1 . Bisectors of two adjacent angles Aand Bof a quadrilateral ABCDintersect each other at a point P. Which one of the following is correct ?
A.  2∠APB= ∠C + ÐD
B.  ∠APB = ∠C+ ∠D
C.  ∠APB=180° – (∠C+ ∠B)
D.  ∠APB=180° – (∠C+ ∠D)
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2 .
A.  20°
B.  30°
C.  35°
D.  40°
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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 These
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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 these
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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.  140πsq cm
B.  146.5π sq cm
C.  70πsq cm
D.  None of these
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7 . For a plot of land of 100 m × 80 m, the length to be raised by spreading the earth from stack of a rectangular base 10 m × 8 m and vertical section being a trapezium of height 2 m. The top of the stack is 8 m × 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 $3^x$ 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 k does 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)$-\sqrt{2}$
A.  a
B.  b
C.  c
D.  d
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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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