#### frequently asked five mark questions chapter one

10th Standard EM

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Maths

Do not involve in any malpractices
Time : 01:15:00 Hrs
Total Marks : 75

Part - A

15 x 5 = 75
1. Let A = {1,2,3,4} and B ={2,5,8,11,14} be two sets. Let f: A ⟶ B be a function given by f(x)=3x−1. Represent this function
(i) by arrow diagram
(ii) in a table form
(iii) as a set of ordered pairs
(iv) in a graphical form

2. Using horizontal line test (Fig.1.35(a), 1.35(b), 1.35(c)), determine which of the following functions are one – one.

3. Let A={1,2,3}, B={4,5,6,7}, and f={(1,4),(2,5),(3,6)}  be a function from A to B. Show that f is one – one but not onto function.

4. If A={-2,-1,0,1,2} and f: A ⟶ B is an onto function defined by f(x)=x2+x+1 then find B.

5. Let f be a function f:N ⟶ N be defined by f(x) = 3x+2, x$\in$N
(i) Find the images of 1, 2, 3
(ii) Find the pre-images of 29, 53
(ii) Identify the type of function

6. Forensic scientists can determine the height (in cms) of a person based on the length of their thigh bone. They usually do so using the function h(b)=2.47b+54.10 where b is the length of the thigh bone.
(i) Check if the function h is one – one
(ii) Also find the height of a person if the length of his thigh bone is 50 cms.
(iii) Find the length of the thigh bone if the height of a person is 14796 cms.

7. Let f be a function from R to R defined by f(x)=x-5. Find the values of a a and b given that (a,4) and (1,b) belong to f.

8. The distance S (in kms) travelled by a particle in time ‘t’ hours is given by S(t)=$\frac { { t }^{ 2 }+t }{ 2 }$. Find the distance travelled by the particle after
(i) three and half hours.
(ii) eight hours and fifteen minutes.

9. If the function f: R⟶ R defined by

(i) f(4)
(ii) f(-2)
(iii) f(4)+2f(1)
(iv) $\frac { f(1)-3f(4) }{ f(-3) }$

10. Let f = {(2, 7); (3, 4), (7, 9), (-1, 6), (0, 2), (5,3)} be a function from A = {-1,0, 2, 3, 5, 7} to B = {2, 3, 4, 6, 7, 9}. Is this (i) an one-one function (ii) an onto function, (iii) both oneone and onto function?

11. A functionf: [-7,6) $\rightarrow$ R is defined as follows.

find 2f(-4) + 3f(2)

12. A functionf: [-7,6) $\rightarrow$ R is defined as follows.

f(-7) -f(-3)

13. A functionf: [-7,6) $\rightarrow$ R is defined as follows.

$\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) }$

14. f(x) = (1+ x)
g(x) = (2x-1)
Show that fo(g(x)) = gof(x)

15. Let A = {1, 2, 3, 4, 5}, B = N and f: A $\rightarrow$B be defined by f(x) = x2. Find the range of f. Identify the type of function.