$\mathrm{In} ∆\mathrm{ABC} \mathrm{if} \mathrm{\theta } \mathrm{is} \mathrm{any} \mathrm{angle}, \mathrm{then} \mathrm{bcos}\left(\mathrm{C} + \mathrm{\theta }\right) + \mathrm{ccos}\left(\mathrm{B} - \mathrm{\theta }\right) = ?$

• $\mathrm{acot}\left(\mathrm{\theta }\right)$

• $\mathrm{acos}\left(\mathrm{\theta }\right)$

• $\mathrm{atan}\left(\mathrm{\theta }\right)$

• $\mathrm{asin}\left(\mathrm{\theta }\right)$

$$\begin{gathered} \mathrm{The} \mathrm{number} \mathrm{of} \mathrm{solutions} \mathrm{of} \mathrm{the} \mathrm{trigonometric} \mathrm{equation} \\ 1 + \cos \left(\mathrm{x}\right) . \cos \left(5\mathrm{x}\right) = {\sin }^2\left(\mathrm{x}\right) \mathrm{in} [0, 2\mathrm{\pi }] \mathrm{is} \end{gathered}$$

• 8

• 12

• 10

• 6

A value of θ for which  is purely imaginary is

• π/3

• π/6

• 
• 

Consider f(x) = tan^-1 . A normal to y = f (x) at x = π/6 also passes through the point

• (0,0)

• (0, 2π/3)

• (π/6 ,0)

• (π/6 ,0)

5.

If 0≤x<2π, then the number of real values of x, which satisfy the equation cosx+cos2x+cos3x+cos4x=0, is :

• 3

• 5

• 7

• 7

• 4

• 3

• 2

• 2

Let  where .Then, a value of y is

If y  = sec (tan^-1 x), then dy/dx at x = 1 is equal to 

• 
• 

• 1

• 1

If A = sin² x + cos⁴ x, then for all real x

• 3/4 ≤ A ≤ 1

• 31/16 ≤ A ≤ 1

• 1≤ A ≤2

• 1≤ A ≤2

If cos^-1 x - cos^-1 y/2 = α, then 4x² − 4xy cos α + y² is equal to

• 2 sin 2α

• 4

• 4 sin² α

• 4 sin² α