PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

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)

Find the equation of the parabola if the focus is at (a, 0) and the vertex is at (a', 0) 

Find the equation of the parabola if  the focus is at (0, 0) and vertex is at the intersection of the lines x + y = 1 and x − y = 3. 

If cot (α + β) = 0, sin (α + 2β) is equal to

The value of \[\cos^2 \left( \frac{\pi}{6} + x \right) - \sin^2 \left( \frac{\pi}{6} - x \right)\] is

If tan θ₁ tan θ₂ = k, then \[\frac{\cos \left( \theta_1 - \theta_2 \right)}{\cos \left( \theta_1 + \theta_2 \right)} =\]

If sin (π cos x) = cos (π sin x), then sin 2x = ______.

If \[\tan\theta = \frac{1}{2}\] and \[\tan\phi = \frac{1}{3}\], then the value of \[\tan\phi = \frac{1}{3}\] is