-\(\frac{5}{4}\)
-\(\frac{4}{5}\)
\(\frac{4}{5}\)
\(\frac{5}{4}\)
Correct answer is C
PQ = \(\begin {pmatrix} 2 & 3\\ -4 & 1\end {pmatrix}\) = \(\begin {pmatrix} 6 \\ 8 \end {pmatrix}\) = \(\begin {pmatrix} 36 \\ - 16\end {pmatrix}\)
\(\begin {pmatrix} 36 \\ -16 \end {pmatrix} \) = k = \(\begin {pmatrix} 45 \\ -20 \end {pmatrix} \)
k = \(\frac{36}{45}\)
= \(\frac{4}{5}\)
Calculate the distance between points (-2, -5) and (-1, 3)
\(\sqrt{5}\) units
\(\sqrt{17}\) units
\(\sqrt{65}\) units
\(\sqrt{73}\) units
Correct answer is C
distance = \(\sqrt{(3 - (-5)^2 + (-1 - (-2)^2)}\)
= \(\sqrt{8^2 + 1^2}\)
= \(\sqrt{65}\) units
Find the value of x for which 6\(\sqrt{4x^2 + 1}\) = 13x, where x > 0
\(\frac{6}{5}\)
\(\frac{25}{24}\)
\(\frac{24}{25}\)
\(\frac{5}{6}\)
Correct answer is A
\(\sqrt{4x^2 + 1}\) = \(\frac{13x}{6}\)
4x\(^2\) + 1 = \(\frac{169x^2}{36}\)
4 + x\(^2\) = \(\frac{169x^2}{36}\)
cross multiply
169x\(^2\) - 144x\(^2\) = 36
25x\(^2\) = 36
x\(^2\) = \(\frac{36}{25}\)
: x = \(\pm\frac{6}{5}\)
Find the sum of the first 20 terms of the sequence -7-3, 1, ......
620
660
690
1240
Correct answer is A
d = -3 - (-7) = 4
S\(_{20}\) = \(\frac{20}{2}\){2(-7) + (20 - 1) 4}
= 10(- 14 + 76)
= 620
\(\frac{3}{2}\)
1
\(\frac{1}{2}\)
0
Correct answer is D
\(\frac{1}{x^2 - 4} = \frac{P}{(x + 2)} + \frac{Q}{(x - 2)}\)
I = p(x - 2) + Q(x + 2)
Let x = 2
I = P(2 - 2) + Q(2+ 2)
I = -4Q
Q = \(\frac{1}{4}\)
Let x = -2
I = P(-2 - 2) + Q(-2 + 2)
I = -4p
P = \(\frac{1}{-4}\)
PQQ = - \(\frac{1}{4} + \frac{1}{4}\)
= 0