PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

If A + B = C, then write the value of tan A tan B tan C.

If sin α − sin β = a and cos α + cos β = b, then write the value of cos (α + β). 

If tan \[\alpha = \frac{1}{1 + 2^{- x}}\] and \[\tan \beta = \frac{1}{1 + 2^{x + 1}}\] then write the value of α + β lying in the interval \[\left( 0, \frac{\pi}{2} \right)\] 

The value of \[\sin^2 \frac{5\pi}{12} - \sin^2 \frac{\pi}{12}\] 

If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to

tan 20° + tan 40° + \[\sqrt{3}\] tan 20° tan 40° is equal to 

If \[\tan A = \frac{a}{a + 1}\text{ and } \tan B = \frac{1}{2a + 1}\] 

If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =

If in ∆ABC, tan A + tan B + tan C = 6, then cot A cot B cot C =

tan 3A − tan 2A − tan A =

Find the equation of the parabola whose: 

focus is (3, 0) and the directrix is 3x + 4y = 1

If A + B + C = π, then \[\frac{\tan A + \tan B + \tan C}{\tan A \tan B \tan C}\] is equal to

Find the equation of the parabola whose: 

 focus is (1, 1) and the directrix is x + y + 1 = 0

Find the equation of the parabola whose: 

 focus is (0, 0) and the directrix 2x − y − 1 = 0

Find the equation of the parabola whose: 

 focus is (2, 3) and the directrix x − 4y + 3 = 0.

Find the equation of the parabola whose focus is the point (2, 3) and directrix is the line x − 4y + 3 = 0. Also, find the length of its latus-rectum.

Find the equation of the parabola if 

 the focus is at (−6, −6) and the vertex is at (−2, 2)

Find the equation of the parabola if 

the focus is at (0, −3) and the vertex is at (0, 0) 

If \[\cos P = \frac{1}{7}\text{ and }\cos Q = \frac{13}{14}\], where P and Q both are acute angles. Then, the value of P − Q is

Find the equation of the parabola if the focus is at (0, −3) and the vertex is at (−1, −3)