1
GATE CE 1998
+1
-0.3
The real symmetric matrix $$C$$ corresponding to the quadratic form $$Q = 4{x_1}{x_2} - 5{x_2}{x_2}$$ is
A
$$\left[ {\matrix{ 1 & 2 \cr 2 & { - 5} \cr } } \right]$$
B
$$\left[ {\matrix{ 2 & 0 \cr 0 & { - 5} \cr } } \right]$$
C
$$\left[ {\matrix{ 1 & 1 \cr 1 & { - 2} \cr } } \right]$$
D
$$\left[ {\matrix{ 0 & 2 \cr 2 & { - 5} \cr } } \right]$$
2
GATE CE 1998
Subjective
+1
-0
Obtain the eigen values and eigen vectors of $$A = \left[ {\matrix{ 8 & -4 \cr 2 & { 2 } \cr } } \right].$$
3
GATE CE 1998
+1
-0.3
A discontinuous real function can be expressed as
A
Taylor's series and Fourier's series
B
Taylor's series and not by Fourier's series
C
Neither Taylor's series nor Fourier's series
D
not by Taylor's series, but by Fourier's series
4
GATE CE 1998
+1
-0.3
The Taylor's series expansion of sin $$x$$ is ______.
A
$$1 - {{{x^2}} \over {2!}} + {{{x^4}} \over {4!}} - ......$$
B
$$1 + {{{x^2}} \over {4!}} + {{{x^4}} \over {4!}} + ......$$
C
$$x + {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} + ......$$
D
$$x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - ......$$
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