Find the value of x for \(\frac{2 + 2x}{3} - 2 \geq \frac{4x - 6}{5}\)
x \(\geq\) -5
x \(\geq\) -1
x \(\leq\) -1
x \(\leq\) 3
Correct answer is C
\(\frac{2 + 2x}{3} - 2 \geq \frac{4x - 6}{5}\)
\(\frac{2 + 2x - 6}{3} \geq \frac{4x - 6}{5}\)
\(\frac{2x - 4}{3} \geq \frac{4x - 6}{5}\)
\(5(2x - 4) \geq 3(4x - 6)\)
\(10x - 20 \geq 12x - 18\)
\(10x - 12x \geq -18 + 20\)
\(-2x \geq 2\)
\(x \leq -1\)
Evaluate \(\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}\)
4
-32
-8
16
Correct answer is C
\(\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}\)
= \(\frac{2\log_3 3^2 \times \log_3 (3^4)^{-2}}{\log_5 (5^4)}\)
= \(\frac{4\log_3 3 \times -8\log_3 3}{4\log_5 5}\)
= -8.
Find the value of k in the equation: \(\sqrt{28} + \sqrt{112} - \sqrt{k} = \sqrt{175}\)
\(\sqrt{28}\)
7
28
\(\sqrt{7}\)
Correct answer is B
\(\sqrt{28} + \sqrt{112} - \sqrt{k} = \sqrt{175}\)
\(\sqrt{4 \times 7} + \sqrt{16 \times 7} - \sqrt{k} = \sqrt{25 \times 7}\)
\(2\sqrt{7} + 4\sqrt{7} - \sqrt{k} = 5\sqrt{7}\)
\(6\sqrt{7} - 5\sqrt{7} = \sqrt{k}\)
\(\sqrt{k} = \sqrt{7}\)
\(\implies k = 7\)
144 ways
15 ways
185 ways
12 ways
Correct answer is D
For the committee to include 2 females, we must have 3 males, so that there should be 5 members.
That is, \(^4C_3 \times ^3C_2\)
= \(\frac{4!}{(4 - 3)! 3!} \times \frac{3!}{(3 - 2)! 2!}\)
= 4 × 3 = 12 ways
{1, 3, 6}
{3, 5, 9, 12}
{3, 9, 15}
{2, 3, 9}
Correct answer is C
μ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {3, 6, 9, 12, 15, 18} B = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} A ∩ B = {3, 9, 15}