AP – POLYCET

2017
Time : 2 Hours Total Marks : 120

SECTION - I
Mathematics

1. In ∆ABC if BC = 3, CA = 4, AB = 5, then cos

BAC =
3
A.
5
3
B.
4
4
C.
5
5
D.
3
2. sin6 A + cos6 A + 3sin2 Acos2 A =
A. 1
B. -1
C. 0
D. None
3. sin2 30o ,sin 45o and sin2 60o are in
 A. AP
B. GPP
C. HP
D. AGP
1
4. If sin cos = , then  =
2
o
A. 0
B. 30o
C. 45o
D. 60o
3
5. If tan = then the value of 1− cos
4 1+ cos
A. 9
1
B.
9
C. 4
1
D.
4
6. A, B and C areinterior angles angle of a triangle
ABC, then tan A + B 
 2 =
C   
A. sin
2
 
 C 
B. cos
2
 C 
C. tan
2
 C 
D. cot sn
2
 
7. If a 6 m height pole casts a shadow 2 3 m long on
the ground, then the sun's angle of elevation is
A. 60°
B. 45°
C. 30°
D. 90°
8. An iron spherical ball of volume 232848 cm3 has
been melted and converted into a cone with vertical
angle of 120°. Then the height of the cone is
A. 42 3 cm
B. 42 cm
C. 21 cm
D. None
9. From a point 30 m from the foot of a tower, the angle
of elevation of the top is 30°. Then the Height of the
tower is
A. 10 m
B. 10 3 m
 C. 15 m
D. 19 m
10. Under the usual notations in probability,
( )
P(E) + P E =
A. 0
1
B.
2
C. 1
D. None
11. Two dice are thrown at the same time. What is the
probability that the sum of the two numbers
appearing on the top of the dice is 8?
A. 31
36
5
B.
36
8
C.
36
D. 1
12. A box contains 5 red marbles, 8 white marbles and 4
green marbles. One marble is taken out of the box at
random. The probability that the marble taken out
will be white is
5
A.
17
 8
B.
17
4
C.
17
8
D.
9
13. The mean of a +1, +3, a + 4 and a + 8
A. a + 7
B. a + 4
C. a – 3
D. none
14. the mean of n observation x1, x2, ……xn. Repeated f1,
f2,………. fn time respectivey is

n
xi
A. i=1


n
i=1 i
f

n

B. fx
i=1 i i


n f
i=1 i
C. fi xi
n

 i=1
fi
15. The sum of lower limit of median class and upper
limit of modal class is
Class 10- 20- 30- 40- 50- 60-
Interval 20 30 40 50 60 70
 Frequency 1 3 5 9 7 3

A. 60
B. 40
C. 90
D. 50
16. A data has 13 observations arranged in descending
order. Which observation represents the median of
the data?
A. 17th
B. 6th
C. 7th
D. None
17. Cumulative frequency is used to calculate
A. Median
B. mode
C. mean
D. None
18. Under the usual notations, the formula for calculating
mode for grouped frequency distribution is
 fi − f0 
A. i −  −f −f
 2 f1 0 2
 f − f 
B. i +  −i f −0 f   h
 f1 0 2
  fi − f0 
C. i +  −f −f
 2 f1 0 2
 fi − f0   h
D. i +  −f −f 
 2 f1 0 2

19. In the given figure, LM || AB, AL = x - 3, AC = 2x,

BM = x - 2 and BC = 2x + 3 Then the value of x is

A. 7
B. 8
C. 9
D. Cannot be determined
20. The diagonals of a quadrilateral ABCD intersect each
AO CO
other at a point 0 such that = Then the
BO DO
quadrilateral ABCD is
A. trapezium
B. square
C. rectangle
D. parallelogram
21. In the given figure, if AB || CD || EF, given that AB =
7.5 cm, DC = y cm, EF = 4.5 cm BC = x cm, then the
value of x is

A. 4
B. 5
C. 6
D. None
22. The diagonals of a trapezium ABCD with AB || DC,
intersect each other at the point 0. If AB = 2CD; then
the ratio of areas of triangles AOB and COD is
A. 4: 1
B. 1 : 4
C. 3 : 4
D. 4 : 3
23. In an equilateral triangle ABC, D is a point on side
1
BC such that BD = BC Then 9 AD 2=
3
2
A. 5AB
B. 7AB2
C. 11AB2
 D. AB2
24. A tangent PQ at a point P of circle of radius 5 cm
meets a line through the centre 0 at the point Q such
that OQ = 12 cm, then length of PQ is
A. 12 cm
B. 13 cm
C. 8.5 cm
D. 199 cm
25. If TP and TQ are two tangents to a circle with centre
0 so that LPOQ = 110°, then ZPTQ is equal to
A. 60°
B. 70°
C. 80°
D. 90°
26. What is the area of the shaded region in the figure? In
which two circles with centres A and B touch each
other at the point C, if AC = 8 cm and AB = 3 cm, is
A. 24 cm2
B. 39 cm2
C. 11 cm2
D. 5  cm2
27. If all the sides of a parallelogram touch a circle, then
the parallelogram is
A. a square
B. a rhombus
 C. a rectangle
D. None
28. PQ is chord of length 8 cm of 'a circle of radius 5 cm.
The tangents at P and Q intersect at a point T. Then
the length of TP is
A. 10
3
B. 25
3
C. 20
3
D. 16
3
29. 3 + 5 is a
A. Positive rational number
B. Negative rational number
C. Positive irrational number
D. Negative irrational number
30. If a + b = 5, ab = 6 then a3 + b3 =
A. 5
B. 25
C. 35
D. 125
31. 2log 3 – 3 log 2 =
A. log 0
 B. log 1
9
C. log
 
