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Question 1
A
B
C
D
Explanation.
2q35 = 778

2 x 52 + q x 51 + 3 x 50 = 7 x 81 + 7 x 80

2 x 25 + q x 5 + 3 x 1 = 7 x 8 + 7 x 1

50 + 5q + 3 = 56 + 7

5q = 63 - 53

q = \(\frac{10}{5}\)

q = 2

Correct Option:
A

Question 2
A
\(5\frac{2}{3}\) 
B
30 
C
\(4\frac{1}{3}\) 
D
50 
Explanation.
\(\frac{3\frac{2}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}\)

\(\frac{\frac{11}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}}\)

\(\frac{110}{54} \div \frac{66}{1620}\)

50

Correct Option:
D

Question 3
A
N150 
B
N220 
C
N130 
D
N250 
Explanation.
S.I. = \(\frac{P \times R \times T}{100}\)

If T = 9 months, it is equivalent to \(\frac{9}{12}\) years

S.I. = \(\frac{5000 \times 4 \times 9}{100 \times 12}\)

S.I. = N150

Correct Option:
A

Question 4
A
B
C
D
Explanation.
M:N:Q == 5:4:3

i.e M = 5, N = 4, Q = 3

Substituting values into equation, we have...

\(\frac{2N - Q}{M}\)

= \(\frac{2(4) - 3}{5}\)

= \(\frac{8 - 3}{5}\)

= \(\frac{5}{5}\)

= 1

Correct Option:
C

Question 5
A
\(\frac{2}{3}\) 
B
\(\frac{1}{2}\) 
C
\(\frac{8}{9}\) 
D
\(\frac{1}{3}\) 
Explanation.
\((\frac{16}{81})^{\frac{1}{4}} \div (\frac{9}{16})^{-\frac{1}{2}}\)

\((\frac{16}{81})^{\frac{1}{4}} \div (\frac{16}{9})^{\frac{1}{2}}\)

\((\frac{2^4}{3^4})^{\frac{1}{4}} \div (\frac{4^2}{3^2})^{\frac{1}{2}}\)

\(\frac{2^{4 \times \frac{1}{4}}}{3^{4 \times \frac{1}{4}}} \div \frac{4^{2 \times \frac{1}{2}}}{3^{2 \times \frac{1}{2}}}\)

\(\frac{2}{3} \div \frac{4}{3}\)

\(\frac{2}{3} \times \frac{3}{4}\)

\(\frac{2}{4}\)

\(\frac{1}{2}\)

Correct Option:
B

Question 6
A
B
C
D
Explanation.
log\(_{3}^{18}\) + log\(_{3}^{3}\) - log\(_{3}^{x}\) = 3

log\(_{3}^{18}\) + log\(_{3}^{3}\) - log\(_{3}^{x}\) = 3log33

log\(_{3}^{18}\) + log\(_{3}^{3}\) - log\(_{3}^{x}\) = log333

log3(\(\frac{18 \times 3}{X}\)) = log333

\(\frac{18 \times 3}{X}\) = 33

18 x 3 = 27 x X

x = \(\frac{18 \times 3}{27}\)

= 2

Correct Option:
B

Question 7
A
\(\frac{1 - \sqrt5}{2}\) 
B
\(\frac{1 - \sqrt5}{4}\) 
C
\(\frac{ \sqrt5 - 1}{2}\) 
D
\(\frac{1 + \sqrt5}{4}\) 
Explanation.
\(\frac{2 - \sqrt5}{3 - \sqrt5}\) x \(\frac{3 + \sqrt5}{3 + \sqrt5}\)

\(\frac{(2 - \sqrt5)(3 + \sqrt5)}{(3 - \sqrt5)(3 + \sqrt5)}\) = \(\frac{6 +2\sqrt5 - 3\sqrt5 - \sqrt25}{9 + 3\sqrt5 - 3\sqrt5 - \sqrt25}\)

= \(\frac{6 - \sqrt5 - 5}{9 - 5}\)

= \(\frac{1 - \sqrt5}{4}\)

Correct Option:
B

Question 8
A
\(\frac{7}{3}\) 
B
\(\frac{5}{3}\) 
C
\(\frac{5}{2}\) 
D
\(\frac{3}{2}\) 
Explanation.
(\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))

\(\sqrt4 - \frac {\sqrt2}{\sqrt3} + \frac {\sqrt2}{\sqrt3} - \frac {1}{\sqrt9}\)

= 2 - \(\frac {1}{3}\)

= \(\frac {16 - 1}{3}\)

= \(\frac{5}{3}\)

Correct Option:
B

Question 9
A
49 
B
170 
C
21 
D
210 
Explanation.
The first poster has 7 ways to be arranges, the second poster can be arranged in 6 ways and the third poster in 5 ways.

= 7 x 6 x 5

= 210 ways

or \(\frac{7}{P_3}\) = \(\frac{7!}{(7 - 3)!}\) = \(\frac{7!}{4!}\)

= \(\frac{7 \times 6 \times 5 \times 4!}{4!}\)

= 210 ways

Correct Option:
D

Question 10
A
\(\sqrt\frac{3T - K}{M}\) 
B
\(\sqrt\frac{3T - M}{K}\) 
C
\(\sqrt\frac{3T + K}{M}\) 
D
\(\sqrt\frac{3T - K}{M}\) 
Explanation.
T = \(\frac{KR^2 + M}{3}\)

3T = KR2 + M

KR2 = 3T - M

R2 = \(\frac{3T - M}{K}\)

R = \(\sqrt\frac{3T - M}{K}\)

Correct Option:
B

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