b1 mathematics

8/9/2019 B1 Mathematics

http://slidepdf.com/reader/full/b1-mathematics 1/5

FAC-REC MATHEMATICS B1

Vasisht House, 7/2, Begampur, Kalu Sarai, Sarvapriya Vihar New. Delhi. – 110017, Ph.:011-46106000, 46106111, 46106114

{1}

1. Sets A and B have 3 and 7 elements each. What can be the minimum number of elements in A B.

A. 0 B. 3C. 4 D. 7

E. 102. Four points A(-1,2), B(3,-4), C(5,-6) and D(-2,8) line in the coordinate plane, if p be any other

point in the co-ordinate plane what is the minimum value of PA PB PC PD A. 13 B. 10C. 23 D. 29

E. 313. Angle between angular bisectors of a triangle is , then which statement out of following can

be correct

A. 91

B. 90

C. 89

D. 60

E. 179

4. Value of a for which 3 1 0x ax and 4 2 1 0x ax have a common root is

A. -1 B. -2C. 1 D. 2

E. 35. If coordinates of three vertices of a triangle are A(1,2), B(3,7) and C(-2,3) and its orthocentre is H

, then the orthocentre of ABH is A. (-2,3) B. (1,2)C. (-3,2) D. (– 3, – 2)

E. (7, 3)6. A right angle has legs a and b. A circle of radius r touches the two legs and has its centre on

the hypotenuse then

A. 1a bab r

B. 2aba br

C. a b r D. a bab = r

E. 2a b

r ab

7. Number of positive integers n for which 1 1n n is rational A. 1 B. 6C. 0 D. infinitely many

E. 2





{2}

8. A hoop is resting vertically at stair case as shown in thediagram AB = 12 cm and BC =8 cm. The radius of the hoop is

A. 13 cm B. 12 2 cm

C.

14 cm D.

13 2 cm E. 15 2 cm

A

C

B

9. A number 20 is divided into four parts that are in A.P. such that product of first and fourth is toproduct of second and third is 2:3, then the largest number is

A. 4 B. 8C. 9 D. 12

E. 1410. A circle of radius 2cm touches 4 circle as shown in fig.

radius of smallest circle is A. 1/4 B. 1/3C. 2/5 D. 3/5

E. 4/7

1

1

11. 2

21 2

5 100n

nlimn n

A. -1 B. 2

5

C. 2

5 D. 1

E. no limit exist

12. The radius of right circular cone A is1

5 of the radius of right circular cone B, and the height of

right circular cone A is1

4 of the height of right circular cone B. What is the ratio of the volume

of right circular cone A to the volume of right circular cone B?

A. 1

16 B.

1

25

C. 1

64 D.

1

80

E. 1

100

13. There are 7 orange disks and 5 green disks in bag X and there are 5 orange disks and 15 greendisks in bag Y. if one disk is selected at random from each bag, what is the probability that bothdisks selected are green?

A. 5

48 B.

7

48





{3}

C. 5

16 D.

7

16

E. 3

4

14. If 2 3 6 f (x) x x and 15617

g(x ) ,x

then what is the value of g( f (x))?

A. 5.8 B. 7.4C. 7.7 D. 8.2

E. 10.315. If a, b, c are three natural numbers in AP such that a + b + c = 21, then the possible number of

ordered triplet (a, b, c) is: A. 13 B. 14C. 15 D. 16

E. 17

16. Which of the following is equivalent to the equation 2 25 1 0x x y in polar form?

A. 2 5 1 0r rcos B. 5 1r r cos

C. 2 5r rcos D. 2 5 1 0r r sin

E. 2 5r r sin

17. How many real solution does the system 2 2 25x y and xy = 10 have?

A. 0 B. 1C. 2 D. 3

E. 418. Which of the following lines is perpendicular to the line 3x – 2y = 16?

A. 3x – 2y = 25 B. 3x +2y = 16C. 2x – 3y = 7 D. 6x +9y = 16

E. 6x – 9 y = 32

19. If 2 1i ,then 23

2

i

A. 3 – 2i B. 4 – 3iC. 7 + 2i D. 8 – 6i

E. 9 + 6i

20. If 22 2 f (x) x , then what is the value of 4 f (x )?

A. 22 4x B. 22 6x C. 22 6x x D. 22 16 32x x

E. 22 16 34x x





{4}

21. If 2

9 26.25,

4

x then x could equal which of the following?

A. 0.11 B. 2.42C. 9.00 D. 10.24

E. 13.7622. If the equations x2 + b2 = 1 – 2bx and x2 + a2 = 1 – 2ax have one and only one root common then

?a b

A. 0 B. 1C. 2 D. 3

E. 4

23. If 1 ,3

y xx

then which of the following statement must be true?

I. x > 1 II. 3x III. 3x

A. I only B. II onlyC. I and III only D. II and III only

E. I, II, and III24. A jeep has four seats, including one driver’s seat and three passenger seats. If Amber, Bunny,

Cassie, and Donna are going for a drive in the jeep, and only Cassie can drive, then how manydifferent seating arrangements are possible?

A. 3 B. 6C. 12 D. 16

E. 24

25. If f(x)= 3 32 5x , then 1(2.5) f

A. 1.74 B. 2.18C. 2.37 D. 2.97

E. 5.1226. If y varies directly as x 2 and y = 24, when x = 3.7, what is the value of y when x = 8.3?

A. 170.67 B. 120.77C. 83.23 D. 64.00

E. 53.83

27. 3 2

22

2 4 8lim4x

x x xx

A. 0 B. 1C. -2 D. 2

E. -1





{5}

28. A regular hexagon is inscribed in the circle with center O. Ifthe circle has a radius of 4, what is the area of the shadedregion?

A. 8.3 B. 8.7

C. 9.0 D. 9.4

E. 10.2

O

29. A regular polygon of 9 sides each of length 2 is inscribed in a circle, then the radius of circle is

A. tan /9 B. cos /9ec

C. 2cos9

ec

D. 25/3

E. 6

7

30. If log 0.3 log 3 0.4,a ax and then 3log x is :

A. 0.12 B. 0.7

C. 3

4 D.

4

3

E. 5

4

b1 mathematics

Documents