In a triangle, ABC, 1 – tan (A/2) tan (B/2) is equal to
(1) 2c/(a + b + c) (2) 2c/(a + b – c) (3) 2b/(a + b + c) (4) none... View Article
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For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. An incorrect statement among the following is
1) there is a regular polygon with r/R = 1/2 2) there is a regular polygon with r/R = 1/√2... View Article
In a ∆ABC, let ∠C = π/2, if r is the inradius and R is the circumradius of the ∆ABC, then 2 (r + R) equals
1) c + a 2) a + b + c 3) a + b 4) b + c Solution: Given... View Article
If p1, p2, p3 are respectively the perpendiculars from the vertices of a triangle to the opposite side, then p1p2p3 is equal to
1) a2b2c2 2) 2 a2b2c2 3) 4 a2b2c3/R2 4) a2b2c2/8R3 Solution: Let p1 be the altitude AD, p2 be the... View Article
Inradius of a circle which is inscribed in an isosceles triangle one of whose angle is 2π/ 3, is √3, then the area of the triangle is
1) 4√3 2) 12 – 7√3 3) 12 + 7√3 4) None of these Solution: Given the triangle is isosceles... View Article
In a ∆ABC, a : b : c = 4 : 5 : 6. The ratio of the radius of the circumcircle to that of the incircle is
1) 15/4 2) 11/5 3) 16/7 4) 16/3 Solution: Given a : b : c = 4 : 5 :... View Article
In a triangle, if r1 = 2r2 = 3r3, then a/b + b/c + c/a is equal to
1) 75/60 2) 155/60 3) 176/60 4) 191/60 Solution: Given r1 = 2r2 = 3r3 We know r1 = ∆/(s... View Article
The value of 1/r12 + 1/r22 + 1/r32 + 1/r2 is
(1) (a2 + b2 + c2)/∆2 (2) 0 (3) ∆2/(a2 + b2 + c2) (4) 1 Solution: We know r... View Article
If A, A1, A2 and A3 and the areas of the incircle and excircles, then 1/√A1 + 1/√A2 + 1/√A3 is equal to
1) 1/√A 2) 2/√A 3) 3/√A 4) 4/√A Solution: The area of excircle, A1 = πr12 A2 = πr22 A3... View Article
The area of a circle and the area of a regular polygon of n sides of the perimeter equal to that of that circle are in the ratio
1) tan π/n : π/n 2) cos π/n : π/n 3) sin π/n : π/n 4) cot π/n : π/n... View Article
In a ∆PQR, P is the largest angle and cos P = 1/3, Further in the circle of the triangle touches the sides PQ, QR, and RP at N, L, and M respectively, such that the lengths of PN, QL, and RM are consecutive even integers, Then, possible length(s) of the side (s) of the triangle is (are)
1) 16 2) 18 3) 24 4) 22 Solution: Let s – a = 2k – 2 s – b... View Article
If the sides of the triangles are p, q, √(p2 + q2 + pq), then the greatest angle is
1) π/2 2) 5π/4 3) 2π/3 4) 7π/4 Solution: Given p, q, √(p2 + q2 + pq) are the sides.... View Article
If in a ∆ABC, the altitudes from the vertices A, B, C on the opposite side are in HP, then sin A, sin B, and sin C are in
1) HP 2) Arithmetico – Geometric Progression 3) AP 4) GP Solution: Consider ∆BDA, cos (90 – B) = AD/c... View Article
If in the ∆ABC, ∠B = 45o, then a4 + b4 + c4 is equal to
1) 2a2 (b2 + c2) 2) 2c2 (a2 + b2) 3) 2b2 (a2 + c2) 4) 2(a2b2 + b2c2 +... View Article
In a ∆ABC, if the sides are a = 3, b = 5 and c = 4, then sin B/2 + cos B/2 is equal to
1) √2 2) (√3 + 1)/2 3) (√3 – 1)/2 4) 1 Solution: Given a = 3, b = 5... View Article
In a ∆ABC, a, c, A are given and b1, b2 are two values of the third side b such that b2 = 2b1, then sin A is equal to
1) √[(9a2 – c2 )/8a2] 2) √[(9a2 – c2 )/8c2] 3) √[(9a2 + c2 )/8c2] 4) None of these Solution:... View Article
The value of log tan [(π / 4) + (ix / 2)] is
1) i tan-1 (sin hx) 2) i tan-1 (sin hx) 3) i tan-1 (cos hx) 4) None of these Solution:... View Article
2 sin h-1 θ =
1) sin h-1 (2θ √1 + θ2) 2) sin h-1 (2θ √1 – θ2) 3) sin h-1 (θ √1 +... View Article
If tan-1 (ɑ + iβ) = x + iy, then x =
1) (1 / 2) tan-1 [(2ɑ) / (1 – ɑ2 – β2)] 2) (1 / 2) tan-1 [(2ɑ) / (1... View Article
The imaginary part of tan-1 (cos θ + i sin θ)
1) tan h-1 (sin θ) 2) tan h-1 (∞) 3) (1 / 2) tan h-1 (sin θ) 4) None of... View Article
