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GATE ME 2005

MCQ (Single Correct Answer)

-0.3

$$\int\limits_{ - a}^a {\left[ {{{\sin }^6}\,x + {{\sin }^7}\,x} \right]dx} $$ is equal to

$$2\int\limits_0^a {Si{n^6}x\,dx} $$

$$2\int\limits_0^a {Si{n^7}x\,dx} $$

$$2\int\limits_0^a {\left( {{{\sin }^6}x + {{\sin }^7}x} \right)dx} $$

zero

GATE ME 2005

MCQ (Single Correct Answer)

-0.6

Which one of the following is an eigen vector of the matrix $$\left[ {\matrix{ 5 & 0 & 0 & 0 \cr 0 & 5 & 0 & 0 \cr 0 & 0 & 2 & 1 \cr 0 & 0 & 3 & 1 \cr } } \right]$$ is

$${\left[ {\matrix{ 1 & { - 2} & 0 & 0 \cr } } \right]^T}$$

$${\left[ {\matrix{ 0 & { 0} & 1 & 0 \cr } } \right]^T}$$

$${\left[ {\matrix{ 1 & { 0} & 0 & -2 \cr } } \right]^T}$$

$${\left[ {\matrix{ 1 & { - 1} & 2 & 1 \cr } } \right]^T}$$

GATE ME 2005

MCQ (Single Correct Answer)

-0.6

A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary wheel and sticks to it. The solid wheel has a mass of 20 kg and a radius of 1 m. assuming that the wheel and the ground are both rigid and that the wheel is set into pure rolling motion, the angular velocity of the wheel immediately after the impact is approximately GATE ME 2005 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 51 English

GATE ME 2005 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 51 English

Zero

1/3 rad/s

$$\sqrt {{{10} \over 3}} \,\,rad/s$$

10/3 rad/s

GATE ME 2005

MCQ (Single Correct Answer)

-0.6

Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on every pair of contacting surfaces is 0.3. the lower book is pulled with a horizontal force F. the minimum value of F for which slip occurs nbetween the two books is

zero

1.06 N

5.74 N

8.83 N

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