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Gate 2021 : Toppers Weekly Quiz 8 (App update required to attempt this test)

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Question 1

The elimination of the arbitrary constants A, B and C from y = A + Bx + Ce^−x leads to the differential equation

Question 2

A 160 meters long train passes a platform in 23 second and a pole in 8 second. What is the length of platform?

Question 3

Speed of boat in still water is 4 times to speed of current. If a person covers 60 km in 10 hrs in upstream then what is speed of boat in still water?

Question 4

Consider the following statements:

(1) For a diagonal matrix a_ij

(2) All the diagonal elements must be equal to one another for a diagonal matrix.

(3) If A & B are diagonal matrices then sum of adj (A) and adj (B) is also diagonal matrix.

Which of the following statements are correct?

Question 5

Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______

Question 6

If the two numbers are in the ratio 2: 4 and LCM of the numbers is 56 then find HCF of those numbers.

Question 7

Let I be a 100-dimensional identity matrix and E be the set of its distinct (no value appears more than once in E) real eigenvalues. The number of elements in E is _________.

Question 8

The selling price of an article is 8/5th of its cost price. Then the gain percentage is

Question 9

Solution of y dx − x dy = x²y dx is

Question 10

For an amount, simple interest at the rate of interest of 12% per annum for 6 years is Rs 25920. What will be the compound interest (in Rs) on same amount at the rate of interest of 8% per annum compounding annually for 2 years?

Question 11

The solution of the differential equation $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE-EE-ME-19-Mar\GATE-ME-2000_files\image011.png$ is

Question 12

Nitin bought some oranges at Rs. 40 a dozen and an equal number at Rs. 30 a dozen. He sold them at Rs. 45 a dozen and made a profit of Rs. 480. The number of oranges (in dozens), he bought, was

Question 13

The value of the line integral

, where is a circle of radius

units is____
Here,

and

is the UNIT tangent vector on the curve C at an arc length s from a reference point on the curve. i and j are the basis vectors in the x-y Cartesian reference. In evaluating the line integral, the curve has to traversed in the counter-clockwise direction.

Question 14

The root of equation f(x) = x +

-1= 0 is calculated using Newton Raphson method. Find second iteration value if starting value is 1

Question 15

If a random variable X has the following probability distribution:

X:	0	1	2	3	4	5	6	7	8
P(X):	a	3a	5a	7a	9a	11a	13a	15a	17a

then value of ‘a’ is

Question 16

A can finish a work in 18 days and B in 36 days. If they work on it together for 9 days, then what percent of work is left?

Question 17

Given a function f( x ,y) = 5x² – 4xy + 2y² + 4x – 4y + 10 ,the optimum value of f(x, y) is

Question 18

What sum of money must be given at simple interest for six months at 4% per annum in order to earn Rs 150 interest?

Question 19

A pipe can fill a tank in 6 hrs. After half tank is filled 3 more similar pipes are opened. What is total time taken to be filled.

Question 20

Given that the determinant of matrix

is 96, then the determinant of the matrix

is __________.

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ESE & GATE CE Engineering Mathematics General Aptitude

Jul 31ESE & GATE CE