Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

If the circles x² + y² = a and x² + y² − 6x − 8y + 9 = 0, touch externally, then a =

If (x, 3) and (3, 5) are the extremities of a diameter of a circle with centre at (2, y), then the values of x and y are

If (−3, 2) lies on the circle x² + y² + 2gx + 2fy + c = 0 which is concentric with the circle x² + y² + 6x + 8y − 5 = 0, then c =

Equation of the diameter of the circle x² + y² − 2x + 4y = 0 which passes through the origin is

Equation of the circle through origin which cuts intercepts of length a and b on axes is

If the circles x² + y² + 2ax + c = 0 and x² + y² + 2by + c = 0 touch each other, then

Prove that:

Prove that:

Prove that: 

Show that :

Show that :

Prove that:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]

Prove that:
cos 40° cos 80° cos 160° = \[- \frac{1}{8}\]

Prove that:
 sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]

Prove that:
cos 20° cos 40° cos 80° = \[\frac{1}{8}\]

Prove that:
tan 20° tan 40° tan 60° tan 80° = 3

Prove that tan 20° tan 30° tan 40° tan 80° = 1.

Prove that:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]

Prove that:
 sin 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]