Correct Answer: (16, 26, 31)

Solution : Given:
(3,13,18), (29, 39, 44)
Add 10 to the first number to get the second number and add 5 to the second number to get the third number –
⇒ (3,13,18)→3 + 10 = 13, 13 + 5 = 18
⇒ (29, 39, 44)→29 + 10 = 39, 39 + 5 = 44

Let's check each option –
First option: (17, 27, 42)→17 + 10 = 27, 27 + 5 = 32 ≠ 42
Second option: (25, 30, 55)→25 + 10 = 35 ≠ 30, 30 + 5 = 35 ≠ 55
Third option: (26, 30, 47)→26 + 10 = 36 ≠ 30, 30 + 5 = 35 ≠ 47
Fourth option: (16, 26, 31)→16 + 10 = 26, 26 + 5 = 31

So, only the fourth option follows the same pattern as followed by the given set of numbers. Hence, the fourth option is correct.

Correct Answer: (1)

Solution : The correct answer is the first option.

Farther should be replaced with further to convey the intended meaning that if he requires additional help, he should be directed to the speaker.

Farther is used to signify physical distance, whereas further is used to refer to something additional to what already exists. Hence, further would be a more appropriate choice for this sentence. The other options, much and best do not go contextually with the sentence.

Therefore, the correct sentence is, "If he wants further help, send him to me".

Correct Answer: 3

Solution : $(a + b + c)^{2} = a^{2}  + b^{2} + c^{2} + 2(ab + bc + ca)$
$⇒(a + b + c)^{2} -3(ab + bc + ca) = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca) –3(ab + bc + ca)$
Putting the values of $a, b,$ and $c$, we get,
$⇒(101 + 102 + 103)^{2}-3(101 \times 102 + 102 \times 103 + 103\times 101) = a^{2} + b^{2} + c^{2} - (ab + bc + ca)$
$⇒a^{2} + b^{2} + c^{2} -ab - bc - ca = 306^2 -3(10302 + 10506 + 10403)$
$⇒a^{2} + b^{2} + c^{2} -ab - bc - ca = 93636 -3(31211)$
$⇒a^{2} + b^{2} + c^{2} -ab - bc - ca = 93636 -93633$
$\therefore a^{2} + b^{2} + c^{2} -ab - bc - ca= 3$
Hence, the correct answer is 3.

Correct Answer:

Haliotis

Solution : The correct option is Haliotis.

"Haliotis" refers to the phylum Mollusca and the genus of sea mollusks usually known as abalones. Abalones are gastropod mollusks prized for their iridescent shells, which are frequently utilised in food and ornamental arts. The term "hyla" typically refers to a genus of tree frogs, and these animals belong to the animal kingdom (Kingdom: Animalia). "Hydra" belongs to the phylum Cnidaria. Hares are mammals, specifically from the family Leporidae, and they are closely related to rabbits.

Correct Answer: 11 cm

Solution :
TP = 15 cm
PB = 2$x$ + 3 cm
PA = 9 cm
If a secant AB and tangent at the point T of a circle intersect at a point T of a circle intersect at a point P outside the circle, then PA × PB = PT²
9 × (2$x$ + 3) = 15²
⇒ 2$x$ + 3 = $\frac{225}{9}$ = 25
⇒ $x$ = $\frac{25-3}{2}$ = 11
Hence, the correct answer is 11 cm.

Correct Answer: 4

Solution : There is no error in the sentence. 

The sentence is devoid of any grammatical or idiomatic errors. It conveys frustration and a strong resolve to depart. The subject, verb, and tenses are synchronised with each other.

Correct Answer: 51A

Solution : The Correct Option is 51A.

Fundamental duties were suggested by the Swaran Singh Committee in 1976, and their importance became apparent during the internal emergency of 1975–1977. Ten Fundamental Duties were introduced to the Indian Constitution by the 42nd Amendment Act of 1976. Later, the 11th Fundamental Duty was added to the list by the 86th Amendment Act of 2002.

Correct Answer:

Solution : According to the given figures, two types of patterns are followed alternatively –
1. The first two elements are interchanging their positions and the last two elements are interchanging their positions respectively.
2. The first two elements are interchanging their positions with the last two elements.

So, following the above pattern, the required figure will be as follows –

Therefore, the figure in the second option is the required figure. Hence, the second option is correct.

Correct Answer: (20, 18, 16)

Solution : Given: 
(36, 24, 65); (40, 54, 19)

The pattern followed here is –
(36, 24, 65) = {(36 ÷ 4) + (24 ÷ 6)} × {(36 ÷ 4) – (24 ÷ 6)}
= {9 + 4} × {9 – 4}
= 13 × 5
= 65
(40, 54, 19) = {(40 ÷ 4) + (54 ÷ 6)} × {(40 ÷ 4) – (54 ÷ 6)}
= {10 + 9} × {10 – 9}
= 19 × 1 
= 19
Let's check the options –
First Option: (10, 21, 321) = {(10 ÷ 4) + (21 ÷ 6)} × {(10 ÷ 4) – (21 ÷ 6)}
= {2.5 + 3.5} × {2.5 – 3.5}
= 6 × –1 
= –6 ≠ 321
Second Option: (20, 18, 16) = {(20 ÷ 4) + (18 ÷ 6)} × {(20 ÷ 4) – (18 ÷ 6)}
= {5 + 3} × {5 – 3}
= 8 × 2 
= 16
Third Option: (13, 8, 98) = {(13 ÷ 4) + (8 ÷ 6)} × {(13 ÷ 4) – (8 ÷ 6)}
= {3.25 + 1.33} × {3.25 – 1.33}
= 4.58 × 1.92
= 8.7936 ≠ 98
Fourth Option: (30, 14, 56) = {(30 ÷ 4) + (14 ÷ 6)} × {(30 ÷ 4) – (14 ÷ 6)}
= {7.5 + 2.33} × {7.5 – 2.33}
= 9.83 × 5.17
= 50.8211 ≠ 56

So, only the second option follows the same pattern as followed by the given set of numbers. Hence, the second option is correct.

Correct Answer: neutron

Solution : The correct option is neutron.

The neutron has the greatest mass among the proton, neutron, electron, and nucleus of hydrogen. The mass of a proton is 1.672621777(74) × 10^-27 kg. The mass of a neutron is 1.674927498(94) × 10^-27 kg. The mass of an electron is 9.1093837015(28) × 10^-31 kg. The mass of a hydrogen nucleus is 1.674927498(94) × 10^-27 kg. A neutron's mass is somewhat larger than that of a proton. An electron's mass is substantially lower than that of a proton or neutron. Because a hydrogen nucleus contains just one proton, its mass is the same as that of a proton.