Qus : 1
1 Suppose that the temperature at a point (x,y), on a metal plate is T ( x , y ) = 4 x 2 − 4 x y + y 2 , An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. What is the highest temperature encountered by the ant?
1 125 2 120 3 0 4 25 Go to Discussion
Qus : 2
3 A particle is at rest at the origin. It moves
along the x −axis with an acceleration x − x 2
, where x is the distance of the
particle at time t. The particle next comes to
rest after it has covered a distance
1 1 2 1/2 3 3/2 4 None of these Go to Discussion
Qus : 3
2 Consider the function
f ( x ) = { − x 3 + 3 x 2 + 1 , i f x ≤ 2 cos x , i f 2 < x ≤ 4 e − x , i f x > 4
Which of the following statements about f(x) is true:
1 f(x) has a local maximum at x =1, which is also the global maximum 2 f(x) has a local maximum at x=2, which is not the global maximum 3 f(x) has a local maximum at x = π , but it is not the global maximum 4 f(x) has a global maximum at x=0 Go to Discussion
Solution Qus : 4
3 The function f ( x ) = x 1 + x tan x , 0 ≤ x ≤ π 2 is maximum when
1 x = s e c x 2 x = tan x 3 x = cos x 4 None of these Go to Discussion
Qus : 5
4 The maximum value of 4 sin2 x + 3 cos2 x + sin(x/2) + cos(x/2) is
1 4 2 3 + √2 3 9 4 4 + √2 Go to Discussion
Qus : 6
4 The critical point and nature for the function f(x, y) = x2 –2x + 2y2 + 4y – 2 is
1 (1, 1) maximum 2 (1, –1) maximum 3 (1, 1) minimum 4 (1, –2) minimum Go to Discussion
Qus : 7
3 A condition that x 3 + a x 2 + b x + c may have no extremum is
1 a 2 ≥ 3 b 2 b 2 < 3 b 3 a 2 < 3 b 4 b 2 ≥ 3 b Go to Discussion
Solution Qus : 8
1 If
, then x = 0 is
1 Point of minima 2 Point of maxima 3 Point of discontinuity 4 None of these Go to Discussion
Qus : 9
2 Two non-negative numbers whose sum is 9 and the product of the one number and square of the other number is maximum, are
1 5 and 4 2 3 and 6 3 1 and 8 4 7 and 2 Go to Discussion
Solution [{"qus_id":"4307","year":"2017"},{"qus_id":"4310","year":"2017"},{"qus_id":"9450","year":"2020"},{"qus_id":"10677","year":"2021"},{"qus_id":"11112","year":"2022"},{"qus_id":"11116","year":"2022"},{"qus_id":"11657","year":"2024"},{"qus_id":"10463","year":"2014"},{"qus_id":"10481","year":"2014"}]