A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.
2x-3y=2
2x-3y=-2
2x+3y=-4
2x+3y=4
Correct answer is D
\(2x+3y = 6 \implies 3y = 6-2x\)
\(y = \frac{6}{3} - \frac{2x}{3}\)
Parallel lines have the same gradient
\(\therefore\) Gradient of the line = \(\frac{-2}{3}\)
Line passes through (-1,2)
Equation: \(\frac{y-2}{x-(-1)} = \frac{y-2}{x+1} = \frac{-2}{3}\)
\(3y-6 = -2x-2 \implies 3y+2x = -2+6 =4\)
\(-\sqrt{3}\)
\(-\frac{\sqrt{3}}{2}\)
\(-\frac{1}{2}\)
\(\frac{\sqrt{2}}{2}\)
Correct answer is B
cos150° = -cos30°
= \(-\frac{\sqrt{3}}{2}\)
1.2
3.6
0.8
0.5
Correct answer is C
\(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\)\(\begin{pmatrix} 5 \\ 4 \end{pmatrix}\) = k\(\begin{pmatrix} 17.5 \\ 40.0 \end{pmatrix}\)
\(\begin{pmatrix} 10 + 4 \\ 20 + 12\end{pmatrix}\) = \(\begin{pmatrix} 14 \\ 32\end{pmatrix}\) = k\(\begin{pmatrix} 17.5 \\ 40.0 \end{pmatrix}\)
k = \(\frac{14}{17.5} = \frac{32}{40} = 0.8\)
How many ways can 6 students be seated around a circular table?
36
48
120
720
Correct answer is C
In a circular seating arrangement, we fix the position of one person and then rotate the others, so we have
\((6-1)! = 5! = 5\times4\times3\times2 = 120\)
Find the 21st term of the Arithmetic Progression (A.P.): -4, -1.5, 1, 3.5,...
43.5
46
48.5
51
Correct answer is B
\(T_{n} = a + (n-1)d\)
\( d = T_{2} - T_{1} = T_{3} - T_{2} = -1.5 - (-4) = 2.5\)
\(T_{21} = -4 + (21 - 1) \times 2.5 = -4 + (20\times 2.5) \)
= \(-4 + 50 = 46\)