For the following questions answer them individually
A shopkeeper bought 80 kg of rice at a discount of 10%. Besides 1 kg rice was offered free to him on the purchase of every 20 kg rice. If he sells the rice at the marked price, his profit percentage will be:
D is the midpointof side BC of $$\triangle ABC$$. Point E lies on AC such that $$CE = \frac{1}{3}AC$$. BE and AD intersect at G. What is $$\frac{AG}{GD}$$?
Two chords AB and CD of a circle with centre O intersect each other at P. If $$\angle BOC = 70^\circ$$ and $$\angle AOD = 100^\circ$$, then $$\angle APC$$ is:
A train takes $$2\frac{1}{2}$$ hours less for a journey of 300 km, if its speed is increased by 20 km/h from its usual speed. How much time will it take to cover a distance of 192 km at its usual speed?
If $$12 \cos^2 \theta - 2 \sin^2 \theta + 3\cos \theta = 3, 0^\circ < \theta < 90^\circ$$, then what is the value of $$\frac{\cosec \theta + \sec \theta}{\tan \theta + \cot \theta}$$?
If $$16a^4 + 36a^2b^2 + 81b^4 = 91$$ and $$4a^2 + 9b^2 - 6ab = 13$$, then what is the value of $$3ab$$?
In $$\triangle ABC, \angle C = 90^\circ, AC = 5 cm$$ and $$BC = 12 cm$$. The bisector of $$\angle A$$ meets BC at D. What is the length of AD?
The value of $$\frac{\sec^6 \theta - \tan^6 \theta - 3\sec^2 \theta \tan^2 \theta + 1}{\cos^4 \theta - \sin^4 \theta + 2 \sin^2 \theta + 2}$$ is:
Sides AB and DC of cyclic quadrilateral ABCD are produced to meet at E, and sides AD and BCare produced to meet at F. If $$\angle BAD = 102^\circ$$ and $$\angle BEC = 38^\circ$$ then the difference between $$\angle ADC$$ and $$\angle AFB$$ is:
If $$5 \sin \theta = 4$$, then the value of $$\frac{\sec \theta + 4 \cot \theta}{4 \tan \theta - 5 \cos \theta}$$ is:
