1
GATE CSE 2007
+1
-0.3
Consider the following two statements about the function $$f\left( x \right) = \left| x \right|:$$\$

$$P.\,\,f\left( x \right)$$ is continuous for all real values of $$x$$
$$Q.\,\,f\left( x \right)$$ is differentiable for all real values of $$x$$

Which of the following is True?

A
$$P$$ is true and $$Q$$ is false.
B
$$P$$ is false and $$Q$$ is true.
C
Both $$P$$ and $$Q$$ are true.
D
Both $$P$$ and $$Q$$ are false.
2
GATE CSE 2003
+1
-0.3
$$\mathop {Lim}\limits_{x \to 0} \,{{Si{n^2}x} \over x} = \_\_\_\_.$$
A
$$0$$
B
$$\infty$$
C
$$1$$
D
$$-1$$
3
GATE CSE 2001
+1
-0.3
The value of the integral is $${\rm I} = \int\limits_0^{{\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}}} {{{\cos }^2}x\,dx}$$
A
$${\pi \over 8} + {1 \over 4}$$
B
$${\pi \over 8} - {1 \over 4}$$
C
$${{ - \pi } \over 8} - {1 \over 4}$$
D
$${{ - \pi } \over 8} + {1 \over 4}$$
4
GATE CSE 1998
+1
-0.3
Consider the function $$y = \left| x \right|$$ in the interval $$\left[ { - 1,1} \right]$$. In this interval, the function is
A
continuous and differentiable
B
continuous but not differentiable
C
differentiable but not continuous
D
neither continuous nor differentiable
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