KARNATAKA COMMON ENTRANCE TEST-MODEL PAPER-6 MATHEMATICS

KARNATAKA COMMON ENTRANCE TEST-MODEL PAPER-6 MATHEMATICS

1. If a ,b and c are three non coplanar vectors, then abc . ab ?ac equals

1) 0

2) [a , b , c ]

3)2 [a , b , c ]

4)- [a , b , c ]

2. If a ,b and c are vectors of length 3, 4, 5 such that a is perpendicular to bc and b

is perpendicular to c a and c is perpendicular to ab then length of abc =

1) 10 2

2)

10

2

3)

5

2

4)None

3. The directions cosines of the lines through the points (3,4,5) and (4,5,6) are

1)(1, 1, 1) 2) 3, 3, 3

3)

1 11

3, 3, 3

4)(2,2,2)

4. If a =i+2j-3k and b =3i-j+2k are the adjacent sides of a parallelogram, then the angle

between the diagonals of parallelogram is

1) 300

2)600

3)900

4)00

5. If 1, , 2 , ....... n-1 are n th roots of unity, then the value of (16- )(16- 2)..........(16- n-1) is

1)

16n-1 8

2)

16 n1 15

3)

16 n-1 15

4)0

6. The smallest positive integer n for which 1 3 i n/2 is real is

1)3

2)0

3)6

d)12

7. The number ii is

1) real and positive 2) real and negetive 3)pure imaginary 4) negetive

8. The differential coefficient of f(logex) w.r.t. x where f(x)=logex is

1)

x loge x

2)

1 x

log

e

x

3)

1 x loge x

4)logx

9. If y=4x-5 is tangent to the curve y2 =px3 +q at (2,3) then

1)p=2, q=-7 2)p=-2, q=7

3)p=-2 q=-7

4)p=2, q=7

10. Area bounded by parabola y2 =4ax and x2 =4by is ....... sq units

1)16ab

2)

16ab 3

3)

16a 2 3

4)

8a 2 3

2

11.

dx

=

0 16cos2 x9 sin2 x

1)

24

2)

12

3)

8

4)0

12.

3sinx- 2cosx 4cosx5sinx

dx

=

1)

7 40

x-

22 41

log

4cosx5sinx

3)

7 41

x-

22 41

log

4cosx5sinx

2)

7 40

x-

22 40

log(4cosx +5sinx)

4)

7 42

x-

22 42

log (4cosx+ 5sinx)

13. The condition that the circles x2+y2 +2gx+2fy=0 and x2 +y2 +2g'x+2f'y=0 touch each other is

1)gf ' =g ' f

2)gg ' =ff ' 3)g+g ' =f +f '

4) ff' =gg'

space for rough work

1-2x; x0 1) f is continuous 2) f is continuous from left 4)f has removable disontinuity

3)f is continous from right

x3 -1; 1 ................
................

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