Correct Answer: 0.016

Solution : Given: The two parallel sides of a trapezium are 27 cm and 13 cm respectively.
Height = 8 cm
$\therefore$ Area of the trapezium
= $\frac{1}{2}\times$ sum of parallel sides × distance between parallel side
= $\frac{1}{2}\times  (27 + 13) \times 8$
= $\frac{1}{2}\times  40 \times  8$
= $160$ cm²
= $\frac{160}{10000}$ m²
= $0.016$ m²
Hence, the correct answer is 0.016.

Correct Answer: 24

Solution : Let the distance the fort CD be $x$.
(Hypotenuse)² = (Base)² + (Perpendicular)² 
⇒ 25² = (Base)² + (16 – 9)² 
⇒ (Base)² = 625 – 49 = 576
⇒ Base = 24 cm
So, the distance between the forts is 24 cm.
Hence, the correct answer is 24.

Correct Answer: fair

Solution : The correct choice is the second option.

Explanation: "Just" refers to fairness, impartiality, or being in accordance with what is morally right or lawful. Among the options provided, "fair" aligns most closely with this meaning. It signifies treating everyone equally and without bias, just like "just" does.

The meanings of the other options are as follows:

Courtly means polite, refined, or elegant in behaviour
Favourite means something that is inclined towards or shows preference for.
Partial means biased or showing favouritism.

Therefore, the correct answer is fair.

Correct Answer: 735

Solution : Checking the factors of all the options for divisibility by 5 and 7.
35 = 5 × 7
175 = 5 × 5 × 7
1225 = 5 × 5 × 7 × 7
735 = 5 × 7 × 7 × 3
735 has a factor of 3 other than 5 and 7.
$\therefore$ 735 is not a factor of $5^p7^q$.
Hence, the correct answer is 735.

Correct Answer: UK and Turkey

Solution : According to given pie chart in question,
Percentage of exports to the United States = 8.40%
Percentage of exports to United Kingdom and Turkey = (4.4 + 4)% = 8.4%
Hence, the correct answer is the UK and Turkey.

Correct Answer: Gas Authority of India (GAIL)

Solution : The correct answer is the Gas Authority of India Limited (GAIL).

GAIL was given the responsibility of the construction, operation, and maintenance of the Hazira-Vijaipur-Jagdishpur (HVJ) pipeline project. It is India's first interstate gas pipeline.

The HVJ is a 1700 km long gas pipeline. It is significant for India since it connects Mumbai and Bassein to western and northern India.

Correct Answer:

Solution : When the given folded paper is unfolded, it will look like this –

Hence, the third option is correct.

Correct Answer: 15

Solution : The correct option is 15

There are two categories for Indian miniratna companies: Category I and Category II. Companies eligible for II mini Ratna status must have a positive net worth and have generated profits for the past three years. There are 15 such businesses in total. Minivans falling under Category II are permitted to invest up to Rs. 300 crore or 50% of their net worth in capital projects without needing permission from the government.

Correct Answer: 50 m due north

Solution : First, we will draw the diagram, as per the given instructions –

Here, A is the starting point and F is the finishing point.
AB = 40 m; CD = 35 m; EF = 25 m
BF = CD – EF
BF = 35 – 25
BF = 10 m
Now, find the distance between his final position (F) and his house (A) –
AF = AB + BF
AF = 40 + 10
AF = 50 m

So, the distance between his final position and his house is 50 m, and he is in the north direction of his house. Hence, the second option is correct.

Correct Answer: $4x-\sqrt{3}$

Solution : $4\sqrt{3}x^{2}+5x-2\sqrt{3}$
= $4\sqrt{3}x^{2}+8x-3x-2\sqrt{3}$
= $4x(\sqrt{3}x+2)-\sqrt{3}(\sqrt{3}x+2)$
= $(4x-\sqrt{3})(\sqrt{3}x+2)$
Hence, the correct answer is $4x-\sqrt{3}$.