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Jr. MATHEMATICS The value of natural number 'a' for which 10. If f(x) = (x] where [x] denotes the greatest integer not exceeding x and g(x)3cos(T x), then the range of the function gof is 3. Efla+k) D16(2" -1), where the function satisfies the relation f (x+y) f(x). fy) for all natural numbers x, y and further f(1)=2 is %3D 1) {0} 2) {-1, 1} 3) {-1, 0, 1} 4) {x:-15xs1} 1) 3 2) 4 3) 2 4) 1 11. If domain of x+x-[x] is (0, 3), then its 4. If f is an even function defined on the interval [-5, 5], then the real values of x satisfying the range is x+1 1) [0, 3) 2) [0, 4) 3) [0, 3] 4) (0, 4) equation f(x)= f are x+2, 12. If f:R-R where f(x) = ax+cos x, if f is -IV5 -3+ 5 1) 2. -3+ 5 -4+5 2) - bijective, then 1) a e R 2. 2) ae R* -2+ 5 -45 4)4EVS 4) a eR-[-1, 1] -4+ 5 -1+ 5 3) a eR 3) 2 13. The function f: RR defined by 2 2 f(x) = 4* + 4 is Let f be an injective map with domain {x, y, z} and range (1, 2, 4} such that exactly one of the following statements is correct and the remaining are false: f(x)=1, f(y)#1, f(z) # 2. The value of f'(1) is 5. 1) one-one and into 2) many one and into 3) one-one and onto 4) many one and onto 14. The function f:(-,-1) (0,e] defined by -3x+2 is f(x) = e*"- 3) z ARSK 1) y 2) x 4) 0 1) Many one and onto 2) Many one and into 3) One - one and onto 4) One - one and into Let f:R R be given by f(x) = (x+1) -1,x 2-1. Then the set of values of x for which f(x)= f(x) is given by O 1) {0} 6. 15. The domain of f(x)=sin is 4+2 sin x %3D 5T 1) TC 2) {-1, 0} 3) {-1} 4) {0, 1} 2) 6. 6. 1-x is V2-1 TC 7. The domain of 3) 4) TC 2 1) [-1, 1]U(-0,-2)U(2, 00) 2) (-, )-[-2, 2] 3) (-00, 00)-[-1, 1] TC 16. Given A = and 4) R f(x)= cos x- x(1+x), then f(A) = %3D %3D The domain of the function f(x)= log, cos x is 8. %3D 1 13 T TC 1+ 3 IT 1+ 6. TC TT TC 1) -(1} 2 3 2 6. 1) 0, {1} 2) 2 2 1 2) TC TC 1+ TT TC TC TC 2. 3) 2 2 4) 2 2 3) [0, 1] 4) [-1, 1] 9. If a function f satisfies the condition 2x -1 17. f:(-1,1) B defined by f(x) = tan 1. (x(*% then domain of f(x) 2. 1-x is bijection then B = 18 TC TC TC TC 2) (-o, 2) -TC TC 1) 3) 2 2 4) 1) (-2, 2) 2 2 2) 2. 3) (2, ) 4) R- (-2, 2) 9. AKASH FAST TRACK CRD 2. 2.