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Question Bank No: 1

1. If [x] denote the greatest integer $\leq$ x then $[\frac{2}{3}]$ + $[\frac{2}{3} + \frac{1}{99}]$ + $[\frac{2}{3} + \frac{2}{99}]$ +.......+ $[\frac{2}{3} + \frac{98}{99}]$ =

a)		99
b)		98
c)		66
d)		65

2. In a city 20 percent of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then persons travelling by car or bus is.

a)		80%
b)		40%
c)		60%
d)		70%

3. In the set Q an opeartion * is defined by the rule a*b=ab/4 then identity element of Q w.r.t*

a)		1
b)		2
c)		3
d)		4

4. In the set I an operation * is defined by the rule p * q = p+q+pq what is identity of I w.r.t *

a)		1
b)		0
c)		1/2
d)		1/6

5. The number of binary operations that can be defined on the set A = {a, b, c} is.

a)		$3^{3}$
b)		$3^{4}$
c)		$3^{9}$
d)		$9^{3}$

6. In the set Q + of all positive rational number, the operation * is defined by the formula a*b = $\frac{ab}{6}$ , then the inverse of 9 with respect to * is

a)		4
b)		3
c)		1/9
d)		1/3

7. The domain of $\sin^{- 1}$ $[\frac{2 x + 1}{3}]$ is

a)		(+2, 1)
b)		[-2, 1]
c)		R
d)		[-1, 1]

8. Let f(x + $\frac{1}{x}$ ) = $x^{2}$ + $\frac{1}{x^{2}}$ , x $\neq$ 0, then f(x) = ?

a)		$x^{2}$
b)		$x^{2}$ - 1
c)		$x^{2}$ - 2
d)		$x^{2}$ + 2

9. If f(x) = log ( $\frac{1 - x}{1 + x}$ ), then f(a) + f(b) =

a)		f(a + b)
b)		f(a b)
c)		f ( $\frac{a + b}{1 + ab}$ )
d)		f ( $\frac{a - b}{1 + ab}$ )

10. If x $\neq$ 1 and f(x) = $\frac{x + 1}{x - 1}$ is a real function, the f f f (2) is

a)		1
b)		2
c)		3
d)		None of these

11. If f(x) = $\frac{2 x + 1}{3 x - 2}$ , then (f o f) (2) is equal to.

a)		1
b)		3
c)		4
d)		2

12. If f(x) = $\frac{x}{x - 1}$ , x $\neq$ 1, then $f^{1}$ (x) is.

a)		$\frac{x}{x - 1}$
b)		$\frac{x - 1}{x}$
c)		$\frac{1 - x}{x}$
d)		$\frac{x}{1 - x}$

13. Let the function f be defined by f(x) = $\frac{2 x + 1}{1 - 3 x}$ ,. Then $f^{1}$ (x) is.

a)		$\frac{x - 1}{3 x + 2}$
b)		$\frac{3 x + 2}{x - 1}$
c)		$\frac{x + 1}{3 x - 2}$
d)		$\frac{2 x + 1}{1 - 3 x}$

14. If f(x) = x - $x^{2}$ + $x^{3}$ - $x^{4}$ +............ to $\infty$ for |x| $<$ 1, then $f^{1}$ (x)=

a)		x
b)		x/(1-x)
c)		(1-x)/x
d)		x/(1+x)

15. If Na = {an : n $\in$ N} then N5 $\cap$ N7 equals.

a)		N7
b)		N
c)		N35
d)		N5

16. The digit at the unit place in the number $19^{2005}$ + $11^{2005}$ - $9^{2005}$ is.

a)		2
b)		1
c)		0
d)		8

17. Which one of the following is (A - B) $\cup$ (B - A) where A and B are any two nonempty sets.

a)		(A $\cup$ B) $\cup$ (A - B)
b)		(A $\cup$ B $\cup$ (A $\cap$ B)
c)		(A $\cup$ B) - (A $\cap$ B)
d)		(A - B) - (B - A)

18. If A and B are not disjoint sets, then n(A $\cup$ B) is equal to.

a)		n (A) + n (B)
b)		n (A) + n (B) - n (A $⋂$ B)
c)		n (A) + n (B) + n (A $\cap$ B)
d)		n (A) n (B)

19. If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A x B and B x A are.

a)		$2^{99}$
b)		$99^{2}$
c)		100
d)		18

20. If A and B are two sets having 3 elements in common, then the number of elements common to the sets A x B and B x A is.

a)		3
b)		6
c)		9
d)		12

21. Two finite sets have m and n elements. the number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then the values of m and n are.

a)		7,6
b)		6,3
c)		6,4
d)		7,4