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CBSE CLASS XII

Functions and Relations (1 Mark)

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1. Is the function f: N → N, defined by f(x) = 3x, onto? Give reasons.
2. If f(x) = [ x ] and g (x) = │x │, then evaluate (f o g) (1/2) – (g o f) (-1/2).
3. If tan^-11 + tan^-1(1/2) = tan^-1α, find α.
4. 1If A and B are two sets such that n (A) = m and n (B) = n then write number of function from A → B.
5. Let f : R – { - 4/3} → R be a function defined as f(x) = 4x / 3x+4. Find the inverse of f.
6. Find the value of tan^-1(1) + cos^-1(-1/2) + sin ^-1 (-1/2).
7. Evaluate Sin [ π– sin^-1 (-1)].
8. Let set A contains 3 elements. Write the total number of binary operation possible.
9. Let ‘*’ be a binary operation defined on the set of integers as a*b=a+b+1 for a, b € I. Find the identity element.
10. Prove that cos²(tan^-12)+sin²(cot^-13) = 3/10.
11. What is the principal value of cos^-1(cos 2 π/3)+sin^-13(sin 2 π/3).
12. If f(x) = 8x³ and g(x) = x^1/3 , find g o f.
13. Find the value of sin^-1(sin 3π/5).
14. Show that the signum function f : R → R given by f(x) = 1, if x is greater than 0, if x = 0, - 1, if x is less than 0 is neither one-to-one nor onto.
15. If , find f o g.
16. N → N, defined by f(x) = 3x onto?Give Reasons.
17. If a binary operation * is defined on the set Z of integers as a*b = 3a –b, then find the value of (2*3)*4.
18. Prove that sec² (tan ^-1 2) + cosec² (cot ^-1 3) = 15.
19. How many relations can be defined from a non-empty set A to non-empty set B , if n(A) = 2 and n(B)=3.
20. Find the principal value of tan^-1[sin(sin^-1x+cos^-1x)] , x ε [ -1,1] .

 

Submitted By Mrs. E.Praveen
Email Id : [email protected]