1
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
2
GATE CSE 1998
Subjective
+5
-0
(a) Find the points of local maxima and minima, if any, of the following function defined $$0 \le x \le 6.\,\,\,{x^3} - 6{x^2} + 9x + 15$$

(b) Integrate $$\,\,\,\int\limits_{ - \pi }^\pi {x\,\cos \,x\,dx}$$

3
GATE CSE 1998
+2
-0.6
Consider the following determinant $$\Delta = \left| {\matrix{ 1 & a & {bc} \cr 1 & a & {ca} \cr 1 & a & {ab} \cr } } \right|$$\$

Which of the following is a factor of $$\Delta$$ ?

A
$$a + b$$
B
$$a - b$$
C
$$a + b + c$$
D
$$abc$$
4
GATE CSE 1998
Subjective
+2
-0
Find the points of local maxima and minima if any of the following function defined in $$0 \le x \le 6,$$ $$\,\,\,\,f\left( x \right) = {x^3} - 6{x^2} + 9x + 15.$$
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