X is directly proportional to the square of Y. When X is 12, then Y is 2. Find the value of X when Y is 3.
If cos θ + cos²θ = 1, find the value of \(
\sqrt{\sin^{4}\theta + \cos^{2}\theta}
\)
Find the HCF of 60, 148 and 382.
Raghav went to a shopping mall to purchase clothes. He had two coupons with him, but only one can be used on a single day. Using the first coupon, a total discount of 30% can be obtained on the total amount. Using the second coupon, he will get 80% off on the price of the costliest shirt if he buys at least 3 shirts. What is the price at which Raghav can purchase 3 shirts at a minimum price if the prices of the three shirts are Rs. 1250 , Rs.1540 and Rs.1375 ?
If sin A = \( \frac{4}{5} \) , then what is the value of sin² A?
\( \frac{26}{25} \)
\( \frac{36}{25} \)
\( \frac{48}{25} \)
\( \frac{16}{25} \)
In the given figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 54°, then ∠OBA = _______.
In the figure, XYZ is a secant and ZT is a tangent to the circle at T. If TZ = 12 cm and YZ = 8 cm, then find the length of XY.