1
GATE CE 2001
MCQ (Single Correct Answer)
+1
-0.3
The product $$\left[ P \right]\,\,{\left[ Q \right]^T}$$ of the following two matrices $$\left[ P \right]\,$$ and $$\left[ Q \right]\,$$
where $$\left[ P \right]\,\, = \left[ {\matrix{ 2 & 3 \cr 4 & 5 \cr } } \right],\,\,\left[ Q \right] = \left[ {\matrix{ 4 & 8 \cr 9 & 2 \cr } } \right]$$ is
A
$$\left[ {\matrix{ {32} & {24} \cr {56} & {46} \cr } } \right]$$
B
$$\left[ {\matrix{ {46} & {56} \cr {24} & {32} \cr } } \right]$$
C
$$\left[ {\matrix{ {35} & {22} \cr {61} & {42} \cr } } \right]$$
D
$$\left[ {\matrix{ {32} & {56} \cr {24} & {46} \cr } } \right]$$
2
GATE CE 2001
MCQ (Single Correct Answer)
+1
-0.3
Limit of the following series as $$x$$ approaches $${\pi \over 2}$$ is
$$f\left( x \right) = x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + - - - - - $$
A
$${{2\pi } \over 3}$$
B
$${\pi \over 2}$$
C
$${\pi \over 3}$$
D
$$1$$
3
GATE CE 2001
MCQ (Single Correct Answer)
+2
-0.6
The solution for the following differential equation with boundary conditions $$y(0)=2$$ and $$\,\,{y^1}\left( 1 \right) = - 3$$ is where $${{{d^2}y} \over {d{x^2}}} = 3x - 2$$
A
$$y = {{{x^3}} \over 3} - {{{x^2}} \over 2} = 3x - 2$$
B
$$y = 3{x^3} - {{{x^2}} \over 2} - 5x + 2$$
C
$$y = {{{x^3}} \over 2} - {x^2} - 5{x \over 2} + 2$$
D
$$y = {x^3} - {{{x^2}} \over 2} + 5x + {3 \over 2}$$
4
GATE CE 2001
MCQ (Single Correct Answer)
+1
-0.3
The number of boundary conditions required to solve the differential equation $$\,\,{{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\partial {y^2}}} = 0\,\,$$ is
A
$$2$$
B
$$0$$
C
$$4$$
D
$$1$$
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