1. If α, β, γ, δ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity k then the value of 4 sin (α/2)
2. The acute angle of a rhombus whose side is a mean proportional between its diagonals is 
3. If secθ + tanθ = 1 then the root of the equation (a - 2b + c)x2 + (b - 2c + a)x + (c - 2a + b) = 0 is
1) secθ 2) tanθ 3) sinθ 4) cotθ
4. The solution set of the equation 1 + sin 2020 x = cos 2021 x is
5. Consider the solution of the equation √2 tan2 x - √10 tan x + √2 = 0 in the range π 0 < x < π/2 . The only one of the following is true.
1) No solution exists for x in the given range
2) Two solutions x1, x2 exists with x1 + x2 = π/4
3) Two solutions x1, x2 exists with x1 + x2 = π/4
4) Two solutions x1, x2 exists with x1 + x2 = π/4
6. If cos−1 (n/2π) > 2π/3 then the minimum and maximum values of integer n are respectively
1) -1 and 1 2) -6 and -4 3) 4 and 6 4) -6 and -3
7. If α is the only real root of the equation x3 + bx2 + cx + 1 = 0 and b < c then the value of tan−1α + tan−1 1/α = 
8. The perimeter of a triangle is 16 cm. One of the side is of length 6 cm. If the area of the triangle is 12 sq cm. Then the triangle is
1) Right angled 2) Isosceles 3) Equilateral 4) Scalene
9. Two vertical poles 20 m and 80 m high stand apart on a horizontal plane. The height of the point of intersection of the lines joining the top of each pole to the foot of the other is
1) 13 m 2) 14 m 3) 15 m 4) 16 m
Numerical Value Type
10. If tan2α tan2β + tan2β tan2γ + tan2γ tan2α + 2 tan2α tan2β tan2γ = 1 then, the value of sin2α + sin2β + sin2γ = 1
11. If 3 tan-1 (2 - √3 ) - tan-1 x = tan-1 1/3
KEY: 1-2; 2-3; 3-1; 4-3; 5-4; 6-2; 7-2; 8-2; 9-4; 10-1; 11- 0.5.
