Exams › JEE Advanced › Maths
The four interior angles of a quadrilateral are in arithmetic progression. If the common difference is 10 degrees, find the smallest angle.
- 60 degrees
- 70 degrees
- 120 degrees
- 75 degrees
Correct answer: 75 degrees
Solution
Let the four angles in AP be: a, a+10, a+20, a+30. Their sum = 4a + 60 = 360, so a = 75 degrees. The smallest angle is 75 degrees.
Related JEE Advanced Maths questions
- If a, b, and c are in harmonic progression, then e raised to the power of -a, e raised to the power of -b, and e raised to the power of -c will be in which progression?
- If x, y, and z represent the pᵗʰ, qᵗʰ, and rᵗʰ terms of both an arithmetic progression and a geometric progression, what is the value of (xʳ)(yᵖ)(zᵠ)?
- Let ϕ(x) represent a quadratic polynomial. Given that ϕ(1) equals ϕ(−1) and the terms a₁, a₂, a₃ form an arithmetic progression, then the values ϕ(a₁), ϕ(a₂), ϕ(a₃) will be in which sequence?
- Let Sₙ = Σ (k+1)/2 * k². Then Sₙ can take value(s)
- If a, b, and c are positive integers such that b is divisible by a, and they form a geometric sequence, while their arithmetic mean equals b + 2, what is the value of (a² + a - 14)/(a + 1)?
- Let bᵢ > 1 for i = 1, 2,..., 101. Assume that logₑb₁, logₑb₂,..., logₑb₁₀₁ form an arithmetic sequence with a common difference of log₂. Also, let a₁, a₂,..., a₁₀₁ form an arithmetic sequence where a₁ = b₁ and a₅₁ = b₅₁. If t represents the sum b₁ + b₂ +... + b₅₁ and s represents the sum a₁ + a₂ +... + a₅₁, then which of the following is true?
⚔️ Practice JEE Advanced Maths free + battle 1v1 →