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Let A = {1, 2, 3}, B = {a, b, c}, C {a(...

Let A = {1, 2, 3}, B = {a, b, c}, C ` {a_(1), b_(1), c_(1), d_(1), e_(1)}` and consider the following statements.
`S_(1)` : The number of one-one functions from A to C is 60.
`S_(2)` : The number of onto functions from C to A is 150
`S_(3)` : The number of onto functions from B to C is 0
`S_(4)` : The number of objective functions from A to B is 6
Which of the following combination is true ?

A

`S_(1)` and `S_(2)` only

B

`S_(1)` and `S_(3)` only

C

`S_(2)` and `S_(4)` only

D

`S_(1), S_(2), S_(3)` and `S_(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
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AAKASH INSTITUTE-RELATIONS AND FUNCTIONS -Assignment (Section - B) Objective Type Questions (one option is correct)
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  2. Let f(x) = ax^(3) + bx^(2) + cx + d, a != 0, where a, b, c, d in R. If...

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  3. Let A = {1, 2, 3}, B = {a, b, c}, C {a(1), b(1), c(1), d(1), e(1)} an...

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  4. Select the correct option

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  5. Let f : [2, 4) rarr [1, 3) be a function defined by f(x) = x - [(x)/(2...

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  6. Identify the correct option

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  7. Which of the following function is an even function ?

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  8. A function f(x) given by f(x)={{:(x^(2)sin""(pix)/(2), |x| lt1),(x|...

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  9. Let f(x+y) + f(x-y) = 2f(x)f(y) for x, y in R and f(0) != 0. Then f(x)...

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  10. Let a real valued function f satisfy f(x + y) = f(x)f(y)AA x, y in R a...

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  11. Let f: R rarr R be a function defined as f(x)=[(x+1)^2]^(1/3)+[(x-1)^2...

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  12. Let f(x) = |sinx| + |cosx|, g(x) = cos(cosx) + cos(sinx) ,h(x)={-x/2...

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  13. Identify the incorrect statement

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  14. Let f(x)=x^2 and g(x)=2^x . Then the solution set of the equation f...

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  15. Let f(x) = tan x, x in (-pi/2,pi/2)and g(x) = sqrt(1-x^2) then g(f(x)...

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  16. Let g(x) be a polynomial function satisfying g(x).g(y) = g(x) + g(y) +...

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  17. "If "f:R to R, g:R and h:R to R be three functions are given by f(x)=x...

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  18. Range ofthe function f(x)=cos(Ksin x) is [-1,1], then the least positi...

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  19. Consider that the graph of y = f(x) is symmetrie about the lines x =...

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  20. Let f(x) be defined in (0, 1), then the domain of definition of f(e^...

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