1 .
If Ais the area of a right angled triangle and bis one of the sides containing the right angle, then what is the length of the altitude on the hypotenuse?
A.  $2Ab \over \sqrt {b^4 + 4 A^2}$
B.  $2A^2 b \over \sqrt {b^4 + 4 A^2}$
C.  $2Ab^2 \over \sqrt {b^4 + 4 A^2}$
D.  $2A^2 b^2 \over \sqrt {b^4 + 4 A^2}$
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2 .
A parallelogram and a rectangle stand on the same base and on the same side of the base with the same height. If $I_ 1$ , $I_ 2$ be the perimeters of the parallelogram and the rectangle respectively, then which one of the following is correct?
A.  $I_ 1$ < $I_ 2$
B.  $I_ 1$ = $I_ 2$
C.  $I_ 1$ > $I_ 2 $ but $I_ 1$ $\neq$2$I_ 2$
D.  $I_ 1$ = 2$l_ 2$
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3 .
The diameter of two circles are 18 cm and 8 cm. The distance between their centres is 13 cm. What is the number of common tangents?
A.  1
B.  2
C.  3
D.  None of the above
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4 .
What is the geometric means of the observations

125, 729, 1331?
A.  495
B.  1485
C.  2221
D.  None of the above
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5 .
The mean of 100 values is 45. If 15 is added to each of the first forty values and 5 is subtracted from each of the remaining sixty values, the new mean becomes
A.  45
B.  48
C.  51
D.  55
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6 .
A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 6 cm and length of the tube is 10 cm. If the thickness of the metal used is 1 cm, then the outer curved surface area of the tube is
A.  140$\pi$sq cm
B.  146.5 $\pi$sq cm
C.  70 $\pi$sq cm
D.  None of the above
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7 .
For a plot of land of 100 m $\times$ 80 m, the length to be raised by spreading the earth from stack of a rectangular base 10 m $\times$ 8 m and vertical section being a trapezium of height 2 m. The top of the stack is 8 m $\times$ 5 m. How many centimeters can the level raised?
A.  3 cm
B.  2.5 m
C.  2 cm
D.  1.5 cm
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8 .
If $3^ x$ + 27($3^ {-x}$ ) = 12, then what is the value of x?
A.  Only 1
B.  Only 2
C.  1 or 2
D.  0 or 1
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9 .
For which value of kdoes the pair of equations$ x^ 2$ - $y^ 2$ = 0 and $(x- k)^ 2$ + $y^ 2$ = 1 yield a unique positive solution of x?
A.  2
B.  0
C.  $\sqrt 2$
D.  - $\sqrt 2$
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10 .
The expression $sin^ 2$ x +$ cos^ 2$ x - 1 = 0 is satisfied by how many values of x?
A.  Only one value of x
B.  Two values of x
C.  Infinite values of x
D.  No value of x
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