Mathematics 2012 | Study Mode

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Question 31
A
\(\frac{11}{3}\) 
B
\(\frac{3}{11}\) 
C
\(-\frac{3}{11}\) 
D
\(-\frac{11}{3}\) 
Explanation.
Share Answer \(\int^2_1(x^2 - 4x)dx\)

\((\frac{x^3}{3} - \frac{4x^2}{2})\)

substituting integrate values

\([\frac{8}{3} - \frac{4 \times 4}{2}] - [\frac{1}{2} - 2]\)

= \(-\frac{11}{3}\)

Correct Option:
D
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Question 33
A
126 
B
180 
C
216 
D
224 
Explanation.
Share Answer \(\frac{x}{7} = \frac{96}{1}\) ==> \(\frac{672 + x}{8} = 112\)

Therefore x = 224

Correct Option:
D
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Question 36
A
3.9 
B
4.9 
C
5.9 
D
6.9 
Explanation.
Share Answer \(\begin{array}{c|c} x & (x - \varkappa) & (x - \varkappa)^2 \\ \hline 2 & -5 & 25 \\ \hline 3 & -4 & 16 \\ \hline 8 & 1 & 1 \\ \hline 10 & 3 & 9 \\ \hline 12 & 5 & 25 \\ \hline & & 76
\end{array}\)

S.D = \(\sqrt{\frac{(x - \varkappa)^2}{n}}\)

S.D = \(\sqrt{\frac{76}{5}}\)

S.D = 3.9

Correct Option:
A
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Question 37
A
3630 
B
3360 
C
1120 
D
560 
Explanation.
Share Answer \(\frac{n + 1 (n - 2)}{(n + 1)!}\)

\(\frac{(n + 1) + (n - 2)!(n - 2)!}{(n + 1)!}\)

\(\frac{(n + 1)(n + 1 -1)(n+1-2)(n+1-3)!}{3!(n-2)!}\)

\(\frac{(n + 1)(n)(n-1)(n-2)!}{3!(n-2)!}\)

\(\frac{(n + 1)(n)(n-1)}{3!}\)

Since n = 15

\(\frac{(15 + 1)(15)(15-1)}{3!}\)

\(\frac{16 \times 15 \times 14}{3 \times 2 \times 1}\)

= 560

Correct Option:
D
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Question 38
A
6720 
B
6270 
C
6207 
D
6027 
Explanation.
Share Answer \(\frac{8!}{3!}\)

\(\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2\times 1}\)

==> 8 x 7 x 6 x 5 x 4 = 6720

Correct Option:
A
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Question 39
A
\(\frac{2}{27}\) 
B
\(\frac{3}{27}\) 
C
\(\frac{4}{27}\) 
D
\(\frac{5}{3}\) 
Explanation.
Share Answer Pass(P) = \(\frac{2}{3}\), Fail(F) = \(\frac{1}{3}\)

T = P.P.F ==> \(\frac{2}{3} \times \frac{2}{3} \times \frac{1}{3}\) = \(\frac{4}{27}\)

Correct Option:
C
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Question 40
A
\(\frac{2}{15}\) 
B
\(\frac{3}{15}\) 
C
\(\frac{7}{15}\) 
D
\(\frac{13}{15}\) 
Explanation.
Share Answer Man lives = \(\frac{2}{3}\) not live = \(\frac{1}{3}\)

Wife lives = \(\frac{3}{5}\) not live = \(\frac{2}{5}\)

\(P(\frac{2}{3} \times \frac{2}{5}) + (\frac{2}{5} \times \frac{1}{3}) + (\frac{2}{3} \times \frac{3}{5})\)

= \(\frac{4}{15} + \frac{3}{15} + \frac{6}{15}\)

= \(\frac{13}{15}\)

Correct Option:
D
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