Mathematics - Online Test
Q1. If E and F are independent, then
Answer : Option A
Explaination / Solution:
we know that
If E and F are independent, then P(E/F) = P(E) and P(F/E) = P(F)
P (E ∩ F) = P (E) P (F).
Q2. The period of the function f(x)=tan3x is
Answer : Option A
Explaination / Solution:
, as the period of tanx =
Q3.
is equal to
Answer : Option D
Explaination / Solution:
( using L’Hospital Rule)
Q4. The statement P ( n ) : “
“ is
Answer : Option C
Explaination / Solution:
Replace n = 1, 2 3 then LHS = RHS
Q5. The length of the chord joining the point ( 4 cos , 4 sin ) and 4 ( cos(+), 4 sin( + )) of the circle is
Answer : Option A
Explaination / Solution:
using distance formulae 
on simplifying we get, 
on simplifying we get,
Q6. Determine order and degree (if defined) of + 3s = 0
Answer : Option C
Explaination / Solution:
Order = 2 , degree = 1.Since the equation has as the highest derivative term.its order is 2 and its index is 1
Q7. The number of ways in which a necklace can be formed by using 5 identical red beads and 6 identical white beads is:
Answer : Option A
Explaination / Solution:
Total number of beads =11
We have 6 beads are alike and next 5 beads are also alike , also since it is a necklace it can be observed from both the sides .
Therefore required number of ways=
Q8. Vector equation of a line that passes through the given point whose position vector is and parallel to a given vector is
Answer : Option A
Explaination / Solution:
Vector equation of a line that passes through the given point whose position vector is and parallel to a given vector is given by : 
Q9. If a = 4, b = 3 and A = then c is a root of the equation
Answer : Option B
Explaination / Solution:
Hence c is the root of the equation
Q10.
The area enclosed by the curve is
Answer : Option A
Explaination / Solution:
Required area :
$= = == =
$= = == =
