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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 = x^{2}y 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 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 radiusunits 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.
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
to find root of f(x) = x + -1= 0 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) = 5x^{2} – 4xy + 2y^{2} + 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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Jan 31ESE & GATE CE
Posted by:
Shreya LaddhaMember since Dec 2019
M.tech from IIT Kanpur (Geotechnical Engineering)
Among top 500 in GATE 2019