On dividing the given number by 119, let k be the quotient and 19 as remainder.

Then, number = 119k + 19

= 17 × 7k + 17 × 1 + 2

= 17 (7k + 1) + 2

Hence, the given number when divided by 17, gives (7k + 1) as quotient and 2 as remainder.

Number just greater than 3 which is divisible by 7 = 7

Number just smaller than 200 which is divisible by 7 = 196

Here, a = 7, a_n = 196,

d = 7, n = 8

a_n = a + (n –1)d

⇒196 = 7 + (n – 1) × 7

⇒ 

⇒ n = 27 + 1 = 28

Note : We can find the answer after dividing 200 by 7. The quotient is our answer.

Let the required number of persons be x.

According to the question, 2x² = 3042

Or

or 

Let number (dividend) be X.

∴ X = 296 × Q + 75 where Q is the quotient and can have the values 1, 2, 3 etc.

= 37 × 8 × Q + 37 × 2 + 1

= 37 (8Q + 2) + 1

Thus we see that the remainder is 1.

[Remark : When the second divisor is a factor of the first divisor, the second remainder is obtained by dividing the first remainder by the second divisor.

Hence, divide 75 by 37, the remainder is 1].

India has decided to purchase 12 Sukhoi SU-30 MKI fighter aircraft.

1. Reason behind the purchase: To enhance and modernize the strength of the Indian Air Force.

2. Manufacture of aircraft: In India by Hindustan Aeronautics Limited (HAL).

3. Price: ₹11,000 crore.

4. Use of aircraft: In both air-to-air and air-to-ground attacks.

5. Impact: To enhance India's defence capabilities and strengthen it as a regional power.

Recently, Rahul Mishra was honoured with France's “Chevalier de l'Ordre des Arts et des Lettres” award.

1. This award has been given to Assam Chief Minister Himanta Biswa Sarma in Singapore.

2. Name of the Award: Lee Kuan Yew Exchange Fellowship

3. Awardee: Government of Singapore

4. Reason for the award: For his role in furthering the cause of development and international harmony

Khadi and Village Industries Commission has recently entered into agreements with the following entities to promote Khadi products:

A. Prasar Bharati
 1. Objective: To increase awareness about Khadi products
 2. Method: Prasar Bharati will use all its media for advertising and promotion of Khadi products.

B. NBCC (India) Limited
 1. Objective: To help in the marketing of Khadi products
 2. Method: NBCC (India) Limited will use its national network to promote and sell Khadi products.

C. Digital India Corporation
 1. Objective: To develop an online marketplace for Khadi products
 2. Method: Digital India Corporation will develop an online marketplace for Khadi products.

These Mous are expected to increase the marketing and sales of Khadi products. This will boost the Khadi industry and provide employment opportunities to rural artisans.