If sin-1 [x – (x2 / 2) + (x3 / 4) – ….. + cos-1 (x2 – (x4 / 2) + (x6 / 4) – …. ) = π / 2. For 0 < |x| < √2, then x =
1) 1 / 2 2) 1 3) – 1 / 2 4) -1 Solution: (2) 1 sin-1 y + cos-1... View Article
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If we consider only the principal values of the inverse trigonometric functions, then the value of tan [cos-1 (1 / 5√2) – sin-1 (4 / √17)] is
1) √29 / 3 2) 29 / 3 3) √3 / 29 4) 3 / 29 Solution: (4) 3 /... View Article
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fences are of same length x. The maximum area enclosed by the park is
1) √(x3/8) 2) x2/2 3) πx2 4) 3x2/2 Solution: Let ABC be the triangle such that AB = AC =... View Article
Points D, and E are taken on the side BC of the ∆ABC, such that BD = DE = EC. If ∠BAD = x, ∠DAE = y and ∠EAC = z, then the value of sin(x + y) sin (y + z)/sin x sin z is
1) 1 2) 2 3) 4 4) None of these Solution: Consider the figure below. From ∆ADC, sin (y +... View Article
The sides of a triangle are in the ratio 1 : √3 : 2, then the angles of the triangle are in the ratio
1) 1 : 3 : 5 2) 2 : 3 : 1 3) 3 : 2 : 1 4) 1... View Article
In a ∆ABC, if tan A/2 = 5/6, tan C/2 = 2/5, then
1) a, c, and b are in AP 2) a, b, and c are in GP 3) b, a, and... View Article
If in ∆ABC, sin A/2 sin C/2 = sin B/2 and 2s is the perimeter of the triangle, then s is equal to
1) 2b 2) b 3) 3b 4) 4b Solution: We know sin A/2 = √((s – b)(s – c)/bc) sin... View Article
In a ∆ABC , (b + c) cos A + (a + c) cos B + (a + b) cos C is equal to
(1) 0 (2) abc (3) a + b + c (4) 1 Solution: (b + c) cos A + (a... View Article
In ∆ABC, if cot A, cot B, and cot C are in AP, then a2, b2, and c2 are in
1) GP 2) AP 3) HP 4) None of these Solution: Given cot A, cot B, and cot C are... View Article
If in a ∆ABC, 4 sin A = 4 sin B = 3 sin C, the cos C is equal to
1) 1/3 2) 1/9 3) 1/27 4) 1/18 Solution: Let 4 sin A = 4 sin B = 3 sin... View Article
In a ∆ABC , if (√3 – 1)a = 2b, A = 3B, then ∠C is equal to
1) 60o 2) 120o 3) 30o 4) 45o Solution: Given (√3 – 1)a = 2b So a/b = 2/(√3 –... View Article
If in a ∆ABC, 2b2 = a2 + c2, then (sin 3B/sin B) is equal to
(1) (c2 – a2)/2ac (2) (c2 – a2)/ac (3) ((c2 – a2)/ac)2 (4) ((c2 – a2)/2ac)2 Solution: We know sin... View Article
In ∆ABC, (a – b)2 cos2 C/2 + (a + b)2 sin2 C/2 is equal to
1) a2 2) b2 3) c2 4) None of these Solution: (a – b)2 cos2 C/2 + (a + b)2... View Article
In any ∆ABC, (tan A/2 – tan B/2)/(tan A/2 + tan B/2) is equal to
(1) (a – b)/(a + b) (2) (a – b)/c (3) c/(a – b) (4) none of these Solution: (tan... View Article
In a ∆ABC, if sin2 A/2, sin2 B/2 and sin2 C/2 are in HP. Then, a, b and c will be in
1) AP 2) GP 3) HP 4) None of these Solution: We have sin2 A/2 = (s – b)(s- c)/bc... View Article
In a ∆ABC, 2a2 + 4b2 + c2 = 4ab + 2ac , then cos B is
1) 0 2) 1/8 3) 3/8 4) 7/8 Solution: Given 2a2 + 4b2 + c2 = 4ab + 2ac a2... View Article
If a = 2√2 , b = 6, A = 45o , then
1) no triangle is possible 2) one triangle is possible 3) two triangles are possible 4) either no triangle or... View Article
In a ∆ABC, if sin A sin B = ab/c2, then the triangle is
1) equilateral 2) isosceles 3) right-angled 4) obtuse-angled Solution: Given sin A sin B = ab/c2 Cross multiply, we get... View Article
In ∆ABC, a = 2, b = 3, and sin A = 2/3 , then B is equal to
1) 30o 2) 60o 3) 90o 4) 120o Solution: Given a = 2, b = 3, and sin A =... View Article
If one side of a triangle is double the other and the angles opposite to these sides differ by 600, then the triangle is
1) obtuse-angled 2) acute-angled 3) isosceles 4) right-angled Solution: Let a = 2b A – B = 600…(i) We have... View Article
