#### Sets, Relations and Functions Important Question Paper

11th Standard

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Mathematics

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. The number of constant functions from a set containing m elements to a set containing n elements is

(a)

mn

(b)

m

(c)

n

(d)

m+n

2. The function f:[0,2π]➝[-1,1] defined by f(x)=sin x is

(a)

one-to-one

(b)

on to

(c)

bijection

(d)

cannot be defined

3. If the function f:[-3,3]➝S defined by f(x)=x2 is onto, then S is

(a)

[-9,9]

(b)

R

(c)

[-3,3]

(d)

[0,9]

4. Given A={5,6,7,8}. Which one of the following is incorrect?

(a)

Ø⊆A

(b)

A⊆A

(c)

{7,8,9}⊆A

(d)

{5}⊆A

(a)

A\B

(b)

B\A

(c)

AΔB

(d)

A'

6. 5 x 2 = 10
7. Write the following in roster form.{x $\in$N:4x+9<52}

8. Write the following in roster form.
$\left\{ x:\frac { x-4 }{ x+2 } =3,x\in R-\{ -2\} \right\}$

9. The total cost of airfare on a given route is comprised of the base cost C and the fuel surcharge S in rupee. Both C and S functions of the mileage m; C(m)=0.4m + 50 and S(m)=0.03m. Determine a function for the total cost of a ticket in terms of the mileage and find the airfare for flying 1600 miles.

10. Check whether the following sets are disjoint where p={x:x is a prime<15} and Q={x:x is a multiple of 2 and x<16}

11. If U={x:1≤x≤10, x∈N}, A={1,3,5,7,9} and B={2,3,5,9,10} then find A'UB'.

12. 5 x 3 = 15
13. Graph the function f(x)=x3 and $g(x)\sqrt[3]x$ on the same co-ordinate plane. Find fog and graph it on the plane as well. Explain your results.

14. Write the steps to obtain the graph of the function y=3(x-1)2+5 from the graph y=x2

15. By taking suitable sets A, B, C, verify the following results:
$\times$ (B$\cap$C)=(A$\times$B) $\cap$ (A$\times$C)

16. Find the pairs of equal sets from the following sets. A = {0}, B = {x: x > 15 and x < 5}, C = {x: x - 5 = 0}, D = {x: x2 = 25}, E = {x: x is an integral positive root of the equation x2 - 2x - 15 = 0}.

17. Which of the following sets are finite and which are infinite?
Set of concentric circles in a plane.

18. 4 x 5 = 20
19. The formula for converting from Fahrenheit to Celsius temperatures is $y={5x\over 9}-{160\over 9}$. Find the inverse of this function and determine whether the inverse is also a function.

20. A simple cipher takes a number and codes it, using the function f(x)=3x-4. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line y=x(by drawing the lines)

21. The cartesian product A x A has 9 elements among which are found (-1, 0) and (0, 1).Find the set A and the remaining elements of A x A.

22. Show that the relation R on the set R of all real numbers defined as R = {(a, b): a < b2} is neither reflexive, nor symmetric nor transitive.