Sets, Relations & Functions · JEE Main previous year questions

2004 5 questions

1. Q422004 · 24 Apr 2004 · Shift 1

   The range of the function f(x) = ${}^{7-x}{P}_{x-3}$ is

   1. A.{1, 2, 3, 4, 5}
   2. B.{1, 2, 3, 4, 5, 6}
   3. C.{1, 2, 3, 4}
   4. D.{1, 2, 3}
   Show answer

   Answer: D

2. Q442004 · 24 Apr 2004 · Shift 1

   The graph of the function y = f(x) is symmetrical about the line x = 2, then

   1. A.$f(x)=-f(-x)$
   2. B.$f(2+x)=f(2-x)$
   3. C.$f(x)=f(-x)$
   4. D.$f(x+2)=f(x-2)$
   Show answer

   Answer: B

3. Q452004 · 24 Apr 2004 · Shift 1

   The domain of the function $f(x)=\frac{{\sin }^{-1}(x-3)}{\sqrt{9-x^2}}$

   1. A.[1, 2]
   2. B.[2, 3)
   3. C.[1, 2)
   4. D.[2, 3]
   Show answer

   Answer: B

4. Q502004 · 24 Apr 2004 · Shift 1

   Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}$. The relation $R$ is :

   1. A.a function
   2. B.transitive
   3. C.not symmetric
   4. D.reflexive
   Show answer

   Answer: C

5. Q602004 · 24 Apr 2004 · Shift 1

   A function $y=f(x)$ has a second order derivative $f^{\prime \prime }(x)=6(x-1)$. If its graph passes through the point $(2,1)$ and at that point the tangent to the graph is $y=3x-5$, then the function is :

   1. A.$(x+1{)}^2$
   2. B.$(x-1{)}^3$
   3. C.$(x+1{)}^3$
   4. D.$(x-1{)}^2$
   Show answer

   Answer: B