If \(
x + \frac{1}{x} = 7,
\) then the value of \(
x^{6} + \frac{1}{x^{6}}
\) is:
A man invests a total sum of ₹10,000 in a company. A part of the sum was invested at 10% simple interest per annum and the remaining part at 15% simple interest per annum. If the total interest accured to him in 2 years equals ₹2400, the sum invested at 15% simple interest per annum is:
AB is the diameter of a circle with centre O. P be a point on it. If ∠AOP = 95°, then ∠OBP is =____________:
If \( \frac{cos β}{sec α} \) = 15 and \( \frac{sin β }{ sec α} \) = 16, then the value of sin2β is ________:
\( \frac{256}{481} \)
- \( \frac{256}{481} \)
\( \frac{481}{256} \)
- \( \frac{481}{256} \)
What is the value of sin 30° + cos 30° + tan 30°
\(\dfrac{5 + \sqrt{3}}{2\sqrt{3}}\)
\(\dfrac{5 - \sqrt{3}}{2\sqrt{3}}\)
\(\dfrac{5 + \sqrt{3}}{\sqrt{3}}\)
\(\dfrac{5 - \sqrt{3}}{\sqrt{3}}\)
If sec²θ + tan²θ = \( \frac{25}{18} \), then the value of sec⁴θ − tan⁴θ is:
\( \frac{18}{25} \)
\( \frac{25}{12} \)
\( \frac{25}{9} \)
\( \frac{25}{18} \)