GATE CE 2017 Set 2 | GATE CE Year Wise Previous Years Questions

GATE CE 2017 Set 2

MCQ (Single Correct Answer)

-0.6

Consider the following definite integral $$${\rm I} = \int\limits_0^1 {{{{{\left( {{{\sin }^{ - 1}}x} \right)}^2}} \over {\sqrt {1 - {x^2}} }}dx} $$$
The value of the integral is

$${{{\pi ^3}} \over {24}}$$

$${{{\pi ^3}} \over {12}}$$

$${{{\pi ^3}} \over {48}}$$

$${{{\pi ^3}} \over {64}}$$

GATE CE 2017 Set 2

MCQ (Single Correct Answer)

-0.6

The tangent to the curve represented by $$y=x$$ $$ln$$ $$x$$ is required to have $${45^ \circ }$$ inclination with the $$x-$$axis. The coordinates of the tangent point would be

$$(1, 0)$$

$$(0,1)$$

$$(1,1)$$

$$\left( {\sqrt {2,} \sqrt 2 } \right)$$

GATE CE 2017 Set 2

MCQ (Single Correct Answer)

-0.6

If $$A = \left[ {\matrix{ 1 & 5 \cr 6 & 2 \cr } } \right]\,\,and\,\,B = \left[ {\matrix{ 3 & 7 \cr 8 & 4 \cr } } \right]A{B^T}$$ is equal to

$$\left[ {\matrix{ {38} & {28} \cr {32} & {56} \cr } } \right]$$

$$\left[ {\matrix{ 3 & {40} \cr {42} & 8 \cr } } \right]$$

$$\left[ {\matrix{ {43} & {27} \cr {34} & {50} \cr } } \right]$$

$$\left[ {\matrix{ {38} & {32} \cr {28} & {56} \cr } } \right]$$

GATE CE 2017 Set 2

MCQ (Single Correct Answer)

-0.3

Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$$3{x_1} + 2{x_2} = {c_1}$$$ $$$4{x_1} + {x_2} = {c_2}$$$

The characteristic equation for these simultaneous equation is

$${\lambda ^2} - 4\lambda - 5 = 0$$

$${\lambda ^2} 4\lambda + 5 = 0$$

$${\lambda ^2} + 4\lambda - 5 = 0$$

$${\lambda ^2} + 4\lambda + 5 = 0$$

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