If P=(1−234) and Q=(−2310), find PQ.
(41−29)
(−4129)
(−43−213)
(−43−29)
Correct answer is D
(1−234)\((−2310)
= ((1×−2)+(−2×1)(1×3)+(−2×0)(3×−2)+(4×1)(3×3)+(4×0))
= (−43−29)
Express 7π6 radians in degrees.
315°
210°
105°
75°
Correct answer is B
\pi = 180°
\frac{7\pi}{6} = \frac{7 \times 180}{6}
= 210°
A rectangle has a perimeter of 24m. If its area is to be maximum, find its dimension.
12, 12
6, 6
4, 8
9, 3
Correct answer is B
Perimeter = 2(l + b) = 24
l + b = 12 \implies l = 12 - b
Area = (12 - b) \times b = 12b - b^{2}
\frac{\mathrm d A}{\mathrm d b} = 12 - 2b = 0 (at maximum)
2b = 12 \implies b = 6
l = 12 - 6 = 6m
Evaluate \int_{1}^{2} (2 + 2x - 3x^{2}) \mathrm {d} x.
-2
2
8
10
Correct answer is A
\int_{1}^{2} (2 + 2x - 3x^{2}) \mathrm {d} x
= (2x + x^{2} - x^{3})|_{1}^{2}
= (2(2) + 2^{2} - 2^{3}) - (2(1) + 1^{2} - 1^{3})
= 0 - 2 = -2
What is the coordinate of the centre of the circle 5x^{2} + 5y^{2} - 15x + 25y - 3 = 0?
(\frac{15}{2}, -\frac{25}{2})
(\frac{3}{2}, -\frac{5}{2})
(-\frac{3}{2}, \frac{5}{2})
(-\frac{15}{2}, \frac{25}{2})
Correct answer is B
Equation for a circle: (x - a)^{2} + (y - b)^{2} = r^{2}
Expanding, we have:
x^{2} - 2ax + a^{2} + y^{2} - 2by + b^{2} = r^{2}
Given: 5x^{2} + 5y^{2} - 15x + 25y - 3 = 0
Divide through by 5,
= x^{2} + y^{2} - 3x + 5y - \frac{3}{5} = 0
Comparing, we have
- 2a = -3; a = \frac{3}{2}
-2b = 5; b = -\frac{5}{2}