GATE CE 2016 Set 1 | GATE CE Year Wise Previous Years Questions

GATE CE 2016 Set 1

Numerical

-0

Newton-Raphson method is to be used to find root of equation $$\,3x - {e^x} + \sin \,x = 0.\,\,$$ If the initial trial value for the root is taken as $$0.333,$$ the next approximation for the root would be _________ (note: answer up to three decimal)

Your input ____

GATE CE 2016 Set 1

MCQ (Single Correct Answer)

-0.6

The solution of the partial differential equation $${{\partial u} \over {\partial t}} = \alpha {{{\partial ^2}u} \over {\partial {x^2}}}$$ is of the form

$$C\cos \left( {kt} \right)\left[ {{C_1}{e^{\left( {\sqrt {k/\alpha } } \right)x}} + {C_2}{e^{ - \left( {\sqrt {k/\alpha } } \right)x}}} \right]$$

$$C\,{e^{kt}}\left[ {{C_1}{e^{\left( {\sqrt {k/\alpha } } \right)x}} + {C_2}{e^{ - \left( {\sqrt {k/\alpha } } \right)x}}} \right]$$

$$C{e^{kt}}\left[ {{C_1}\,\cos \left( {\sqrt {k/\alpha } } \right)x + {C_2}\,\sin \left( { - \sqrt {k/\alpha } } \right)x} \right]$$

$$C\sin \left( {kt} \right)\left[ {{C_1}\,\cos \left( {\sqrt {k/\alpha } } \right)x + {C_2}\,\sin \left( { - \sqrt {k/\alpha } } \right)x} \right]$$

GATE CE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

Type $${\rm I}{\rm I}$$ error in hypothesis testing is

acceptance of the null hypothesis when it is false and should be rejected

rejection of the null hypothesis when it is true and should be accepted

rejection of the null hypothesis when it is false and should be rejected

acceptance of the null hypothesis when it is true and should be accepted

GATE CE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

If the entries in each column of a square matrix $$M$$ add up to $$1$$, then an eigenvalue of $$M$$ is

$$4$$

$$3$$

$$2$$

$$1$$

PREVIOUS NEXT

GATE CE Papers

2024