Karthik read $7^ 13$th of a book in 1st week and $5^ 9$ of the remaining book in $2^ {nd}$ week. If there were 96 pages unread after $2^ {nd}$ week, then how many pages were there in the book ?

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2 .

Two trains running in opposite directions cross a man standing on the platform in 27 and 17 seconds respectively and they cross each other in 23 seconds. What is the ratio of their speeds?

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3 .

Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours, while machine R can print the same in 12 hours. All the machines started printing at 9 a.m. Machine P is stopped at 11 a.m. and the remaining two machines complete the work. Approximately, at what time will the printing of one lakh books be completed?

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4 .

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

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5 .

If $1 \over x + y$ = $1 \over x$ + $ 1 \over y$ (x $\neq$ 0, y $\neq$ 0, x $\neq$ y) then value of $x^2$ + $y^2$ + xy is

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6 .

If cos$\theta$ = $1 \over \sqrt 5$ , then value of $6 sin\theta + 3 cos\theta \over sin^3 \theta + 2 cos^3 \theta + 3 cos \theta$ is

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7 .

The base of a parallelogram is (p + 4), altitude to the base is (p - 3) and the area is ($p^2$ - 4). Find its area.

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8 .

A can complete a work in 12 days while working 8 hours per day. B can complete the same work in 8 days while working 10 hours a day. If A and B work together, while working 8 hours a day, then the work can be completed in ___ days.

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9 .

In a $\Delta$ABC, points M and N respectively lie on side AB and AC such that area of triangle ABC is double than the area of trapezium BMNC. The ratio AM : MB is

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10 .

If $\alpha$ is an acute angle and 2sin$\alpha$+ 15$cos^2$ $\alpha$= 7, then value of $tan^ 2$$\alpha$is

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