct answer is 1.

Correct Answer: Collar cells

Solution : The correct answer is Collar cells.

Choanocytes, also called collar cells, are special cells that cover the inside of the central cavity (spongocoel) and canals in sponges. These cells have tiny, hair-like structures called flagella. The flagella move in a coordinated way to create a flow of water that goes in one direction, towards the opening at the top called the osculum. This flow helps the sponge filter and collect nutrients from the water, kind of like a natural water pump for the sponge.

Correct Answer:

Solution : In the given figure, follow the directions to find the next term –

Hence, the first option is correct.

Correct Answer: Shirts are not bought by him.

Solution : The correct choice is the first 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 the subject in the passive voice. 

The structure of the passive sentence in the simple present tense is: Object + are + not + past participle form of the verb + by + agent of action.

So, the correct sentence is: Shirts are not bought by him.

Correct Answer: 991026973

Solution : Here, (997)³ = (1000 – 3)³
= 1000³ – 3³ – 3 × 1000 × 3 × (1000 – 3) [Using the formula (a – b)³ = a³ – b³ – 3ab(a – b)]
= 1000000000 – 27 – 9000(997)
= 991026973
Hence, the correct answer is 991026973.

Correct Answer: The difference between gross national product and depreciation is net national product.

Solution : The correct answer is The difference between gross national product and depreciation is net national product.

The term "net national product" refers to gross national product, which is the total market value, less depreciation, of all finished goods and services generated by a nation's or other polity's factors of production over a specific period. As a result, NNP is equal to national income, or the total amount of money that can be spent on goods and services in the economy. The net national product is the amount that remains after depreciation, which subtracts it from the gross national product.

Correct Answer: Baikal rocks are formed from the dissolved materials that precipitate from the solution

Solution : The correct option is Baikal rocks are formed from the dissolved materials that precipitate from the solution.

The rocks around Lake Baikal in Siberia, Russia, are primarily of igneous origin. Lake Baikal is known for its unique geological and environmental features, but the formation of rocks in the region is not primarily related to the precipitation of dissolved materials from solutions.

Correct Answer: aptitude for

Solution : The most appropriate option to substitute the underlined segment is the first option.

For is the correct preposition to use with "aptitude" when referring to a skill or talent in a particular field or activity.

Therefore, the correct sentence is, "The young boy displayed an aptitude for scientific research."

Correct Answer: 100489

Solution : The least six-digit number is 100000.
Using the long division method to find its square root, we see that it is not a perfect square.
⇒ (316)² = (100000 – 144) = 99856, a 5-digit number.
But (317)² = 100489, a 6-digit number.
Therefore, the smallest six-digit number which is also a perfect square is 100489.
Hence, the correct answer is 100489.

Correct Answer: BACD

Solution : The third option is the correct choice.

Firstly, sentence B sets the stage by introducing Alessandro, his age, and his activity of wandering among the bushes. Sentence A details Alessandro's encounter with the bear, emphasising his knowledge of how to handle the situation. Sentence C describes Alessandro's mother's reaction and the boy's response to maintain silence, creating tension in the narrative. Finally, sentence D concludes the sequence by explaining the outcome—once Alessandro safely enters his house, the bear stops following him, resolving the potential threat.