For the following questions answer them individually
If $$3 - 2 \sin^2 \theta - 3 \cos \theta = 0, 0^\circ < \theta < 90^\circ$$, then what is the value of $$(2 \cosec \theta + \tan \theta)$$ ?
The total number of students in class A and B is 96. The number of students in A is 40% more than that in B. The average weight (in kg) of the students in B is 50% more than that of the students in A. If the average weight of all the students in A and B taken together is 58 kg, then what is the average weight of the students in B?
Abhi sold two articles for ₹5,220 each. On one, he gained 16% and on the other, he lost 10%. His profit or loss on the whole was:
If $$a + b + c = 5$$, and $$a^2 + b^2 + c^2 = 33$$, then what is the value of $$a^3 + b^3 + c^3 - 3abc$$?
What is the compound interest on a sum of ₹4,096 at 15% p.a. for $$2\frac{1}{2}$$ years, if the interest is compounded 10-monthly?
In a circle, chords AB and CD intersect each other at E. If CD = 18 cm, DE = 6 cm and AE = 18 cm, then BE = ?
If $$3 \cos^2 A + 6 \sin^2 A = 3, 0^\circ \leq A \leq 90^\circ$$, then the value of A is:
Let $$\triangle ABC \sim \triangle QPR$$ and $$\frac{ar(\triangle ABC)}{ar(\triangle PQR)} = \frac{9}{16}$$. If AB = 12 cm, BC = 6 cm and AC = 9 cm, then QP is equal to:
A train x running at 84 km/h crosses another train y running at 52 km/h in opposite direction in 12 seconds. If the length of y is two-third that of x, then what is the length of x?
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