Let A = {9,10,11,12,13} and let f : A → N be defined by f (n) = the highest prime factor of n. Find the range of f.

 11th cbse ncert chapter 2 relations and functions miscellaneous exercise

12. Let A = {9,10,11,12,13} and let f : A → N be defined by f (n) = the highest prime factor of n. Find the range of f.

9 = 3*3 therefore f(9)=3  

10= 2*5 therefore f(10)=5

11 =11 therefore f(11)=11

12 = 2 * 2 * 3 therefore f(12)=3

13 =13 therefore f(13)=13  

range of f = {3,5,11,13}

11. Let f be the subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a
function from Z to Z? Justify your answer.

choose a =(-1), b=(-1)

a*b = (-1)*(-1)  = 1

a+b = (-1)+(-1) = (-2)

therefore ( 1, -2 ) belongs to f

now choose a =1 , b =1

a*b = 1*1 = 1

a+b = 1+1 =2

therefore (1,2) belongs to f

therefore the element 1 has more than one image under f namely 

(-2) and 2.

Therefore f is not a function .

 

10. Let A ={1,2,3,4}, B = {1,5,9,11,15,16} and f = {(1,5), (2,9), (3,1), (4,5), (2,11)}
Are the following true?
(i) f is a relation from A to B
(ii) f is a function from A to B.
Justify your answer in each case. 

clearly  each element of f belongs to A x B. So f is a relation on A to B

both (2,9) and (2,11) belong to f 

so f has more than one image under f

so f is not a function.

 

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11th cbse ncert chapter 2 relations and functions miscellaneous exercise

12. Let A = {9,10,11,12,13} and let f : A → N be defined by f (n) = the highest prime factor of n. Find the range of f.

solution

 

11. Let f be the subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a
function from Z to Z? Justify your answer.

solution

 

ncert cbse 11th mathematics chapter 11 conic section 

miscellaneous

 If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus

solution

2. An arch is in the form of a parabola with its axis vertical. The arch is 10 m high
and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

solution

 

3. The cable of a uniformly loaded suspension bridge hangs in the form of a parabola.The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the
middle.

solution  

4. An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre.Find the height of the arch at a point 1.5 m from one end. 

solution  

 5. A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

solution

Find the area of the triangle formed by the lines joining the vertex of the parabola
x^2 = 12y to the ends of its latus rectum.  

solution 

7. A man running a racecourse notes that the sum of the distances from the two flagposts from him is always 10 m and the distance between the flag posts is 8 m.
Find the equation of the posts traced by the man

solution 

8. An equilateral triangle is inscribed in the parabola (y^2) = 4 ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

 solution 

 

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