Mathematics - Online Test
Q1. The locus of a variable point whose distance from the point ( 2, 0) is times its distance from the line is
Answer : Option A
Explaination / Solution:
Let the point be (x,y)
Hence (x-2)2 + (y-0)2 =
(x- 2)2 + y2 = (x - 9/2)
On simplifying we get the equation of an ellipse
Q2. In a triangle ABC, if a, b, c are in A. P., then tan are in
Answer : Option A
Explaination / Solution:
Q3. The nth terms of the series 4+14+30+52+80+114+….. is =
Answer : Option B
Explaination / Solution:
When n = 1 we get 3. When n = 2 we get 12+2= 14...
Q4. Three prizes are distributed among three persons at random. The chances that none of the persons gets all the prizes is
Answer : Option B
Explaination / Solution:
No Explaination.
Q5. The equation 
represents
represents
Answer : Option B
Explaination / Solution:
The equation 
which represent generally YZ plane i.e. X=0 plane
which represent generally YZ plane i.e. X=0 plane
Q6. The system of linear equations ax+ b y= 0, cx + dy = 0 has a non-trival solution if
Answer : Option A
Explaination / Solution:
The given system of equations has a non – trivial solution if :
Q7. If then is equal to
Answer : Option C
Explaination / Solution:
Q8. The number of ways, in which a student can choose 5 courses out of 8 courses, when 2 courses are compulsory, is
Answer : Option B
Explaination / Solution:
Total number of courses available=8
Number of courses which are not compulsary=8-2=6
Since two courses are compulsory a student can choose them in different ways.
The remaining 3 courses can be chosen from the 6 non-compulsory courses in
Therefore total number of ways=.=
Q9. For a complex number z, 
is
is
Answer : Option D
Explaination / Solution:
Q10. In the following case, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. 2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z – 1 = 0
Answer : Option B
Explaination / Solution:
We have,
2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z = 0 . Here ,
Therefore , the given planes are parallel.
2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z = 0 . Here ,
Therefore , the given planes are parallel.
