IIT-JEE 2007 Paper 2 Offline | Limits, Continuity and Differentiability Question 59 | Mathematics

1

IIT-JEE 2007 Paper 2 Offline

MCQ (Single Correct Answer)

+4

-0

Let $$f(x) = {{{x^2} - 6x + 5} \over {{x^2} - 5x + 6}}$$.

Match the conditions/expressions in Column I with statements in Column II.

	Column I		Column II
(A)	If $$ - 1 < x < 1$$, then $$f(x)$$ satisfies	(P)	$$0 < f(x) < 1$$
(B)	If $$1 < x < 2$$, then $$f(x)$$ satisfies	(Q)	$$f(x) < 0$$
(C)	If $$3 < x < 5$$, then $$f(x)$$ satisfies	(R)	$$f(x) > 0$$
(D)	If $$x > 5$$, then $$f(x)$$ satisfies	(S)	$$f(x) < 1$$

A

$$\mathrm{A-(p), (s);B-(q),(s);C-(q),(s);D-(p),(r)}$$

B

$$\mathrm{A-(p), (q), (s);B-(q),(s);C-(q),(s);D-(p),(r),(s)}$$

C

$$\mathrm{A-(s);B-(q),(s);C-(q),(s);D-(s)}$$

D

$$\mathrm{A-(p), (q), (s);B-(q),(s);C-(s);D-(r),(s)}$$

2

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

In the following [x] denotes the greatest integer less than or equal to x.

Match the functions in Column I with the properties Column II.

	Column I		Column II
(A)	$$x\|x\|$$	(P)	continuous in ($$-1,1$$).
(B)	$$\sqrt{\|x\|}$$	(Q)	differentiable in ($$-1,1$$)
(C)	$$x+[x]$$	(R)	strictly increasing in ($$-1,1$$)
(D)	$$\|x-1\|+\|x+1\|$$	(S)	not differentiable at least at one point in ($$-1,1$$)

A

A - (p), (q), (r), B - (p), (s), C - (r), (s), D - (p), (q)

B

A - (p), (q), B - (p), (s), C - (r), (s), D - (p)

C

A - (p), (q), (r), B - (p), C - (r), D - (p), (q)

D

A - (p), (r), B - (p), (s), C - (r), D - (p), (q)

3

IIT-JEE 2006

MCQ (Single Correct Answer)

+3

-1

For $x>0, \mathop {\lim }\limits_{x \to 0}\left((\sin x)^{1 / x}+(1 / x)^{\sin x}\right)$ is :

A

0

B

-1

C

1

D

2

4

IIT-JEE 2005 Mains

MCQ (Single Correct Answer)

+3

-1

If $$f(x-y)=f(x) \circ g(y)-f(y) \circ g(x)$$ And $$g(x-y) =g(x) \circ g(y)+f(x) \circ f(y)$$ for all $$x, y \in \mathrm{R}$$. If right-hand derivative at $$x=0$$ exists for $$f(x)$$, find the derivative of $$g(x)$$ at $$x=0$$

A

0

B

1

C

2

D

3

JEE Advanced Subjects