Solution of Triangles JEE Advanced Previous Year Questions Chapter Wise Subjective Type with Answer Key & Solution
Question 1: Let ABC and ABC’ be two non congruent triangles with sides AB = 4, AC = AC’ = 2√2 and angle B = 30ᵒ. The absolute value of the difference between the areas of these triangles is. {IIT JEE 2009}.
Answer: the absolute value of the difference between the areas of these triangles is 4.
Solution:
Question 2: If SinA SinB SinC + CosA CosB = 1, then the value of SinC is equal to. {IIT JEE 2006}.
Answer: the value of SinC is equal to 1.
Solution:
Question 3: In a triangle ABC, a:b:c = 4:5:6, the ratio of the radius of the circumcircle to that of the incircle is. {IIT JEE 1996}.
Answer: the required ratio is 16:7.
Solution:
Question 4: If in a triangle ABC, (2CosA/a) + (CosB/b) + (2CosC/c) = (a/bc) + (b/ca), then the value of angle A is. {IIT JEE 1994}.
Answer: the value of angle A is 90ᵒ.
Solution:
Question 5: Consider a triangle ABC and let a, b and c denotes the lengths of sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15√3. If angle ACB is obtuse and if r denotes the radius of the incircle of a triangle, then r² is equal to. {IIT JEE 2010}.
Answer: the value of r² is equal to 3.
Solution:
Question 6: If sides a, b, and c of triangle ABC are in AP and cosθ₁ = a/(b + c), cosθ₂ = b/(a + c), and
cosθ₃ = c/(a + b), then the value of tan²(θ₁/2) + tan²(θ₃/2) is. {IIT JEE 2006}.
Answer: the value is 2/3.
Solution:
Question 7: In the triangle ABC, AD is the altitude from A. Given b > c, angle C = 23ᵒ and AD = (abc/(b² – c²)). Then angle B is equal to. {IIT JEE 1994}.
Answer: angle B is equal to 113°.
Question 8: ABC is an isosceles triangle inscribed in a circle of radius r. If AB = AC and h is the altitude from A to BC, then the triangle ABC has perimeter P = , area ∆ = and Lim(ₕ→₀)(∆/P³) = _.
{IIT JEE 1989}.
Answer: perimeter P = 2(√(2hr – h²) + √(2hr)), area ∆ = h(√(2hr – h²), Lim(ₕ→₀)(∆/P³) = (1/128r).
Question 9: The sides of a triangle inscribed in a given circle subtend angles α, β, and γ at the center. The minimum value of the arithmetic mean of cos(α + π/2), cos(β + π/2), and cos(γ + π/2) is equal to. {IIT JEE 1987}.
Answer: the minimum value of the arithmetic mean is -(√3/2).
Question 10: A polygon of 9 sides each of length 2 is inscribed in a circle. The radius of the circle is. {IIT JEE 1987}.
Answer: the radius of the circle is cosec20°.