Correct Answer: Rustom

Solution : The correct option is Rustom.

Akshay Kumar won the National Film Award for Best Actor for his performance in the film "Rustom." He received this award at the 64th National Film Awards held in 2017. "Rustom" is a crime thriller film released in 2016, and Akshay Kumar's portrayal of the character Rustom Pavri, a naval officer, earned him critical acclaim.

Correct Answer: Vartak

Solution : The correct option is Vartak.

The Nechiphu Tunnel excavation work falls under Project Vartak, one of the Border Roads Organisation's (BRO) most prominent projects. Project Vartak, established in 1960, is responsible for constructing, and maintaining roads in Arunachal Pradesh, and adjoining districts of Assam. The tunnel's construction significantly enhances connectivity in the region, particularly during harsh weather conditions.

Correct Answer: 0

Solution :
$A, B, C$, and $D$ are the angles of a quadrilateral and they are concyclic.
So, $\angle A+\angle C=\angle B+\angle D=180°$
$\angle A=180°–\angle C$
$\therefore\cos\ A=\cos(180°-C)=–\cos\ C$
Similarly, $\cos\ D=–\cos\ B$
$\cos\ A+\cos\ B+\cos\ C+\cos\ D$
$=\cos\ A+\cos\ B-\cos\ A-\cos\ B$
$=0$
Hence, the correct answer is $0$.

Correct Answer: Sikkim

Solution : The correct option is Sikkim.

Nearly half of India's bird species, wild trees, orchids, rhododendrons, and a third of the nation's floral plants can be found at Kanchenjunga National Park. The Indian state of Sikkim is home to Kanchenjunga National Park, often referred to as the Kanchenjunga Biosphere Reserve.

Correct Answer:

Solution : As per the mirror image properties, closer things appear closer to the mirror in the reflection.
So, according to the above property and the information provided, the mirror is placed on the top side of the figure (on line RS). So, the top side of the reflected image will appear as the bottom side and the bottom side will appear as the top side. However, the left and right of the reflected image will remain the same.

Thus, the correct mirror image of the given figure will be –

Hence, the fourth option is correct.

Correct Answer: (3)

Solution : The sentence can be improved using the third alternative.

"Under" is the correct preposition, which is to be used in place of "on" to correctly fit into the context of the sentence and convey its intended meaning i.e., she sat under the tree, meaning below the tree to protect herself from rain.

Therefore, the correct sentence is: She sat under the tree to protect herself from the rain.

Correct Answer: (4)

Solution : The fourth option is the correct choice.

The phrasal verb take off means to remove shoes from the feet, which is the intended meaning here.

The meanings of the other options are as follows:

• Put away means to store something.
• Extract means to obtain something.
• Put off means to postpone.

Therefore, the correct sentence is: "Take off your shoes before you enter the temple."

Correct Answer: 100 : 12

Solution :  Let's check the options –

First option: 297 : 33→33 × 9 = 297
Second option: 189 : 21→21 × 9 = 189
Third option: 100 : 12→12 × 9 = 108 ≠ 100
Fourth option: 63 : 7→7 × 9 = 63

So, only the third option doesn't follow the same pattern as followed by the given set of numbers. Hence, the third option is correct. 

Correct Answer: 13

Solution : Like in, the first tree, 4 × 3 = 12; 12 × 3 = 36
And in, the third tree, 8 × 2 = 16; 16 × 2 = 32
Similarly, in the second tree 13 × 1 = 13; 13 × 1 = 13

Therefore, the missing number is 13. Hence, the second option is correct.

Correct Answer: To promote equal justice and to provide free legal aid.

Solution : The correct option is To promote equal justice and provide free legal aid.

Article 39A of the Indian Constitution pertains to the promotion of equal justice and the provision of free legal aid. It states: The State shall secure that the operation of the legal system promotes justice on a basis of equal opportunity and shall, in particular, provide free legal aid, by suitable legislation or schemes or in any other way, to ensure that opportunities for securing justice are not denied to any citizen because of economic or other disabilities.