Gate 2021 : Toppers Weekly Quiz 8 (App update required to attempt this test)
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The elimination of the arbitrary constants A, B and C from y = A + Bx + Ce−x leads to the differential equation
A 160 meters long train passes a platform in 23 second and a pole in 8 second. What is the length of platform?
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?
Consider the following statements:
(1) For a diagonal matrix aij
(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?
Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______
If the two numbers are in the ratio 2: 4 and LCM of the numbers is 56 then find HCF of those numbers.
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 _________.
The selling price of an article is 8/5th of its cost price. Then the gain percentage is
Solution of y dx − x dy = x2y dx is
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?
The solution of the differential equation is
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
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.
to find root of f(x) = x + -1= 0 using Newton Raphson method. Find second iteration value if starting value is 1
If a random variable X has the following probability distribution:
thenvalue of ‘a’ is
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?
Given a function f( x ,y) = 5x2 – 4xy + 2y2 + 4x – 4y + 10 ,the optimum value of f(x, y) is
What sum of money must be given at simple interest for six months at 4% per annum in order to earn Rs 150 interest?
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.
Given that the determinant of matrix is 96, then the determinant of the matrixis __________.