1). The value of k for which kx+ 3y-k+ 3=0 and 12x+ky=k, have infinite solutions, is
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2). In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1 : 2. Based on the information; the total number of coins in the collection now becomes.
A). 90 |
B). 80 |
C). 60 |
D). 50 |
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3). If \( \Large \frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}}=2 \), then x is equal to
A). \( \Large \frac{5}{12} \) |
B). \( \Large \frac{12}{5} \) |
C). \( \Large \frac{5}{7} \) |
D). \( \Large \frac{7}{5} \) |
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4). In an examination, a student scores 4 marks for every correct answer and losses 1 mark for every wrong answer. A student attempted all the 200 questions stud and scored 200 marks. Find the number of questions he answered correctly.
A). 82 |
B). 80 |
C). 68 |
D). 60 |
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5). The graphs of ax + by = c, dx + ey = f will be
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 |
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6). 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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7). 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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8). 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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9). 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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10). 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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