1
IIT-JEE 2007
+3
-0.75
Let $$\,\,\,$$$$f\left( x \right) = 2 + \cos x$$ for all real $$X$$.

STATEMENT - 1: for eachreal $$t$$, there exists a point $$c$$ in $$\left[ {t,t + \pi } \right]$$ such that $$f'\left( c \right) = 0$$ because
STATEMENT - 2: $$f\left( t \right) = f\left( {t + 2\pi } \right)$$ for each real $$t$$.

A
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
C
Statement-1 is True, Statement-2 is False
D
Statement-1 is False, Statement-2 is True.
2
IIT-JEE 2005 Screening
+2
-0.5
If $$f(x)$$ is a twice differentiable function and given that $$f\left( 1 \right) = 1;f\left( 2 \right) = 4,f\left( 3 \right) = 9$$, then
A
$$f''\left( x \right) = 2$$ for $$\forall x \in \left( {1,3} \right)$$
B
$$f''\left( x \right) = f'\left( x \right) = 5$$ for some $$x \in \left( {2,3} \right)$$
C
$$f''\left( x \right) = 3$$ for $$\forall x \in \left( {2,3} \right)$$
D
$$f''\left( x \right) = 2$$ for some $$x \in \left( {1,3} \right)$$
3
IIT-JEE 2004 Screening
+2
-0.5
If $$y$$ is a function of $$x$$ and log $$(x+y)-2xy=0$$, then the value of $$y'(0)$$ is equal to
A
$$1$$
B
$$-1$$
C
$$2$$
D
$$0$$
4
IIT-JEE 2001 Screening
+2
-0.5
Let $$f:\left( {0,\infty } \right) \to R$$ and $$F\left( x \right) = \int\limits_0^x {f\left( t \right)dt.}$$ If $$F\left( {{x^2}} \right) = {x^2}\left( {1 + x} \right)$$, then $$f(4)$$ equals
A
$$5/4$$
B
$$7$$
C
$$4$$
D
$$2$$
EXAM MAP
Medical
NEET