1
GATE CSE 1998
Subjective
+2
-0
Solve the following recurrence relation

$$\,\,\,\,\,\,\,{x_n} = 2{x_{n - 1}} - 1\,\,n > 1$$
$$\,\,\,\,\,\,\,{x_1} = 2$$

2
GATE CSE 1998
MCQ (Single Correct Answer)
+2
-0.6
The rank of the matrix given below is: $$\left[ {\matrix{ 1 & 4 & 8 & 7 \cr 0 & 0 & 3 & 0 \cr 4 & 2 & 3 & 1 \cr 3 & {12} & {24} & {2} \cr } } \right]$$\$
A
3
B
1
C
2
D
4
3
GATE CSE 1998
MCQ (Single Correct Answer)
+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
4
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 $$\,\,\,\int\limits_{ - \pi }^\pi {x\,\cos \,x\,dx}$$

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