If α and β be any two real positive values of x for which 2cosx, |cosx|, 1 – 3cos²x are in geometric progression. Then the minimum value of |α – β | is

a)  

b)  

c)  

d)  

The question has four distinct choices, only one of which is the correct answer. Select one of them which is correct
Statement I: The equation sin (cos x) = cos (sin x) does not possess real roots.
Statement II: If sin x > 0, then 2nπ < x < (2n + 1) π

a) Statement I is false, Statement II is true.

b) Statement I is true, Statement II is true. Statement II is a correct explanation for the statement I.

c) Statement I is true, Statement II is true. Statement II is not a correct explanation for the statement I.

d) Statement I is true, Statement II is false

The value of α for which the equations x² – (sinα – 2)x – (1 + sinα) = 0 has roots whose sum of squares is least is

a)

b)

c)

d)

The most general solutions of the equation
sin x – 1 =  tanx are given by

a) nπ +

b) 2nπ, 2nπ +

c) 2nπ

d) None of these

The maximum value of sin + cos  in the interval  is attained at

a) x =

b) x =

c) x =

d) x =

If sin³x sin3x = cosmx where C₀, C₁, - - - - -C_n are constants and C_n ≠ 0 then the value of n is

a) 1

b) 0

c) 6

d) 15

If cos A = m cos B and cot  = λ tan , then λ =

a)

b)

c)

d)

The value of tan  is

a)

b)

c)

d)

If | cos { sinθ +  } |= k then the greatest value of k is

a)

b)

c)

d)

For the equation cos^-1x + cos^-12x + π = 0, the number of real solutions is

a) 1

b) 2

c) 0

d)

If 1 + sinθ + sin²θ + ……… = 4 + , 0 < θ < π, θ ≠  then

a) θ =

b) θ =

c) θ =  or 

d) θ =  or 

Show that the value of  wherever defined, never lies between  and 3.

If 0 < x < 1, then  is equal to

Number of solutions of  lying in the interval  is

a) 0

b) 1

c) 2

d) 3

The minimum value of the expression  where  are real numbers satisfying  is

a) Positive

b) Zero

c) Negative

d) –3

The area of the equilateral triangle which contains three coins of unit radius is

a)  square units

b)  square units

c)  square units

d)  square units

a) True

b) False

a) True

b) False

The value of  is equal to

a)

b)

c)

d)

Match the following  is

Let n be an odd integer. If sin nθ =  for every value of θ, then

a) = 1, = 3

b) = 0, = n

c) = −1, = n

d) = 1, =

Multiple choices
Let and  (x is measured in radians) then x lies in the interval

a)

b)

c)

d)

Multiple choices
For a positive integer n, let
 
.  .  . then

a)

b)

c)

d)