Correct Answer:

Solution : Because there is no restriction on the rotation of the figure, we will check all the possible angles where the question figure can fit itself in the given option figures.
By comparison of all the option figures, the given question figure is embedded only in the third option figure.

Hence, the third option is correct.

Correct Answer: Ionic

Solution : The correct answer is Ionic.

The interaction that takes place in ionic compounds is called ionic bonding, which is a kind of chemical bonding that involves the electrostatic attraction between oppositely charged ions or between two atoms with dramatically differing Electronegativity.

Correct Answer: 135

Solution : Let the number of failed students be $x$.
Total marks obtained = 180 × 50 = 9000
According to the question,
40$x$ + (180 – $x$) × 80 = 9000
⇒ 40$x$ + 14400 – 80$x$ = 9000
⇒ 40$x$ = 5400
⇒ $x$ = 135
Hence, the correct answer is 135.

Correct Answer: 3

Solution : The total export for the five years = 10.4 + 13 + 15.6 + 21.6 + 18.8 = 79.4 lakh tons of rice
$\therefore$ The average yearly export = $\frac{79.4}{5}$ = 15.88 lakh tons of rice per year.
The exports were less than the average in three years: 2010, 2011, and 2012.
$\therefore$ The export of rice was less than the average export in 3 years.
Hence, the correct answer is 3.

Correct Answer: 820

Solution : According to the question,
$a + b$ = 10 and $ab$ = 6
⇒ $(a + b)^{2}$ = 102
⇒ $a^{2} + 2ab + b^{2}$ = 100
⇒ $a^{2} + 2(6) + b^{2}$ = 100
⇒ $a^{2} + 12 + b^{2}$ = 100
⇒ $a^{2} + b^{2}$ = 88
Now,
⇒  $a^{3} + b^{3} = (a + b)(a^{2} − ab + b^{2})=(10)(88 − 6)=10 × 82$ = 820 
Hence, the correct answer is 820.

Correct Answer: An inflexible person who is hard to convince

Solution : The correct choice is the second option.

The idiom hard nuts to crack refers to individuals who are difficult to understand, persuade, or influence. They are resistant to change or persuasion, making it challenging to get them to agree or cooperate.

Therefore, the correct answer is, an inflexible person who is hard to convince.

Correct Answer: Mendicant

Solution : The correct answer is the fourth option.

The term "mendicant" is a one-word substitute that accurately represents the given phrase "one who goes from place to place, begging." A mendicant is an individual, often associated with a religious order, who survives by asking for alms or charity. 

The meanings of the other options are as follows:

• A misogamist is a person who dislikes marriage.
• Malleable means someone who is capable of being shaped or influenced, usually referring to something flexible or adaptable.
• Meticulous means showing great attention to detail and being very careful and precise in work or tasks.

Therefore, the correct answer is mendicant.

Correct Answer: HWJS

Solution : Given:
PORK, NQPM, LSNO, JULQ, ?

In the above-given series, subtract 2 from the place values of the first and third letters, and add 2 to the place values of the second and fourth letters to obtain the next letter cluster.
PORK→P – 2 = N; O + 2 = Q; R – 2 = P; K + 2 = M
NQPM→N – 2 = L; Q + 2 = S; P – 2 = N; M + 2 = O
LSNO→L – 2 = J; S + 2 = U; N – 2 = L; O + 2 = Q
JULQ→J – 2 = H; U + 2 = W; L – 2 = J; Q + 2 = S

So, HWJS is the missing term of the series. Hence, the third option is correct.

Correct Answer: 105°

Solution :
According to the given figure in question,
Given $\angle$AOE = 150° and $\angle$DAO = 51°
Now, $\angle$EOB + $\angle$AOE = 180°
⇒ $\angle$EOB = 180° – 150° = 30°
Also, OE = OB
⇒ $\angle$OEB = $\angle$OBE = $\frac{150}{2}$ = 75°
⇒ $\angle$CBE = 180° – 75° = 105°
Hence, the correct answer is 105°.

Correct Answer: Rink

Solution : Given:
Wrestling : Arena :: Ice–Skating : ?

The second term is an area where the sport given in the first term has been played –
Like in, Wrestling : Arena → The area where wrestling is played is known as Arena.
Similarly, follow the same pattern for Ice–Skating : ? → The area where the Ice–Skating is played is known as the Rink.

So, the rink is related to the king in the same way as the convent is related to the nun. Hence, the second option is correct.