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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 ECGeneralDec 15ESE & GATE EC