If 2y\(^2\) + 7 = 3y - xy, find \(\frac{dy}{dx}\)
\(\frac{-y}{4x+y-3}\)
\(\frac{y}{4x+y-3}\)
\(\frac{-y}{4x+x-3}\)
\(\frac{y}{4x+x-3}\)
Correct answer is D
2y\(^2\) + 7 = 3y - xy, find \(\frac{dy}{dx}\)
4y \(\frac{dy}{dx}\) + 0 = 3 \(\frac{dy}{dx}\) - x \(\frac{dy}{dx}\) + y
{4x+x-3} \(\frac{dy}{dx}\) = y
= \(\frac{y}{4x+x-3}\)
A fair die is tossed 60 times and the results are recorded in the table
| Number of die | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 15 | 10 | 14 | 2 | 8 | 11 |
Find the probability of obtaining a prime number.
\(\frac{7}{30}\)
\(\frac{1}{6}\)
\(\frac{7}{15}\)
\(\frac{8}{15}\)
Correct answer is D
Prime number in the experiment are 2,3 and 5 with frequencies 10,14 and 8
P(obtaining a prime number) = \(\frac{10+14+8}{60}\)
= \(\frac{32}{60}\) or \(\frac{8}{15}\)
129.9N
75N
60.0N
7.5N
Correct answer is B
Let the normal reaction be R
R = Wcosø = mgcosø
= 15 * 10cos 60°
= 150 * 0.5000
= 75N
{1,4,9,36}
{3,9.36}
{9,36}
{36}
Correct answer is D
P = {3,6,9,12,18,36}; Q = { 4,36}
P n Q = {36}
Find the inverse of \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\)
\(\begin{pmatrix} 1 & 1 \\ -1.5 & -2 \end{pmatrix}\)
\(\begin{pmatrix} 1 & -1 \\ 1.5 & -2 \end{pmatrix}\)
\(\begin{pmatrix} -2 & 1 \\ 1.5 & 1 \end{pmatrix}\)
\(\begin{pmatrix} -2 & -1 \\ 1.5 & 1 \end{pmatrix}\)
Correct answer is A
Let A = \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\);
|A| = -8 - (-6) = -8 + 6
|A| = -2
A\(^{-1}\) = \(\frac{1}{-2}\) = \(\begin{pmatrix} -2 & 2- \\ 3 & 4 \end{pmatrix}\)
= \(\begin{pmatrix} 1 & 1 \\ -1.5 & -2 \end{pmatrix}\)