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GATE ME 2021: National Champion Quiz 6 (App update required to attempt this test)

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Question 1

Matrix B =

has a eigen vectors as

. Find the corresponding eigen values for the given eigen vectors.

Question 2

The rod PQ of length

, and uniformly distributed mass of M=10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ. Assume acceleration due to gravity, g=10 m/s². The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML²/12). At this instant, the magnitude of angular acceleration (in radian/s²) of the rod is _____

Question 3

The bar graph given below shows the per acre yield (in kg) of different countries. Study the graph carefully and answer the questions

Writing the yields of all countries in ascending order, the difference between the sum of yields of first three countries to that of last three countries is

Question 4

Select the most appropriate option to fill in the blank.

The severe thunderstorm caused ________ damage that recovery would take years.

Question 5

In a mixture of 150 liters oil, 80% is petrol and rest are diesel. How much more diesel should be added so that, petrol become 75% in the new mixture?

Question 6

Select the most appropriate option to fill in the blank.

Every evening, they used to sit down for dinner and _________ before eating their meal.

Question 7

The system of equations x-4y+7z = 12 , 3x+8y-2z = 10, 26 z -8y = 6

Question 8

A function f of the complex variable

is given as

where

The value of k, for which the function is analytic, is _____ .

Question 9

P(0,3), Q(0.5, 4), and R (1,5) are three points on the curve defined by f(x). Numerical integration is carried out using both Trapezoidal rule and Simpson‟s rule within limits x = 0 and x =1 for the curve. The difference between the two results will be.

Question 10

A probability density function is of the form

The value of K is

Question 11

If a ball which is dropped from a height of 2.25 m on a smooth floor attains the height of bounce equal to 1.00 m, the coefficient of the restitution between the ball and the floor is equal to:

Question 12

A force F has magnitude of 15 N. Direction of F is at 37° from negative x-axis towards positive y-axis. Represent F in terms of

and

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ESE & GATE ME English Comprehension Engineering Mathematics Engineering Mechanics General Aptitude

Jul 15ESE & GATE ME