Mathematics - Online Test
Q1. 
is equal to
is equal to
Answer : Option D
Explaination / Solution:
Q2. 
are
are
Answer : Option A
Explaination / Solution:
are collinear vectors , because they are parallel in direction and having the same magnitude.
are collinear vectors , because they are parallel in direction and having the same magnitude.
Q3. Evaluate P(A ∪ B), if 2P(A) = P(B) = and P(A|B) =
Answer : Option A
Explaination / Solution:
Q4. is equal to
Answer : Option B
Explaination / Solution:
Q5. Let f(x) = x – [x], then f ‘ (x) = 1 for
Answer : Option B
Explaination / Solution:
f(x) = x - is derivable at all x R – I , and f ‘(x) = 1 for all x R – I
Q6. The number of tangents to the circle through the point ( - 1, 2) is
Answer : Option A
Explaination / Solution:
The given equation of the circle can be written as
(x-1)2 - 1 + (y- 2)2 - 4 = 0
(x - 1)2 + (y + 2)2 = 5
This implies the radius is and the centre is (1,-2)
The given point is (-1,2)
The distance between the centre of the circle and the given point is
=
Sice this is greater than the radius, the point lies outside the circle. Hence two tangents can be drawn.
Q7. Let that for all natural numbers n. also , if P ( m ) is true , m N , then we conclude that
Answer : Option D
Explaination / Solution:
This criteria is from the basic principle of mathematical induction.
Q8. In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals
Answer : Option D
Explaination / Solution:
cosecA(sinBcosC+cosBsinC)=cosecA.sin(B+C)[∵A+B+C=π]=sin(B+C)sinA=sin(π−A)sinA=sinAsinA=1
Q9. Find the shortest distance between the lines : 
Answer : Option D
Explaination / Solution:
On comparing the given equations with:
, we get:
, we get:
Q10. The number of ways in which n ties can be selected from a rack displaying 3n different ties is
Answer : Option B
Explaination / Solution:
The number of selections of r objects from the given n objects is denoted by and we have
Now n ties can be selected from a rack displaying 3n different ties in different ways
