Mathematics - Online Test
Q1.
Answer : Option A
Explaination / Solution:
The tangents are
since .
It passes through ( -2 , 0 ).
The tangents are :
Required area :
since .
It passes through ( -2 , 0 ).
The tangents are :
Required area :
Q2. If a unit vector makes angles , then find
Answer : Option C
Explaination / Solution:
Let
It is given that
, then,
Putting these values in (1), we get:
It is given that
, then,
Putting these values in (1), we get:
Q3. If f (x) = f (a –x), then , is equal to
Answer : Option C
Explaination / Solution:
Q4. cos(cos−1(725))=
Answer : Option D
Explaination / Solution:
Q5. The line y = m x + c, touches the parabola if
Answer : Option D
Explaination / Solution:
y = m x + c ---(i)
---(ii)
putting the value of y from (i) in (ii), we get
=>
here
discriminant =
=
when discriminant >0 line touches parabola at two points,
when discriminant < 0 line do not touches parabola and
when discriminant = 0 line touches parabola at one point
and we know that tangent is a line that touches the curve at exactly one point
so putting discriminat = 0 and solving
we get
on putting the value of y from line in the parabola and solving for equal roots.
Q6.
If and , then
Answer : Option A
Explaination / Solution:
Q7. For all n N , is divisible by
Answer : Option A
Explaination / Solution:
Replace n = 1 , we have 64.
Q8. If A and B are two mutually exclusive events, then P (A + B) is equal to
Answer : Option C
Explaination / Solution:
No Explaination.
Q9. The points A ( 0 , 0 , 0 ) , B ( 1 , , 0 ) , C ( 2 , 0 , 0 ) and D ( 1 , 0 , ) are the vertices of
Answer : Option B
Explaination / Solution:
No Explaination.
Q10. The equations, x + 4 y – 2 z = 3, 3 x + y + 5 z = 7, 2 x + 3y +z = 5 have
Answer : Option D
Explaination / Solution:
The given system of equations does not have solution if :
