XI_Maths_Limits and Derivatives_3 Online Test

The function f(x)=[x]2-[x2] (where [y] is the greatest integer less than or equal to y), is discontinuous at
all integers
all integers except 0 and 1
all integers except 0
all integers except 1
The function f (x) = (x2 -1) | x2 -3x +2| + cos(|x|) is NOT differentiable at
-1
0
1
2
The direction cosines of the line  are ____.
1, 1, 1
None of the above
Direction ratios of the normal to the plane passing through the points (0, 1, 1), (1, 1, 2) and (–1, 2, – 2) are ____.
(1, 1, 1)
(2, 1, –1)
(1, 2, –1)
(1, – 2, – 1)
If the co-ordinates of the points  be (1, 2, 3), (4, 5, 7), (– 4, 3, – 6) and (2, 0, 2) respectively, then ____.
None of the above
Let h(x) =min{x,x2}, for every real number of x. Then
h is continuous for all x
h is differentiable for all x
h’(x)=1, for all x>1
h is not differentiable at two values of x
1, 3 and 4
2 and 4
Let f(x) be a quadratic expression which is positive for all the real values of x. If g(x) +f’(x) +f’’(x), then for any real x,
g(x)<0
g(x)>)
g(x)=0
g(x)>0
The differential coefficient of the function  at the point  ____.
– 2
0
2
Undefined
 ____.
None of the above
If  be a homogeneous function of degree  in  then  ____.
None of the above
Description:

This test consist of 10 questions.Students should ideally take 10 minutes to complete the test. This test is useful for those students who are preparing for IIT JEE, AIEEE or any other engineering entrance test. This test cosist of questions from Limits and Derivatives which, in general, is focused in AIEEE and IIT JEE. Last year only 2 questions was asked from this chapter in AIEEE. In Limits and Derivatives, Limits and derivatives of trigonometric functions are key topics and mostly application based questions are asked.

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