Mathematics - Online Test
Q1. 
then equals
then equals
Answer : Option C
Explaination / Solution:
Because , the determinant of a skew symmetric matrix of odd order is always zero and of even order is a non zero perfect square.
Q2. If the points representing the complex numbers - 4 +3i , 2 – 3i and 0 + pi are collinear , then the value of p is
Answer : Option A
Explaination / Solution:
Let us take the coordinates as (-4,3), (2,-3) and (0,p).
If the points are collienear the |x1(y2 - y3) + x2(y3 - y1) + x3(y1-y2)| = 0
Now substituting the values |-4(-3 - p) +2(p -3) +0(3+3)|= 0
12 +4p +2p -6 +0 = 0
6p +6 = 0
6p = -6
Therefore p = -1
Q3. The contrapositive of p→(∼q→∼r) is
Answer : Option B
Explaination / Solution:
The contrapositive of p→q is ∼q→∼p
Q4. ∫log x dx is equal to
Answer : Option C
Explaination / Solution:
Q5. If f (x) be a function such thatthen f (x) is equal to
Answer : Option A
Explaination / Solution:
Integrating both sides, we get
Q6. Find the sum of the vectors 
Answer : Option C
Explaination / Solution:
We have:
vectors
vectors
Q7. holds true for all
Answer : Option D
Explaination / Solution:
This is true for all real values of x ∈[0,1].
Q8. The value of 
where δ(t) is the Dirac delta function, is
where δ(t) is the Dirac delta function, is
Answer : Option A
Explaination / Solution:
Q9.
The line y = m x + c is a normal to the circle
Answer : Option A
Explaination / Solution:
has center (-g,-f)
As normal passes through center so center will satisfy the equation of normal
put y=-f and x=-g in equation of the line y=mx+c
-f = m(-g) +c
which gives mg =f+c.
Q10. If x and then is equal to
Answer : Option D
Explaination / Solution:
