Correct Answer: C. 6

Explanation

\(^nC_2\) = 15

\(\frac{n!}{(n - 3)! 2!}\) = 15

\(\frac{n(n - 1)(n - 2)!}{(n - 2)!2}\) = 15

n\(^2\) - n = 30

n\(^2\) - n - 30 = 0

(n - 6)(n + 5) = 0

n = 6 or n = -5

Correct Answer: C. \(\frac{4}{5}\)

Explanation

PQ = \(\begin {pmatrix} 2 & 3\\ -4 & 1\end {pmatrix}\) = \(\begin {pmatrix} 6 \\ 8 \end {pmatrix}\) = \(\begin {pmatrix} 36 \\ - 16\end {pmatrix}\)

\(\begin {pmatrix} 36 \\ -16 \end {pmatrix} \) = k = \(\begin {pmatrix} 45 \\ -20 \end {pmatrix} \)

k = \(\frac{36}{45}\)

= \(\frac{4}{5}\)

Correct Answer: C. 1 and 4

Explanation

The two points of contact of the curve with the x-axis are x = 1 and x = 4. The roots of the equation are x = 1 and x = 4

Correct Answer: C. 282m

Correct Answer: A. \(\frac{2}{t}\)

Explanation

t = \(2^{-x} = \frac{1}{2^{x}}\)

\(\implies 2^{x} =\frac{1}{t}\)

\(2^{x+1} = 2^{x} \times 2^{1}\)

= \(\frac{1}{t} \times 2 = \frac{2}{t}\)

Correct Answer: B. onto

Explanation

The function \(y = g(x)\) is one- to- one but \(z = h(y)\) is not one- to- one but onto.

\(\therefore h(g(x)) = onto\)

Correct Answer: A. 246cm

Correct Answer: D. 2

Explanation

\((\log_{2} m)^{2} - \log_{2} m^{3} = 10\)

Let \(\log_{2} m\) = x.

\((\log_{2} m)^{2} - 3\log_{2} m - 10 = 0\)

\(\implies x^{2} - 3x - 10 = 0\)

\(x^{2} + 2x - 5x - 10 = 0 \)

\(x(x + 2) - 5(x + 2) = 0\)

\(\implies x = \text{-2 or 5}\)

When \(\log_{2} m = -2 \implies m = 2^{-2} = \frac{1}{4}\)

When \(\log_{2} m = 5 \implies m = 2^{5} = 32\).

Correct Answer: C. 37

Explanation

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an odd amount of numbers so we just count from each side until we find the number in the middle. 14,22,22,31,32,35,36,37,39,41,42,48,50,58,63 This gives us a final answer of 37 for the median.