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PARTIIIMATHEMATICS

1. Let and be the roots of the equation .012 xx The equation whose roots are 425 , is

A) 012 xx B) 012 xx C) 012 xx D) 012 xx

2. Let .2n If 1,2

ie ni

, then )1(...)1()1(12

n is

A) 2 B) n C) n (n 1) D) n (n 2)

3. The curve described parametrically by 22 ttx and 22 tty represents

A) a pair of straight lines B) an ellipse

C) a parabola D) a hyperbola

4.Suppose a

and b

are vectors such that kjiba 2

and kjiba

. The least value of

a

is

A)2

1 B) 2 C) 2 D) 12

5.Let ,2 kjiv

kiw 3

and u

is a unit vector, then the maximum value of wvu

,, is

A) 1 B) 59 C) 60 D) 610

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6. A value ofc for which the conclusion of mean value theorem holds for the function xxf elog)( on

[1, 3] is

A) e3log2 B) 3log2

1e

C) e3log D) 3loge

7. The area bounded by the curve ),(xfy the x-axis and the ordinate x= 1 and x= b is (b1) sin (3b +

4). Then )(xf is

A) )43(cos)1( xx B) )43(sin x

C) )43(cos)1(3)43(sin xxx D) )43(sin)1(3)43(cos xxx

8.A general solution to 05 yy is

A) tcecyt

2

5

1 B) tctcy 5sin5cos 21

C)tt etcecy 52

5

1 D)tt ececy

44 5

2

5

1

9.The differential equation representing the family of curves ,22 cxcy where c > 0, is a

parameter, whose order and degree is as follows

A) order 1, degree 2 B) order 1, degree 1 C) order 1, degree 3 D) order 2, degree 2

10. In a binary communication channel, the probability that a transmitted zero is received as zero is 0.95 and

the probability that a transmitted one is received as one is 0.90. If the probability that a zero is

transmitted is 0.4, then the probability that a one was transmitted, given that a one was received is

A)28

17B)

37

27C)

37

29D)

28

27

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