JEE Main 24 Jan Shift 2 2024 Question Paper with Solution PDF- Download Here

The plane parallel to (x - 2y + 2z - 5 = 0) has the same normal vector ((1, -2, 2)). Using the formula for the distance from a point to a plane and ensuring it is 1 unit away from the origin, the correct equation is (x - 2y + 2z - 3 = 0).

Using the formula for projectile motion, the horizontal range R is given by:

R = (u^2 * sin(2θ)) / g

For a maximum height of 10 m, we calculate the initial velocity u to be approximately 14.0 m/s. With the optimal angle of 45 degrees, the horizontal range is about 20 m.

Calculate the differences between consecutive terms:

36 - 10 = 26, 68 - 36 = 32, 130 - 68 = 62.

The differences are increasing by a certain pattern: 32 - 26 = 6, 62 - 32 = 30.

The next difference is 30 + 24 = 54. Adding this to the last term (130), the missing number is 130 + 54 = 184.

The digit 3 appears in:

• One-digit numbers: Only 3 itself (1 time).
• Two-digit numbers: 10 numbers for each position (tens and units), giving 18 occurrences.
• Three-digit numbers: For each hundreds digit (except 3), tens and units can each have 10 values, giving 270 occurrences.

Total = 1 + 90 + 270 = 300.

Vicuna is a natural fiber obtained from the Vicuna animal, unlike synthetic fibers such as Nylon, Acrylic, and Polyester.

The President of the United States lives in the White House, located at 1600 Pennsylvania Avenue NW, Washington, D.C. It serves as the official residence and workplace of the President.

Downing Street is the official residence of the Prime Minister of the United Kingdom. The Prime Minister resides and works at 10 Downing Street, located in London.

The Notre Dame Cathedral, officially known as Notre-Dame de Paris, is located in Paris, France. It is situated on the Île de la Cité, a small island in the Seine River.

Shalimar Bagh in Srinagar, India, was built by Emperor Jahangir in 1619 for his wife Nur Jahan. It was originally named "Farah Baksh" ("the delightful").

The Moti Masjid in the Red Fort was built by Mughal Emperor Aurangzeb for personal use. It is well-known for its white marble, intricate floral carvings, and elegant proportions.

The beautiful white exterior of the Lotus Temple in Delhi is made of Pentelikon Marble, a specific type of marble from Mount Penteli in Greece. This type of marble has also been used in iconic landmarks like the Parthenon.

The architect of the Sydney Opera House was Jørn Utzon, a Danish architect who won an international design competition in 1957. His innovative design features shells made of precast concrete segments, making it an iconic structure.

Load transfer to the earth in buildings follows a Gravity Load Path:

• Slabs and Beams: Transfer weight to supporting beams.
• Columns and Walls: Beams transfer accumulated load to columns or walls.
• Foundation: Columns and walls transfer the load to the foundation, which distributes it to the soil.

Concrete is made up of the following components:

• Cement: Acts as the binding agent, typically Portland cement.
• Water: Activates the cement for hydration and binding.
• Air: May be intentionally added for improved workability.
• Sand: A fine aggregate providing strength and stability.
• Gravel: A coarse aggregate forming the skeleton of the concrete.

LEED stands for Leadership in Energy and Environmental Design. It is a widely used green building rating system providing a framework for creating environmentally efficient and cost-effective buildings.