1 .
Karthik read $7\over13$th of a book in 1st week and $5\over 9$ 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 ?
A.  518
B.  452
C.  468
D.  502
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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?
A.  Insufficient data
B.  3 : 1
C.  1 : 3
D.  3 : 2
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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?
A.  3 pm
B.  2 pm
C.  1 pm
D.  1 am
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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?
A.  1800
B.  900
C.  2500
D.  2700
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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
A.  - $1 \over 2$
B.  $3 \over 2$
C.  1
D.  0
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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
A.  3
B.  4
C.  6
D.  9
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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.
A.  40 sq. units
B.  54 sq. units
C.  36 sq. units
D.  60 sq. units
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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.
A.  4$4 \over 9$
B.  3$7 \over 11$
C.  5$5 \over 11$
D.  5$5 \over 9$
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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
A.  (2 - $\sqrt 2$) : 1
B.  (2 + $\sqrt 2$) : 1
C.  ($\sqrt 2$ + 1) : 1
D.  ($\sqrt 2$ - 1) : 1
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10 .
If $\alpha$ is an acute angle and 2sin$\alpha$+ 15$cos^2$ $\alpha$= 7, then value of $tan^ 2$$\alpha$is
A.  $4 \over 3$
B.  $9 \over 16$
C.  $16 \over 9$
D.  $3 \over 4$
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11 .
A circle is inscribed in an equilateral triangle of side 24 cm, touching its sides. What is the area of the remaining portion of the triangle?
A.  144$\sqrt 3$ - 48$\pi$$cm^2$
B.  121$\sqrt 3$ - 36$\pi$$cm^2$
C.  144$\sqrt 3$ - 36$\pi$$cm^2$
D.  121$\sqrt 3$ - 48$\pi$$cm^2$
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12 .
A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is
A.  4.4 km/h
B.  4.25 km/h
C.  4.25 km/h
D.  5.15 km/h
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13 .
In an examination, a student's average marks were 63. If he had obtained 20 more marks in Geography and 2 more marks in history, then his average would have been 65. How many subjects were there in the examination?
A.  12
B.  11
C.  13
D.  14
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14 .
A booster pump can be used for filling as well as emptying a tank. The capacity of the tank is 2400 $m^3 $. The emptying capacity of the tank is 10 $m^ 3$ /min higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?
A.  20 $m^3$
B.  40$m^3$
C.  50$m^3$
D.  60$m^3$
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15 .
A and B walking around a circular park at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, then how many times shall they meet each other before 9.30 a.m.?
A.  5
B.  6
C.  7
D.  8
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