1). If \( \Large 3^{x+y}=81 \) and \( \Large 81^{x-y}=3 \), then what is the value of x?
A). \( \Large \frac{17}{16} \) |
B). \( \Large \frac{17}{8} \) |
C). \( \Large \frac{17}{4} \) |
D). \( \Large \frac{15}{4} \) |
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2). Ten chairs and six tables together cost Rs.6200, three chairs and two tables together cost Rs.1900. The cost of 4 chairs and 5 tables is
A). Rs.3000 |
B). Rs.3300 |
C). Rs.3500 |
D). Rs.3800 |
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3). The system of equations 3x + y - 4 = 0 and 6x + 2y - 8 = 0 has
A). a unique solution x = 1, y=1 |
B). a unique solution x = 0, y = 4 |
C). no solution |
D). infinite solutions |
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4). If x+ y - 7 = 0 and 3x + y -13 = 0, then what is \( \Large 4x^{2} + y^{2} + 4xy\) equal to?
A). 75 |
B). 85 |
C). 91 |
D). 100 |
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5). The solution of the equations \( \Large \frac{p}{x}+\frac{q}{y} \ and \ \frac{q}{x}+\frac{p}{y} \) n is
A). \( \Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{p^{2}-q^{2}}{np-mq} \) |
B). \( \Large x=\frac{p^{2}-q^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq} \) |
C). \( \Large x=\frac{p^{2}-q^{2}}{mp-nq}, y=\frac{p^{2}-q^{2}}{np-mq} \) |
D). \( \Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq} \) |
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6). If \( \Large \frac{3}{x+y}+\frac{2}{x-y}=2 \) and \( \Large \frac{9}{x+y}-\frac{4}{x-y}=1 \), then what is the value of \( \Large \frac{x}{y} \)?
A). \( \Large \frac{3}{2} \) |
B). 5 |
C). \( \Large \frac{2}{3} \) |
D). \( \Large \frac{1}{5} \) |
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7). If \( \Large \frac{a}{b}-\frac{b}{a}=\frac{x}{y} \) and \( \Large \frac{a}{b}+\frac{b}{a}= x - y \) , then what is the value of x?
A). \( \Large \frac{a+b}{a} \) |
B). \( \Large \frac{a+b}{b} \) |
C). \( \Large \frac{a-b}{a} \) |
D). None of these |
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8). If \( \Large \frac{x}{2}+\frac{y}{3}=4 \) and \( \Large \frac{2}{x}+\frac{3}{y}=1 \) then what is x + y equal to?
A). 11 |
B). 10 |
C). 9 |
D). 8 |
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9). A mason can build a tank in 12 h. After working for 6 h, he took the help of a boy and finished the work in another 5 h. The time that the boy will take alone to complete the work is
A). 30 h |
B). 45 h |
C). 60 h |
D). 64 h |
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10). A and B can do a job together in 12 days. A is 2 times as efficient as B. In how many days can B alone complete the work ?
A). 36 |
B). 12 |
C). 18 |
D). 9 |
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I. parallel, if the system has no solution.

II. coincident, if the system has finite numbers of solutions.

III. intersecting, if the system has only one solution.

Which of the above statements are correct?

A) Only I and II

B) Only ll and Ill

C) Only I and III

D) I, II and Ill

Correct Answer:

Description for Correct answerax + by = c and dx + ey = f

\( \Large \frac{a_{1}}{a_{2}}=\frac{a}{d}, \frac{b_{1}}{b_{2}}=\frac{b}{e}, \frac{c_{1}}{c_{2}}=\frac{c}{f} \)

Because, \( \Large \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} \)

Therefore, \( \Large \frac{b}{e} = \frac{c}{f} \)

It represents a pair of parallel lines.

Because, \( \Large \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \)

Therefore, \( \Large \frac{a}{d} = \frac{b}{e}\)

Therefore, system has unique solution and represents a pair of intersecting lines.