1. If \( r\cos\theta = 1 \) and \( r\sin\theta = \sqrt{3} \), then the value of \( \theta \) is—

(a) \(\cfrac{π}{2}\) (b) \(\cfrac{π}{3}\) (c) \(\cfrac{π}{4}\) (d) \(\cfrac{π}{6}\)

2. If \(p+q=\sqrt{13}\) and \(p−q=\sqrt{5}\), then the value of \(pq\) is—

(a) 2 (b) 18 (c) 9 (d) 8

3. If \(sinθ−cosθ=0,\) \( (0°<θ<90°)\) and \(secθ+cosecθ=x\), then the value of \(x\) is—?

(a) \(1\) (b) \(2\) (c) \(\sqrt2\) (d) \(2\sqrt2\)

4. If the assumed mean is 22, class width is 10, total frequency is 80, and the value of \(\sum{f_iu_i}\) is 16, then the actual (or true) mean will be —

(a) 23 (b) 24 (c) 25 (d) 26

5. If the data arranged in ascending order is 6, 9, 11, 12, x+2, x+3, 17, 20, 21, 24 and the median is 21, then the value of x will be —

(a) 13.5 (b) 15.5 (c) 18.5 (d) 21.5

6. If the area, perimeter, and height of an equilateral triangle are \(a\), \(s\), and \(h\) respectively, then the value of \(\dfrac{2a}{sh}\) is —

(a) 1 (b) \(\frac{1}{2}\) (c) \(\frac{1}{3}\) (d) \(\frac{1}{4}\)

7. If the area of a circular region is \(x\) square units, the circumference is \(y\) units, and the diameter is \(z\) units, then the value of \(\cfrac{x}{yz}\) is —

(a) \(\cfrac{1}{2}\) (b) \(\cfrac{1}{4}\) (c) 1 (d) \(\cfrac{1}{8}\)

8. If \(a = \cfrac{1}{2+\sqrt3}\) and \(b = \cfrac{1}{2-\sqrt3}\), then what is the value of \(\cfrac{1}{a+1}+\cfrac{1}{b+1}\)?

9. If \(α\) and \(β\) are the roots of the equation \(3x^2 + 8x + 2 = 0\), then the value of \(\left(\cfrac{1}{α} + \cfrac{1}{β}\right)\) is —

(a) \(-\cfrac{3}{8}\) (b) \(\cfrac{2}{3}\) (c) -4 (d) 4

10. If the data arranged in ascending order is 8, 9, 12, 17, x+2, x+4, 30, 31, 34, 39 and the median is 24, then the value of x is—

(a) 22 (b) 21 (c) 20 (d) 24

11. If a sphere's volume and surface area have equal numerical values, then the numerical value of its radius is ——.