Mathematics - Online Test
Q1. If f(x) = then
Answer : Option C
Explaination / Solution:
therefore , f is neither continuous nor differentiable at x = 0
Q2. S and T are the foci of an ellipse and B is an end of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is
Answer : Option B
Explaination / Solution:
s = (ae,0) and T = (-ae,0) and B = (0,b)
Since it is an equilateral triangle, ST2 = TB2
This implies 4a2e2 = a2e2 + b2
3a2e2 = b2
3a2e2 = a2(1 - e2)
3e2 = 1 - e2
Therefore e = 1/2
Q3. The smallest positive integer n , for which holds :
Answer : Option C
Explaination / Solution:
When n = 1 we get ,which is invalid. When n = 2 we get, which is valid.
Q4. If sin = 2, then
Answer : Option D
Explaination / Solution:
Q5. Find the shortest distance between the lines 
Answer : Option D
Explaination / Solution:
Q6. The number of ways in which the 6 faces of a cube can be painted with 6 different colours is
Answer : Option C
Explaination / Solution:
We have a cube has 6 faces and we have to colour it with 6 different colours .
Then the no of ways of colouring ==720, but in this we will be getting many overcountings.
We have there are 24 ways in which we can orient a cube
Hence the number of distinct ways of colouring a cube with 6 different colours is
Q7. Skew lines are
Answer : Option D
Explaination / Solution:
Skew lines are those lines which lie in different planes and never meet
Q8. If for a matrix A, where I is the identity matrix, then A equals
Answer : Option D
Explaination / Solution:
Q9. General solution of is
Answer : Option C
Explaination / Solution:
Q10. is
Answer : Option B
Explaination / Solution:
