1
GATE ECE 2014 Set 1
Numerical
+1
-0
Consider the matrix $${J_6} = \left[ {\matrix{ 0 & 0 & 0 & 0 & 0 & 1 \cr 0 & 0 & 0 & 0 & 1 & 0 \cr 0 & 0 & 0 & 1 & 0 & 0 \cr 0 & 0 & 1 & 0 & 0 & 0 \cr 0 & 1 & 0 & 0 & 0 & 0 \cr 1 & 0 & 0 & 0 & 0 & 0 \cr } } \right]$$

Which is obtained by reversing the order of the columns of the identity matrix $${{\rm I}_6}$$. Let $$P = {{\rm I}_6} + \alpha \,\,{J_6},$$ where $$\alpha $$ is a non $$-$$ negative real number. The value of $$\alpha $$ for which det $$(P)=0$$ is _______.

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2
GATE ECE 2014 Set 1
Numerical
+1
-0
$$A$$ real $$\left( {4\,\, \times \,\,4} \right)$$ matrix $$A$$ satisfies the equation $${A^2} = {\rm I},$$ where $${\rm I}$$ is the $$\left( {4\,\, \times \,\,4} \right)$$ identity matrix. The positive eigen value of $$A$$ is _______.
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3
GATE ECE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The Taylor series expansion of $$3$$ $$sin$$ $$x$$ $$+2cos$$ $$x$$ is
A
$$2 + 3x - {x^2} - {{{x^3}} \over 2} + - - - $$
B
$$2 - 3x + {x^2} - {{{x^3}} \over 2} + - - - $$
C
$$2 + 3x + {x^2} + {{{x^3}} \over 2} + - - - $$
D
$$2 - 3x - {x^2} + {{{x^3}} \over 2} + - - - $$
4
GATE ECE 2014 Set 1
Numerical
+2
-0
The volume under the surface $$z\left( {x,y} \right) = x + y$$ and above the triangle in the $$xy$$ plane defined by $$\left\{ {0 \le y \le x} \right.$$ and $$\,\left. {0 \le x \le 12} \right\}$$ is _________.
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