Correct Answer: LNQW

Solution : Let's check each option –

First option: EGKQ; G – E = 2; K – G = 4; Q – K = 6; The difference between the letters follows the increasing order of the even numbers.
Second option: CEIO; E – C = 2; I – E = 4; O – I = 6; The difference between the letters follows the increasing order of the even numbers.
Third option: LNQW; N – L = 2; Q – N = 3; W – Q = 6; The difference between the letters does not follow the increasing order of the even numbers.
Fourth option: PRVB; R – P = 2; V – R = 4; B – V = 6; The difference between the letters follows the increasing order of the even numbers.

So, LNQW is different from the other three. Hence, the third option is correct.

Correct Answer: 9

Solution : Given:
1. She was working is written as 592
2. I was curious is written as 267
3. She is curious is written as 987

By comparing, all three coded sentences –
 In sentences 1 and 2, was and 2 are common.
In sentences 1 and 3, she and 9 are common.
In statements 2 and 3, curious and 7 are common.
The remaining word and code in sentence 1 are working and 5; in sentence 2 are I and 6; in sentence 3 are is and 8.

So, she will be coded as 9. Hence, the first option is correct.

Correct Answer: $300(\sqrt3 - 1)$ m

Solution :
$AB$ = height of peak = 300 m
$CD$ = length of Bridge
We are given the angle of depression,
i.e., $\angle EAC = 45°$ and $\angle EAD = 30°$
⇒ $\angle ACB = 45°$ and $\angle ADB = 30°$
Now, \(In \triangle ABC\)
\(\tan\theta = \frac{P}{B}\)
\(\tan45 ^{\circ} =\frac{AB}{BC}\)
\(1=\frac{AB}{BC}=AB:BC=1:1\)
\(In\ \triangle ABD,\)
⇒ \(\tan30 ^{\circ} =\frac{AB}{BD}\)
⇒ \(\frac{1}{\sqrt{3}}=\frac{AB}{BD}\Rightarrow AB:BD=1:\sqrt{3}\)
Now,
\(CD = BD - BC\)
⇒ \(CD \Rightarrow \sqrt{3}-1\)
$AB$ = 1 unit = 300 metre
So, $CD=(\sqrt{3}-1)$ units = $300(\sqrt{3}-1)$ metres
Hence, the correct answer is $300(\sqrt3 - 1)$ m.

Correct Answer: Rs. 1052

Solution : Given: Principal = Rs. 800, Amount = Rs. 956, and Time = 3 years
Rate of interest, $R$ = 4% for extra interest
Use the formula below.
Extra Simple Interest = $\frac{\text{Principle×Rate×Time}}{100}$ 
= $\frac{800×3×4}{100}$
= Rs. 96
So, the total amount received = 956 + 96 = Rs. 1052
Hence, the correct answer is Rs. 1052.

Correct Answer: OPR – JKL

Solution : Let's check each option –
First option: OPR – JKL;  The opposite letter of O is not J; the opposite letter of P is K; and the opposite letter of R is not L.
Second option: BFX –  YUC;  The opposite letter of B is Y; the opposite letter of F is U; and the opposite letter of X is C.
Third option: PHJ –  KSQ;  The opposite letter of P is K; the opposite letter of H is S; and the opposite letter of J is Q.
Fourth option: RTV –  IGE; The opposite letter of R is I; the opposite letter of T is G; and the opposite letter of V is E.

Therefore, the first option is different from the others as it does not have opposite letters. Hence, the first option is correct.

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.