# CDS Exam 2016 Mathematics Sample Paper Part – 4

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34. If both 112 and 33arefactors of the number a * 4^{3} * 6^{2 }* 13^{11 }what is the smallest possible value of ‘a’?

(A) 121

(B) 3267

(C) 363

(D) 33

35. 1O^{25}-7 is divisible by___

(A) 2

(B) 3

(C) 9

(D) Both (2) and (3)

36. If m and n are whole numbers and m^{n} =196, what is the value of (m- 3) ^{(n+1)}?

(A) 2744

(B) 1

(C) 121

(D) 1331

37. What is the value of (2x 4 x 5)^{5n}

(A) 2^{5n }+ 4^{5n }+ 5^{5n}

(8) (40^{5})^{n}

(C) (4O)^{5n}

(D) (40n)^{5}

38. If 5^{(a + b) }= 5 x 25 x 125, what is (a + b)^{2}

(A) 12

(B) 16

(C) 34

(D) 36

39. 1O^{222} + 10^{220} =?

(A) 10

(B) 100

(C) 1000

(0)10000

40. (132)^{?} X (132)^{?} = (132)^{115}

(A) 3

(B) 3.5

(C) 4

(D) 43

41. Convert the following SOP expression to an equivalent POS expression.

(A)

(B)

(C)

(D)

42. Applying DeMorgan’s theorem to the expression, we get

(A)

(B)

(C)

(D)

43. Determine the values of A, B, C, and D that make the product term equal to 1

(A)

(B)

(C)

(D)

44.

(A) True

(B) False

45. if, What IS the value of

(A) 36

(B) 7776

(C) 216

(D) 1296

46. A right triangle with sides 3cm, 4cm and 5 cm is rotated the side of 3 an to form a cone. The volume of the cone so formed is:

(A)

(B)

(C)

(D)