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

In a G.P. if the (m + n)^th term is p and (m − n)^th term is q, then its m^th term is 

Mark the correct alternative in the following question: 

Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then p²R³ : S³ is equal to 

Find the maximum and minimum values of each of the following trigonometrical expression:

 12 sin x − 5 cos x 

Find the maximum and minimum values of each of the following trigonometrical expression: 

12 cos x + 5 sin x + 4 

Find the maximum and minimum values of each of the following trigonometrical expression: 

\[5 \cos x + 3 \sin \left( \frac{\pi}{6} - x \right) + 4\]

Find the maximum and minimum values of each of the following trigonometrical expression:

sin x − cos x + 1

Reduce each of the following expressions to the sine and cosine of a single expression: 

\[\sqrt{3} \sin x - \cos x\] 

Reduce each of the following expressions to the sine and cosine of a single expression: 

cos x − sin x 

Reduce each of the following expressions to the sine and cosine of a single expression: 

24 cos x + 7 sin x 

Show that sin 100° − sin 10° is positive. 

Prove that \[\left( 2\sqrt{3} + 3 \right) \sin x + 2\sqrt{3} \cos x\]  lies between \[- \left( 2\sqrt{3} + \sqrt{15} \right) \text{ and } \left( 2\sqrt{3} + \sqrt{15} \right)\]

If α + β − γ = π and sin² α +sin² β − sin² γ = λ sin α sin β cos γ, then write the value of λ. 

If x cos θ = y cos \[\left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right)\]then write the value of \[\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\] 

Write the maximum and minimum values of 3 cos x + 4 sin x + 5. 

Write the maximum value of 12 sin x − 9 sin² x. 

If 12 sin x − 9sin² x attains its maximum value at x = α, then write the value of sin α.

Write the interval in which the value of 5 cos x + 3 cos \[\left( x + \frac{\pi}{3} \right) + 3\] lies. 

If tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B. 

If \[\frac{\cos \left( x - y \right)}{\cos \left( x + y \right)} = \frac{m}{n}\]  then write the value of tan x tan y. 

If a = b \[\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}\] then write the value of ab + bc + ca.