Given n = 3, evaluate 1(n−1)!−1(n+1)!
12
212
2
1124
Correct answer is D
n = 3, 1(n−1)!−1(n+1)!=1(3−1)!−1(3+1)!
= 12−124=12−124
= 1124
80
90
110
120
Correct answer is D
nP5nC5=n!(n−5)!÷n!(n−5)!5!
= n!(n−5)!×(n−5)!5!n!=5!=120
If log10y+3log10x≥log10x, express y in terms of x.
y≥1x
y≤1x
y≤1x2
y≥1x2
Correct answer is D
log10y+3log10x≥log10x
⟹log10y≥log10x−3log10x
log10y≥−2log10x=log10y≥log10x−2
log10y≥log10(1x2)⟹y≥1x2
Solve for x in the equation 5x×5x+1=25
−2
−12
12
2
Correct answer is C
5x×5x+1=25
5x×5x+1=52
5x+x+1=52, equating powers,
2x+1=2⟹2x=1
∴
If (2t - 3s)(t - s) = 0, find \frac{t}{s}
\frac{3}{2} or 1
\frac{3}{2} or -1
\frac{-3}{2} or -1
\frac{-3}{2} or 1
Correct answer is A
(2t - 3s)(t - s) = 0 \implies (2t - 3s) = \text{0 or} (t - s) = 0
2t - 3s = 0 \implies 2t = 3s \therefore \frac{t}{s} = \frac{3}{2}
t - s = 0 \implies t = s \therefore \frac{t}{s} = 1
\frac{t}{s} = \frac{3}{2} or 1