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GATE 2021: Topper's Weekly Quiz-5

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Question 1

In the following question, out of the four alternatives, select the word similar in meaning to the given word.

Conjecture

Question 2

Consider the matrix A =

. The condition on m for which the eigen values of matrix are of opposite sign ___.

Question 3

A parametric curve defined by

in the range

is rotated about the x-axis by 360 degrees. Area of the surface generated is,

Question 4

The value of integral

, where |Z| = 2 is-

Question 5

The probability density function of a continuous random variable is given by

The standard deviation will be

Question 6

The real roots of the equation x³ - 15x² + 72x + 18 = 0, is calculated using Newton-Raphson method. The sum of different values of x₀ for which the Newton-Raphson method fails for the equation is

Question 7

The value of

,where R is the region in the first quadrant bounded by the curves y= x², x+y=2 and x=0 is_____ .

Question 8

The particular integral of the given differential equation will be-

Question 9

Let A be a 3 x 3 real matrix with eigen values 1, 2, 3 and let B = A^-1 + A², then the trace of B is _______.

Question 10

In the following question, out of the four alternatives, select the word opposite in meaning to the word given.

HOARSE

Question 11

There are 3 fair coins and 1 false coin with tails on both sides. A coin is chosen at random and tossed 4 times. If ‘tails’ occurs in all 4 times, then the probability that the false coin has been chosen for tossing is ___.

Question 12

Select the most appropriate option to fill in the blank.

Although his brother is blind, he is very fast _________ calculations.

Question 13

The product of two numbers is 2028 and their H.C.F is 13. The numbers of such pair is:

Question 14

Two trains one 160 m and the other 140 m long are running in opposite directions on parallel rails, the first at 77 km an hour and the other at 67 km an hour. How long will they take to cross each other?

Question 15

In the following question, a sentence is given with blanks to be filled in with an appropriate word(s). Select the correct alternative out of the four and indicate it by selecting the appropriate option.

He is _____ rich, yet he _____ about high taxes.

Question 16

The population of a village decreases at the rate of 20% per annum. If its population 2 years ago was 10,000, the present population is

Question 17

If a landlord sell a portion of land for Rs. 40000, one-fourth of the outlay was gained. What should be the selling price in order to have loss of 25%?

Question 18

A function f(x) is defined as f(x) = 3x⁴ – 2x³ – 6x² + 6x + 1, 0 ≤ x ≤ 2. The value of f(x) at the point of minimum is__________.

Question 19

Direction: The following bar graph shows the number of students (in thousands) admitted and graduated per year in a degree collage in years 2012 to 2016. Study the graph and answer the question. All the values plotted on graph are natural numbers.

The percent increase in the number of students admitted in 2015 over that in 2013 is

Question 20

Direction: Following bar graph shows the Income and Expenditure of a company over the year (in lakhs of rupees).

The ratio of average income of all the year to the average expenditure of all the year is:

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ESE & GATE EC General

Dec 15ESE & GATE EC