Elementary Mathematics - Solved Questions and answers

1). If \( \Large a\ast b = 2a-3b+ab \), then \( \Large 3\ast 5+5\ast 3 \) is equal to:
A). 22
B). 24
C). 26
D). 28
2). If \( \Large p \times q = p+q+\frac{p}{q} \), the va1ue of \( \Large 8 \times 2 \) is:
A). 6
B). 10
C). 14
D). 16
3). Two numbers x and y (x > y) such that their sum is equal to three times their difference. Then value of \( \Large \frac{3xy}{2 \left(x^{2}-y^{2}\right) } \) will be;
A). \( \Large \frac{2}{3} \)
B). 1
C). \( \Large 1\frac{1}{2} \)
D). \( \Large 1\frac{1}{3} \)
4). The value of \( \Large \left(1+\frac{1}{x}\right) \left(1+\frac{1}{x+1}\right) \left(1+\frac{1}{x+2}\right) \left(1+\frac{1}{x+3}\right) \) is:
A). \( \Large 1+\frac{1}{x+4} \)
B). x+4
C). \( \Large \frac{1}{x} \)
D). \( \Large \frac{x+4}{x} \)
5). If \( \Large x = 7-4\sqrt{3} \), then the value of \( \Large x+\frac{1}{x} \)
A). \( \Large 3\sqrt{3} \)
B). \( \Large 8\sqrt{3} \)
C). \( \Large 14+8\sqrt{3} \)
D). 14


6). If \( \Large \frac{a}{b}=\frac{2}{3}\ and\ \frac{b}{c}=\frac{4}{5} \) , then the ratio \( \Large \frac{a+b}{b+c} \) equal to:
A). \( \Large \frac{20}{27} \)
B). \( \Large \frac{27}{20} \)
C). \( \Large \frac{6}{8} \)
D). \( \Large \frac{8}{6} \)
7). If \( \Large a\ast b=2 \left(a+b\right) \), then \( \Large 5\ast 2 \) is equal to:
A). 3
B). 10
C). 14
D). 20
8). If \( \Large \frac{2a+b}{a+4b}=3 \), then find the value of \( \Large \frac{a+b}{a+2b} \)
A). \( \Large \frac{5}{9} \)
B). \( \Large \frac{2}{7} \)
C). \( \Large \frac{10}{9} \)
D). \( \Large \frac{10}{7} \)
9). If \( \Large a\ast b=a+b+ab \), then \( \Large 3\ast 4-2\ast 3 \) is equal to:
A). 6
B). 8
C). 10
D). 12
10). If \( \Large x \circledast y = 3x+2y \), then \( \Large 2 \circledast 3+3 \circledast 4 \) is equal to
A). 18
B). 29
C). 32
D). 38
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