For the following questions answer them individually
A is as efficient as B and C together. Working together A and B can complete a work in 36 days and C alone can complete it in 60 days. A and C work together for 10 days. B alone will complete the remaining work in:
If $$2\cos^2 \theta + 3\sin \theta = 3$$, where $$0^\circ < \theta < 90^\circ$$, then what is the value of $$\sin^2 2\theta + \cos^2 \theta + \tan^2 2\theta + \cosec^2 2\theta$$?
The radius and the height of a right circular cone are in the ratio 5 : 12. Its curved surface area is 816.4 $$cm^2$$, What is the volume (in $$cm^3$$) of the cone? (Take $$\pi = 3.14$$)
Given that $$(5x - 3)^3 + (2x + 5)^3 + 27(4 - 3x)^3 = 9(3 - 5x)(2x + 5)(3x - 4)$$, then the value of $$(2x + 1)$$ is:
The sides of a triangle are 12 cm, 35 cm and 37 cm. What is the circumradius of the triangle
The base of a right pyramid is an equilateral triangle with area $$16\sqrt{3}cm^2$$. If the area of one of its lateral facesis 30 $$cm^2$$, then its height (in cm) is:
A vessel contains a 32 litre solution of acid and water in which the ratio of acid and water is 5 : 3, If 12 litres of the solution are taken out and $$7\frac{1}{2}$$ litres of water are added to it, then what is the ratio of acid and water in the resulting solution?
A sphere of maximum volume is cut out from a solid hemisphere. What is the ratio of the volume of the sphere to that of the remaining solid?
If $$5\sqrt{5}x^3 + 2\sqrt{2}y^3 = (Ax + \sqrt{2}y)(Bx^2 + 2y^2 + Cxy)$$, then the value of $$(A^2 + B^2 - C^2 )$$ is:
The value of $$(1 + \cot \theta - \cosec \theta )(1 + \cos \theta + \sin \theta)\sec \theta = ?$$
