A person standing on the bank of a river observes the angle of elevation of the top of the tree on the opposite bank of the river is 60° and when he retires 40 m away from the tree the angle of elevation becomes 30°. The breadth of the river is
a) 20m
b) 30m
c) 40m
d) 60m
Your Answer
If cos-1x – cos-1 = α then 4x2 – 4xycosα + y2 is equal to
a) -4sin2α
b) 4sin2α
c) 4
d) 2sin2α
If in a triangle ABC, the altitude from the vertices A, B, C on opposite sides are in harmonic progression, then sin A, sin B, sin C are in
a) Harmonic Progression
b) Arithmetico – Geometric Progression
c) Arithmetical Progression
d) Geometric Progression
Let α, β be such that π < α – β < 3π. If sin α + sin β = and cos α + cos β = then the value of cos is
a)
b)
c)
d)
The sides of a triangle are sinα, cosα and for some 0 < α < then the greatest angle of the triangle is
a) 60°
b) 90°
c) 120°
d) 150°
If f : R Ś̨, defined by f(x) = sin x cos x + 1, is onto then the interval of Ś̨ is
a) [ 0, 3 ]
b) [-1, 1 ]
c) [0, 1 ]
d) [-1, 3]
In a triangle ABC, a cos2 + c cos2 = then the sides a, b, c are in
a) Arithmetic Progression
b) Geometric Progression
c) Harmonic Progression
d) Satisfy a+ b = c
The trigonometric equation sin-1x = 2sin-1α has a solution for
a) < |α | <
b) All real values of α
c) |α | ≤
d) |α | ≥
cot-1() – tan-1 () = x then sin x is equal to
a) tan2
b) cot2
c) tanα
d) cot
In a triangle ABC, 2ca sin is equal to
a) a2 + b2 – c2
b) c2 + a2 – b2
c) b2 – c2 – a2
d) c2 – a2 – b2
sin2θ = is true if and only if
a) x – y ≠ 0
b) x = y
c) x ≠ .y
d) x ≠ 0, y ≠ 0
The value of is
a) 1
d) 2
If sin (α + β) = 1, sin (α β) = , then tan (α + 2β) tan (2α + β) is equal to
b) 1
c) Zero
d) None of these
If y = sin2θ + cosec2θ, θ ≠ 0 then
a) y = 0
b) y ≤ 2
c) y ≥ 2
d) y ≥ 2
In a triangle ABC, a= 4, b =3, angle A = 60° then c is a root of the equation
a) c2 3c 7 = 0
b) c2 + 3c + 7 = 0
c) c2 3c + 7 = 0
d) c2 + 3c 7 = 0
In a triangle tan = , tan = , then
a) a, c, b are in Arithmetic Progression
b) a, b, c are in Arithmetic Progression
c) b, a, c are in Arithmetic Progression
d) a, b, c are in Geometric Progression
If α is a root of 25cos2θ + 5cosθ 12 = 0, < α < π then sin2α is equal to
tan-1 + tan-1 is equal to
a) cos-1
b) sin-1
c) tan-1
d) tan-1
The equation a sin x + b cos x = c where |c| > has
a) a unique solution
b) infinite number of solutions
c) no solution
d) none of these
The angles of a triangle are in Arithmetic Progression and let . Find the angle A.
Root(s) of the equation 2sin2θ + sin22θ = 2
Let P = and be two sets then
a) P⊂Q and Q – P = ϕ
b) Q P
c) P Q
d) P = Q
The positive integer satisfying the equation is
The value of x satisfying tan−1 (x + 3) − tan−1 (x – 3) = sin−1 are
= 
, tan 
= 
, then
