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GATE 2021: Topper's Weekly Quiz-8 (App update required to attempt this test)

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Question 1

p(A) = 2/5, p(A | B) = 1/3 and p(B | A) = 1/2. Determine the value of p(A B).

Question 2

Match the application to appropriate numerical method.

Question 3

The value of p such that the vector Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-1_files\image026.png is an eigenvector of the matrix Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-1_files\image027.png is ________.

Question 4

A function Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-1_files\image005.png is defined in the closed interval [–1, 1]. The value of x, in the open interval (–1, 1) for which the mean value theorem is satisfied, is

Question 5

If the conjugate of a complex number is then that complex number is

Question 6

An electric bus has onboard instruments that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bust travels on stretches M, N, O and P, in that order. The cumulative distances traveled and the corresponding electricity consumption are shown in the Table below
Description: Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-2_files\image001.png
The stretch where the electricity consumption per km is minimum is

Question 7

From a circular sheet of paper of radius 30cm, a sector of 10% area is removed. If the remaining part is used to make a conical surface, then the ratio of the radius and height of the cone is ________.

Question 8

In which of the following options will the expression P < M be definitely true?

Question 9

Which of the following phrases should be placed in the blank spaces so as to make a grammatically correct and meaningful sentence.
Even though the institute had lot of space.______

Question 10

The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The subprime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers in 2008. The sub-prime lending refers to the provision of loans to those borrowers who may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis.

Which one of the following sequences shows the correct precedence as per the given passage?

Question 11

In the following question, the first and the last sentence of the passage are in order and numbered 1 and 6. The rest of the passage is split into 4 parts and numbered as 2,3,4, and 5. These 4 parts are not arranged in proper order. Read the sentences and arrange them in a logical sequence to make a passage and choose the correct sequence from the given options.
1) One Diwali, the family rises early in the morning.
2) The whole family, including the young and the old enjoy doing this,
3) Children let off fireworks later in the night with their friends.
4) At sunset, the lamps are lit and the family performs various rituals
5) Father, mother, and children visit relatives and exchange gifts and sweets.
6) Houses look so pretty with lighted lamps all around.

Question 12

In the question, there are 4 statements followed by 4 conclusions numbered as (a), (b), (c) and (d), assume the given statements to be true even if they are at variance with commonly known facts, identify the conclusion which following from the given 3 statements
S1: Some guitars are posters.
S2: All posters are doors.
S3: Some doors are tablets.
S4: All tablets are books
C1: Some doors are guitars.
C2: Some books are posters.
C3: Some tablets are guitars.

Question 13

A tiger is 50 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer’s 4. If the tiger and the deer cover 8 meters and 5 meters per leap respectively. What distance in metres will be tiger have to run before it catches the deer?

Question 14

Find the sum to n terms of the series 10 + 84 + 734 + ……

Question 15

There are two candidates P and Q in an election. During the campaign, 40PERCENTAGE-TAG--- of the voters promised to vote for P, and rest for Q. However, on the day of election 15PERCENTAGE-TAG--- of the voters went back on their promise to vote for P and instead voted for Q. 25PERCENTAGE-TAG--- of the voters went back on their promise to vote for Q and instead voted for P. Suppose, P lost by 2 votes, then what was the total number of voters?

Question 16

The value of integral where c is the circle , will be

Question 17

The ordinary differential equation
Is to be solved using the forward Euler method. The largest time step that can be used to solve the equation without making the numerical solution unstable is______

Question 18

If then over the path shown in the figure is

Question 19

The real part of an analytic function is x3 – 3xy2 + 3x2 – 3y2, then the imaginary part of the function will be

Question 20

Consider the series obtained from the Newton-Raphson method. The series converges to
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