For the following questions answer them individually
A and B are two prime numbers such that A > B and their LCM is 209. The value of $$B^{2}$$ -A is:
If $$2\sqrt{2}x^{3} - 3\sqrt{3}y^{2} = \left(\sqrt{2}x- \sqrt{3}y)(Ax^{2} - Bxy + Cy^{2}\right)$$ , then the value of $$\left(A^{2} + B^{2} + C^{2}\right)$$ is:
P and Q start a shop with a capital of ₹1,50,000 and ₹4,50.000, respectively. After a year, out of the profit of ₹1,60.000, P gets his share of profit plus some money that is not a part of the profit, as his salary. If P gets a total of ₹70,000, what is the salary (in ₹) he received?
A sum of ₹4,620 is to be paid back in 2 equal annual instalments. How much is each instalment (in ₹) if the interest is compounded annually at 10% per annum?
The expression $$\left(cos^{6} \theta + sin^{6} \theta- 1\right)\left(\tan^{2} \theta + \cot^{2} \theta + 2\right) + 3$$ is equal to:
A train covers a distance of 225 km in $$2\frac{1}{2}$$ hours at a uniform speed. The time taken by the train (in hours) to cover 2 a distance of 630 km at the same speed is:
In $$\triangle$$ ABC , D is a point on side BC such that $$\angle ADC = \angle BAC$$. If CA= 15 cm and CD= 9 cm, then CB (in cm)=?
A shopkeeper marks an article at a price 20% higher than its cost price and allows 10% discount. Find his gain percentage.
The value of $$\frac{48.3\times\left[\left(4.95\right)^{2}+4.95\times13.25\right]}{\left[\left(12.55\right)^{2}-\left(5.65\right)^{2}\right]\times19.8}$$
If $$5\sin \theta - 4\cos \theta = 0. 0^{\circ} < 0 < 90^{\circ}$$ , then the value of $$\frac{5\sin \theta- \cos \theta}{5\sin \theta- 3\cos \theta}$$
