Given below are two statements: Statement (I): 4 boys and 8 girls completed \(\frac{1}{3}\)rd of work in 5 days. After that 3 boys and 3 girls increased, and they completed \(\frac{1}{3}\)rd more work in 3 days. If the remaining work is to be completed in 2 days, then the number of girls that should be increased is 32. Statement (II): The ratio of time taken by A and C to do a work is 1 : 2 respectively. B is \(166\frac{2}{3}\)% more efficient than C. Time taken by A to complete 6% of work is 6 days. Then, the time taken by B and C together to complete the whole work is \(54\frac{6}{11}\) days. In light of the above statements, choose the most appropriate answer from the options given below.

Which of the following statements are True in the context of circles? A. A tangent of a circle touches it at two points. B. A circle can have two parallel tangents at the most. C. There is no tangent to a circle passing through a point inside the circle. Choose the correct answer…

The radii of two cones are in the ratio 2 : 3 and their volumes in the ratio 1 : 3. Then the ratio of their heights is

If the pair of linear equations \(2x+3y=7\) and \(2px+(p-q)y=28\) has an infinite number of solutions, then \((p,q)=\)

The area of the circle that can be inscribed in a square of side 6 cm is

\(\sqrt{3+\sqrt{5}} =\)

The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, then the 13th observation is

If \(\sin\theta - \cos\theta = 0\), the value of \(\sin^4\theta + \cos^4\theta\) is

Let A and B be two events such that P(A) = 0.25, P(B) = 0.50 and \(P(A\cap B)=0.14\). The probability that neither A nor B occurs is