Mathematics - Online Test
Q1. dx is equal to
Answer : Option A
Explaination / Solution:
∫cos((x−a)+a)cos(x−a)dx=∫cos(x−a)cosa−sin(x−a)sinacos(x−a)dx=∫{cosa−sinatan(x−a)}dx.xcosa+sinalog|cos(x–a)|+C
Q2. In the figure which are the Equal vectors?
Answer : Option B
Explaination / Solution:
are equal vectors , because they have equal magnitude and same direction.
are equal vectors , because they have equal magnitude and same direction.
Q3. If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A|B)
Answer : Option B
Explaination / Solution:
We have ,
P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4
P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4
Q4. If then is equal to
Answer : Option C
Explaination / Solution:
sin−1x+cos−1x=π2cos−1x=π2−sin−1x=π2−π5=3π10.
Q5. If f(x) = then
Answer : Option C
Explaination / Solution:
therefore , f is neither continuous nor differentiable at x = 0
Q6. 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
Q7. 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.
Q8. If sin = 2, then
Answer : Option D
Explaination / Solution:
Q9. Find the shortest distance between the lines 
Answer : Option D
Explaination / Solution:
Q10. 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
