Correct Answer: B. 22.2m/s

Explanation

80km/h = \(\frac{80}{60}\) x \(\frac{1000}{60}\) = 3 x 3= \(\frac{40 x 5}{9}\)

= \(\frac{200m/s}{9}\) = 22.22m/s

Correct Answer: D. 120

Explanation

\(\frac{^{n}P_{5}}{^{n}C_{5}} = \frac{n!}{(n-5)!} ÷ \frac{n!}{(n-5)!5!}\)

= \(\frac{n!}{(n-5)!} \times \frac{(n-5)!5!}{n!} = 5! = 120\)

Correct Answer: B. 10 in

Explanation

The easiest way to do this is first to find the total number of flowers: 12+5+4=21 Now, the median element is the middle term. To find the middle, you can divide 21 by 2: 21/2=10.5 Since you have an odd number of elements, you unsurprisingly get a fraction. This means that there 10 items to the left of the median and 10 to its right. The 11th term is your median. Now, your group of flowers looks like this: 1-12: 10 inches 13-17: 12 inches 18-21: 15 inches The 11th item is going to be in that first group, meaning that the median is 10 inches. If you prefer to write out all of the terms, it will be: 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 15, 15, 15, 15

Correct Answer: D. 1800

Correct Answer: D. 4.20m

Explanation

Let the actual length of the room = y m

\(\therefore \frac{y - 3.99}{y} \times 100% = 5%\)

\(100(y - 3.99) = 5y \implies 100y - 399 = 5y\)

\(100y - 5y = 399 \implies y = \frac{399}{95}\)

y = 4.2 m

Correct Answer: D. 36

Explanation

The nth term of a GP is given by: \(T_{n} = ar^{n-1}\).

\(T_{3} = ar^{3-1} = ar^{2} = 81\).......(1)

\(T_{7} = ar^{7-1} = ar^{6} = 16 \) ...... (2)

Dividing (2) by (1), we have \(r^{4} = \frac{16}{81} = (\frac{2}{3})^{4} \implies r = \frac{2}{3}\)

Putting \(r = \frac{2}{3}\) in equation (1), we have \(81 = a \times (\frac{2}{3}\)^{2} = a \times \frac{4}{9} \implies a = \frac{729}{4}\)

\(T_{5} = ar^{5-1} = ar^{4} = \frac{729}{4} \times (\frac{2}{3})^{4}\)

= \(\frac{729}{4} \times \frac{16}{81} = 36\)

Correct Answer: D. 14

Correct Answer: A. (P∩Q)∪(P∩R)

Correct Answer: D. 3x

Explanation

If 30% of y = x, then 30% of 3y = 3x

Correct Answer: B. 140%

Explanation

cost price = $50

Selling price = 15 * 8 = $120

percentage profit = \(\frac{sp-cp}{cp}\) * 100 → \(\frac{120-50}{50}\) * 100

percentage profit = 70 * 2 → 140%