Correct Answer: 6 and 5, – and ×

Solution : Given:
18 – 6 + 11 × 5 + 18 = 113

Replace the symbols and numbers given in the equation with the assigned symbols and numbers in the options one by one –
First option: 6 and 5, + and ×
⇒ 18 – 5 × 11 + 6 × 18 = 113
Solving the L.H.S of the equation –
= 18 – 5 × 11 + 6 × 18
= 18 – 55 + 108
= 71 ≠ 113
Second option: 18 and 5, + and ×
⇒ 5 – 6 × 11 + 18 × 5 = 113
Solving the L.H.S of the equation –
= 5 – 6 × 11 + 18 × 5
= 5 – 66 + 90
= 95 – 66
= 29 ≠ 113
Third option: 6 and 5, – and ×
⇒ 18 × 5 + 11 – 6 + 18 = 113
Solving the L.H.S of the equation –
= 18 × 5 + 11 – 6 + 18
= 90 + 11 – 6 + 18
= 119 – 6
= 113
Fourth option: 18 and 5, – and ×
⇒ 5 × 6 + 11 – 18 + 5 = 113
Solving the L.H.S of the equation –
= 5 × 6 + 11 – 18 + 5
= 30 + 11 – 18 + 5
= 46 – 18
= 28 ≠ 113

So, only the third option satisfies the equation. Hence, the third option is correct.

Correct Answer: Bankim Chandra Chattopadhyay 

Solution : Correct Answer is Bankim Chandra Chattopadhyay 

Vande Mataram is a Sanskrit poem written by Bankim Chandra Chatterjee. It is included in the Bengali novel ‘Anandamath’. The poem was later made the national song of the country. The poem was written by Bankim Chatterjee. The national song ‘Vande Mataram’ was composed by him. The poem was a great inspiration for the people of the country in their fight for freedom. The poem has the same status as the national anthem of the country.

Correct Answer: NCWN

Solution : Given:
NMQR, NQYD, NUGP, NYOB, ?

In the given series, the first letter (N) is constant. Add 4, 8, and 12 to the place value of the first, second, third, and fourth letters.
NMQR→N; M + 4 = Q; Q + 8 = Y; R + 12 = D
NQYD→N; Q + 4 = U; Y + 8 = G; D + 12 = P
NUGP→N; U + 4 = Y; G + 8 = O; P + 12 = B
NYOB→N; Y + 4 = C; O + 8 = W; B + 12 = N

So, the missing term is NCWN. Hence, the third option is correct.

Correct Answer: 87.5%

Solution : Given: The cost price is INR 20 per kg.
The selling price is INR 30 per kg.
So, the profit percentage if he sold 1 kg $=\frac{10}{20}\times 100 = 50$%
Now, the gain as a result of the incorrect weight:
$=\frac{\text{Error}}{\text{True weight – Error}}\times 100$
$=\frac{200}{1000 – 200}\times 100$
$=\frac{200}{800}\times 100$
$= 25$%
The actual profit percentage:
$=P_{1}+P_{2}+\frac{P_{1}\times P_{2}}{100}$
$=50 + 25 + \frac{50\times 25}{100}$
$=75 + 12.5$
$=87.5$%
Hence, the correct answer is 87.5%.

Correct Answer: Shri Sreedharan

Solution : The correct option is - Shri Sreedharan

Elattuvalapil Sreedharan is an Indian engineer and politician best known for overseeing the Delhi Metro and the Konkan Railway. In charge of the Delhi Metro Rail Corporation (DMRC) from 1995 to 2012, he served as managing director. He is referred to as the Metro Man.

Correct Answer: 15th August, 1947

Solution : The correct option is - 15th August, 1947

India attained Dominion Status on August 15, 1947. This status marked India's transition from being a colony under British rule to a self-governing, independent nation within the British Commonwealth. The Indian Independence Act of 1947, passed by the British Parliament, provided the legal framework for this transition. This act granted India the status of a dominion, which meant that it had full control over its domestic and foreign affairs, except in areas where it chose to remain associated with the British Crown. On that day, India's first Prime Minister, Jawaharlal Nehru, raised the Indian flag above the Lahori Gate of the Red Fort in Delhi, marking the birth of independent India.

Correct Answer: Mahatma Gandhi

Solution : The correct option is Mahatma Gandhi.

During the Quit India Movement in 1942, Mahatma Gandhi encouraged people with the powerful slogan "Do or Die". This movement was an important step in India's fight for independence from British rule. Gandhi urged Indians to use non-violent means and take strong action to achieve freedom, even if it meant facing serious challenges.

Correct Answer: chloroform

Solution : The correct option is chloroform.

Chloroform is the most popular term for trichloromethane, which is also known as formyl trichloride and methane trichloride. A member of the class of volatile organic compounds (VOC), trichloromethane is a chlorinated organic chemical. It is an odourless, colourless liquid that is very flammable.

Correct Answer: 104

Solution : Given:
MADRAS is written as 112 and JAMMU is written as 82.

Add the reverse position values of the letters of the word MADRAS then add the total number of letters in the word to obtain the required code –
M→14; A→26; D→23; R→9; A→26; S→8
Now, add the reverse position values of the word MADRAS then add the total number of letters in the word –
14 + 26 + 23 + 9 + 26 + 8 = 106 + 6 = 112
Thus, MADRAS is coded as 112.
And, JAMMU is written as 82 –
J→17; A→26; M→14; M→14; U→6
Now, add the reverse position values of the word JAMMU then add the total number of letters in the word –
17 + 26 + 14 + 14 + 6 = 77 + 5 = 82
Thus, JAMMU is coded as 82.
Similarly, follow the same pattern for PUNJAB – 
P→11; U→6; N→13; J→17; A→26; B→25
Now, add the reverse position values of the word PUNJAB then add the total number of letters in the word –
11 + 6 + 13 + 17 + 26 + 25 = 98 + 6 = 104

So, PUNJAB is coded as 104. Hence, the second option is correct.

Correct Answer: 50 km

Solution :
By Pythagoras theorem,
$(AC)^2 = (AB)^2+(BC)^2$
⇒ $(AC)^2=(14)^2 + (48)^2$
⇒ $(AC)^2 = 196+ 2304$
⇒ $AC = \sqrt{2500}$
⇒ $AC = 50\ \mathrm{km}$
Hence, the correct answer is 50 km.