\(1 ms^{-2}\)
\(2 ms^{-2}\)
\(3 ms^{-2}\)
\(4 ms^{-2}\)
Correct answer is C
The two time differentiation of distance with respect to time will give the acceleration.
\(s = \frac{3}{2}t^{2} - 3t\)
\(\frac{\mathrm d s}{\mathrm d t} = v = 3t - 3\)
\(\frac{\mathrm d v}{\mathrm d t} = a = 3\)
\(\frac{4}{7}\)
\(\frac{2}{7}\)
\(\frac{1}{7}\)
\(\frac{1}{12}\)
Correct answer is A
P(one blue, other red) = P(1st red then blue) or P(1st blue then red)
= \((\frac{4}{7} \times \frac{3}{6}) + (\frac{3}{7} \times \frac{4}{6})\)
= \(\frac{2}{7} + \frac{2}{7} = \frac{4}{7}\)
Find the acute angle between the lines 2x + y = 4 and -3x + y + 7 = 0.
40°
44°
45°
54°
Correct answer is C
\(2x + y = 4 \equiv y = 4 - 2x \implies m_{1} = -2\)
\(-3x + y + 7 = 0 \equiv y = -7 + 3x \implies m_{2} = 3\)
\(\tan \theta = \frac{m_{1} - m_{2}}{1 - m_{1}m_{2}} = \frac{-2 - 3}{1 - (-2)(3)} = \frac{-5}{-5} = 1\)
\(\tan \theta = 1 \implies \theta = 45°\)
Find the number of different arrangements of the word IKOTITINA.
30240
60840
120960
362880
Correct answer is A
IKOTITINA has 9 letters with 2Ts and 3Is. Therefore, the number of different arrangements
= \(\frac{9!}{2!3!} = \frac{9.8.7.6.5.4}{2} = 30240\)
2x + 3y + 6 = 0
3x - 2y - 6 = 0
-3x + 2y - 6 = 0
-2x + 3y - 6 =0
Correct answer is D
Equation of a straight line : y = mx + b
where m = the slope of the line
b = y- intercept
Given the two points (-3, 0) and (0, 2).
\(m = \frac{2 - 0}{0 - (-3)} = \frac{2}{3}\)
\(y = \frac{2}{3}x + 2 \implies 3y = 2x + 6\)
\(-2x + 3y - 6 = 0\)