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GATE 2019: Engineering Mathematics Rapid Quiz-1 (App update required to attempt this test)
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Question 1
For a 1-D heat conduction problem in a slab given by differential equation,
Where Ta is the atmospheric temperature.
Find T(x) if boundary condition is given as T (0) = To.
Where Ta is the atmospheric temperature.
Find T(x) if boundary condition is given as T (0) = To.
Question 2
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_____ .
,where R is the region in the first quadrant bounded by the curves y= x2, x+y=2 and x=0 is_____ .Question 3
The value of the limit is
Question 4
A pair of fair dice is thrown independently three times. The probability of getting a score of exactly ‘9’ twice is
Question 5
For the vector 
ï the value of 
____________
ï the value of ____________ Question 6
The inverse Laplace transform of 
is __________.
is __________.Question 7
Newton-Raphson method is used to find the roots of the equation. 
. If the initial guess is 
, then the value of x after 
iteration is ____
. If the initial guess is , then the value of x after iteration is ____Question 8
The surface integral 
over the surface S of the sphere x2 + y2 + z2 = 9, where F=(x+y)i+(x+z)j+(y+z) k and n is the unit outward surface normal, yields ______.
over the surface S of the sphere x2 + y2 + z2 = 9, where F=(x+y)i+(x+z)j+(y+z) k and n is the unit outward surface normal, yields ______. Question 9
The differential equation 
for y(x) with the two boundary conditions has
and 
.
Solution for Differential equation
Question 10
The area of a triangle formed by the tips of vectors 
, and 
is
, and isQuestion 11
Consider an ant crawling along the curve (x-2)2 + y2 = 4, where x and y are in meters. The ant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters per second. The time taken by the ant to reach the point (2, 2) is (in seconds) ________
Question 12
Match each differential equation in Group I to its family of solution curves from Group II.
Group-I
P.
Q.
R.
S.
Group-II
1. Circles
2. Straight lines
3. Hyperbolas
Group-I
P.
Q.
R.
S.
Group-II
1. Circles
2. Straight lines
3. Hyperbolas
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