If P = n2+1:n=0,2,3 and Q = n+1:n=2,3,5, find P∩ Q.
{5, 10}
{4, 6}
{1, 3}
{ }
Correct answer is D
P=n2+1:n=0,2,3∴
Q = {n + 1: n = 2,3,5} \therefore Q = {3, 4, 6}
P \cap Q = { }
Given that f(x) = 2x^{2} - 3 and g(x) = x + 1 where x \in R. Find g o f(x).
2(x^{2} - 1)
2x^{2} + 4x - 1
2x^{2} + 6x - 1
3(x^{2} - 1)
Correct answer is A
f(x) = 2x^{2} - 3; g(x) = x + 1
g o f(x) = g (2x^{2} - 3)
= 2x^{2} - 3 + 1 = 2x^{2} - 2 = 2(x^{2} - 1)
10ms^{-2}
12ms^{-2}
14ms^{-2}
17ms^{-2}
Correct answer is C
accl = \frac{\mathrm d V}{\mathrm d t}
V = 3t^{2} + 2t - 1 \therefore a = \frac{\mathrm d V}{\mathrm d t} = 6t + 2
a \text{(after 2 seconds)} = (6\times 2) + 2 = 12+2 = 14ms^{-2}
Find the magnitude and direction of the vector p = (5i - 12j)
(13, 113.38°)
(13, 067.38°)
(13, 025.38°)
(13, 157.38°)
Correct answer is D
p = (5i - 12j); |p| = \sqrt{5^{2} + (-12)^{2}}
= \sqrt{169} = 13
\tan\theta = \frac{-12}{5} = -2.4 \implies \theta = -67.38°
Direction = 90° - (-67.38°) = 157.38°
Solve 3^{2x} - 3^{x+2} = 3^{x+1} - 27
1 or 0
1 or 2
1 or -2
-1 or 2
Correct answer is B
3^{2x} - 3^{x+2} = 3^{x+1} - 27
= (3^{x})^{2} - (3^{x}).(3^{2}) = (3^{x}).(3^{1}) - 27
Let 3^{x} be B; we have
= B^{2} - 9B - 3B + 27 = B^{2} - 12B + 27 = 0.
Solving the equation, we have B = 3 or 9.
3^{x} = 3 or 3^{x} = 9
3^{x} = 3^{1} or 3^{x} = 3^{2}
Equating, we have x = 1 or 2.