8
D. log (72)
32. log2 log25 5 =
A. 0
B. 1
C. -1
1
D. −
2 y
 a 
33. If ax =   = k m , then 1 − 1 =
k x y
A. 0
B. 1
C. M
1
D.
m
34. lf A= {1, 2,3, 4, 5, 6}, B= {4, 5 C 7, 8}, C= (4, 5, 6},
then A  B =
A. A
B. B
C. C
D. None
35. If A and B are subsets of a universal set , then
A  Bc =
A. A – B
B. 15
C. 20
D. 25
36. If n(A) = 15, n(B) = 10, n ( A  B) = 5, then
n ( A  B)=
A. 5
B. 15
C. 20
D. 25
37. If 𝖺 and β are the zeros of the polynomial p(x) = 3x2
– x – 4, then 𝖺β =
1
A.
3
1
B.-
3
4
C.
3
4
D.-
3
38. If p(x) = 5x7 – 6x5 + 7x – 6, then the degree of p(x) is
A. 0
 B. 1
C. 5
D. 7
39. A factor of x3 – 3x2 + x + 1 is
A. x + 1
B. 2x – 1
C. 2x + 1
D. x – 1
10 2
40. + and 15 − 5 = −2, then
x+ y x− y x+ y x− y
A. x = 3, y = 2
B. x = 3, y = -2
C. x = -3, y = 2
D. x = -3, y = -2
41. The larger of two supplementary angles exceeds the
smaller by 18°. The angles are
A. 80°, 100°
B. 81°, 99°
C. 82o, 98o
D. 83o, 97o
2 3 4 9
42. + = 2 and − = −1, then
x y x y
A. x = 3, y =2
B. x = 3, y = 4
 C. x = 2, y = 3
D. x = 4, y = 3
43. The value of k for which the pair of equations 3x +
4y + 2 = 0 and 9x + 12y+ k = 0 represent coincident
lines is
A. 2
B. 3
C. 6
D. 12
44. If 2x + 3y = 17, 2x+2 − 3y+1 = 5, then
A. x = 3, y = 2
B. x = 3, y = 4
C. x = 2, y = 3
D. x = 4, y = 3
45. if the sum of the squares of the roots of x2 + px – 3 =
0 is 10, then p =
A. ±2
B. ±3
C. ±5
D. ±6
46. If one root of x2 – 8x + 13 = 0 is 4 + 3 , then the
other root is
A. 2 + 3
B. 2 - 3
 C. -4 + 3
D. 4 - 3
47. If 𝖺 and β are the roots of a quadratic equation x2 –
 
px + q = 0, then + =
 
p 2 − 2q
A.
q
p + 2q
2
B.
q
p −q
2
C.
q
p2 + q
D.
q
48. The root of the quadratic equation 2x 2 − 2 2x +1 = 0
are
1
A. 2, .
2
1 1
B. ,
2 2
1 1
C. ,
2 2
D. 2, 2
49. If the product of five numbers in GP is 1024, then the
middle number is
A. 8
B. 4
C. 2
D. None
50. If the second term of a GP is 2 and the sum of infinite
terms is 8, then the first term is
A. 8
B. 6
C. 4
D. 3
51. If a, b and c are in AP and also in GP, then
A. a = b ≠ c
B. a ≠ b = c
C. a ≠ b ≠ c
D. a = b = c
52. The end points of a line are (Z 3), (4, 5). Then its
slope is
A. 4
B. 3
C. 2
D. 1
53. The value of k for which the points (7, - 2), (5, 1), (3,
k) are collinear is
 A. 4
B. 3
C. 2
D. None
54. The points A(7, 3), B(6, 1), C(8, 2) and D(9, 4) taken
in that order are the vertices of a
A. square
B. rhombus
C. parallelogram
D. trapezium
55. The points of trisection of the line segment joining
(2, - 2), (-7, 4) are
A. (1, 0), (-4, 2)
B. (- 1. 0), (-4, 2)
C. (-1, 0), (-4, -2)
D. (1, 0), (4, 2)
56. The points which divide the line segment joining A(-
2, 2)and B(Z
7  8) into four
13  equal parts are,
A. −1, , ( 0,5 ) , 1,
 2  2
 7    13 
B. −1, , ( 0, −5), 1, −
 2  2
 7    13   
C. 1, , ( 0,5 ) , 1, .
 2  2
   
  7  13 
D. 1, , ( 0, −5), 1,
 2  2
   
57. If a cylinder and cone have bases of equal radii and
are equal heights, then the ratio of their ' volumes is
A. 1 : 3
B. 2 : 3
C. 3 : 1
D. 3 : 2
58. If the curved surface area of a cone is 4070 cm2 and
its diameter is 70 cm, then its slant height is
A. 27 cm
B. 37 cm
C. 47 cm
D. 57 cm
59. Under the usual notations, the total surface area of a
cuboid is
A. lb + bh + hl
B. lb + bh + hl
.
2
C. 2 ( lb + bh + hl )
D. None
60. If sec + tan = 3, then cos  =
3
A.
4
 3
B.
5
2
C.
3
2
D.
5