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#### Relations and Functions Book Back Questions

10th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
4 x 1 = 4
1. If f: A ⟶ B is a bijective function and if n(B) =8, then n(A) is equal to

(a)

7

(b)

49

(c)

1

(d)

14

2. Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

(a)

f(xy) = f(x).f(y)

(b)

f(xy) ≥ f(x).f(y)

(c)

f(xy) ≤ f(x).f(y)

(d)

None of these

3. If g={(1,1), (2,3), (3,5), (4,7)} is a function givrn by g(x)=αx+β then the values of α and β are

(a)

(-1,2)

(b)

(2,-1)

(c)

(-1,-2)

(d)

(1,2)

4. f(x) = (x+1)3 - (x-1)3 represents a function which is

(a)

linear

(b)

cubic

(c)

reciprocal

(d)

5. 4 x 2 = 8
6. Represent the function f(x)=$\sqrt { 2x^{ 2 }-5x+3 }$ as a composition of two functions.

7. If f(x)=3x-2, g(x)=2x+k and if f o g = f o f, then find the value of k..

8. Find k if f o g(k) = 5 where f(k)=2k-1.

9. Find x if gff(x) = fgg(x), given f(x) = 3x+1 and g(x)=x+3.

10. 2 x 5 = 10
11. 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.

12. If the function f: R⟶ R defined by

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

13. 1 x 8 = 8
14. Let X = {3, 4, 6, 8}. Determine whether the relation R={(x,f(x)) |x$\in$X, f(x)=x2+1}. is a function from X to N?