Consider an obtuse-angled triangle ABC in which the difference between the largest and the smallest angle is \(\frac{\pi}{2}\) and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.Let a be the area of the triangle ABC. Then the value of (64a)2 is
The line \(x=8\) is the directrix of the ellipse \(E : \frac{x^2}{ a ^2}+\frac{y^2}{b^2}=1\)with the corresponding focus \((2,0)\) If the tangent to \(E\)at the point \(P\) in the first quadrant passes through the point \((0,4 \sqrt{3})\)and intersects the\(x\)-axis at \(Q\), then \((3 PQ )^2\)is equal to ____
The sequence of folding a paper and the manner in which the folded paper has been cut is shown in the following figures. How would this paper look when unfolded?
On the following questions, select the related word/letters from the attractive MASTER: OCUVGT :: LABOUR:?
Rajeev failed in the examination because his answers were not ……. to the questions asked
Two point-like objects of masses 20 gm and 30 gm are fixed at the two ends of a rigid massless rod of length 10 cm. This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass, as shown in the figure. The resulting torsional pendulum undergoes small oscillations. The torsional constant of the wire is 1.2 × 10−8 N m rad−1. The angular frequency of the oscillations in 𝑛 × 10−3 rad s−1. The value of 𝑛 is _____.
