Given:

sin 60° cos 30° + tan 45° cos 60° sin 30°

Concept used:

Calculation:

sin 60° cos 30° + tan 45° cos 60° sin 30°

The correct answer is Alkyne.

Key Points

• A hydrocarbon in which two carbon atoms are joined by a triple bond is called an Alkyne.
• A hydrocarbon is an organic compound consisting entirely of hydrogen and carbon.

Important Points

• Alkane
  • These are organic compounds that consist entirely of single-bonded carbon and hydrogen atoms and lack any other functional groups.
  • General Formula- C_nH_2n+2
  • They are the principal constituent of gasoline and lubricating oils and are extensively employed in organic chemistry.
•  Alkene
  • These are a class of hydrocarbons unsaturated compounds with at least one carbon-to-carbon double bond.
  • General Formula-C_nH_2n
  • Alkenes are more reactive than alkanes due to the presence of the double bond.
  • They are used in the synthesis of alcohols, plastics, lacquers, detergents, and fuels as starting materials.
• Alkyne
  • These are organic molecules made of the functional group carbon-carbon triple bonds.
  • Chemical Formula-C_nH_2n−2
  • Alkynes are commonly used to artificially ripe fruits.

The correct answer is Kevlar.

Key Points

• Kevlar is the most commonly used material as armour for protection against bullets used in handguns because of its impact resistance, high strength, and low weight.
• These properties make kevlar an ideal material to be used in bullet-proof vests as compared to other materials.
• Kevlar is a synthetic material known for its high strength and resistance to impact, heat, and chemicals.
• It was developed by Stephanie Kwolek in 1965 while she was working at DuPont, a chemical company.
• Kevlar is a type of aramid fibre, which is a class of heat-resistant and strong synthetic fibres.
• Uses of Kevlar:
  • Aerospace: Kevlar is used in the construction of aircraft and spacecraft, where its lightweight and high-strength properties are valuable.
  • Sporting Goods: It's used in the production of sporting equipment such as helmets, gloves, and bicycle tyres.
  • Industrial Applications: Kevlar is employed in conveyor belts, hoses, and cables for its durability and resistance to abrasion.
  • Marine: Kevlar composites can be used in boat hulls for their strength and impact resistance

As per the given conditions:

As it can be seen that the persons started walking from the north direction.

Hence, the correct answer is "Option2: North".

The correct answer is Pakistan.

Key Points

• Hinglaj Mata-
  • Bhagwan Shiva's first wife Sati's Brahmrandhra fall in Hinglaj, so this place and Mata is known as Hinglaj.
  • She is worshipped by Chngla Khanp Musalman/ Charan Musalman.
  • She is also known as Changli Mai.
  • Her original temple is situated in Baluchistan in Pakistan.
  • In Rajathan her temples are:
    • Koyaliya cave, Siwana, Barmer
    • Fatehpur, Sikar
    • Beedasar, Churu
    • Lodrawa, Jaisalmer
    • Arai, Ajmer
  • Hinglaj Mata' sal is situated between the Ghadseesar pond.
  • She is the favorite goddess of Pushkarna samaj in Jaisalmer.

Additional Information

• Maudra, Jalore place is related to Ashapura Mata.
• Bhunas, Nagore place is related to Jamway Mata.
• Rewasa, Sikar place is related to Jeen Mata.

A alone can finish the work in 48 days

A’s one day work = 1/48

Remaining work = 1 – [1/9] = 8/9

B complete 8/9 work in = 6 days

⇒ B complete whole work in = 6 × [9/8] = 27/4 days

⇒ B alone can finish 4 times the same work in = [27/4] × 4 = 27 days

Important Points

• The first six letters are common in each word: I, D, E, N, T, I.
• So, we will compare the words from the seventh letter of the word.

Given order: Identify, Identifier, Identifiable, Identikit, Identity

Dictionary order: Identifiable < Identifier < Identify < Identikit < Identity.

Hence, the correct answer is 3 - 2 - 1- 4 - 5.

Concept:

sin²x + cos²x = 1

Calculation:

Given: sin x + sin² x = 1

As we know that, sin2x + cos2x = 1

⇒ sin x + (1 – cos² x) = 1

⇒ sin x = cos² x ----(1)

⇒ sin² x = cos⁴ x (Using (1)) 

⇒ cos² x + cos⁴ x = sin x + sin² x = 1

The Pattern followed here is:-

Hence, 19 is the wrong term.