Mathematics - Online Test
Q1. If A is a square matrix of order 2 , then det (adj A) =
Answer : Option C
Explaination / Solution:
Let A be a square matrix of order 2 then , because where n is the order of square matrix.
Q2.
The equations of the lines through ( 1 , 1 ) and making angles of with the line x + y = 0
Answer : Option C
Explaination / Solution:
If the lines make equal angles of 450 with the given line, x+y =0.
Then these lines must be perpendicular with each other.
This is possible only when the two lines are parallel to X axis and Y axis.
That is the equations should be x = a constant and y = a constant.
Since it passes through (1,1)
The equations should be x = 1 or x-1=0 and y=1 or y-1 =0
Q3. p∧(q∧r) is logically equivalent to
Answer : Option D
Explaination / Solution:
Associative law
Q4. The area bounded by the parabolas y =
Answer : Option D
Explaination / Solution:
Q5. Find a unit vector perpendicular to each of 
where 
where
Answer : Option D
Explaination / Solution:
It is given that:
Therefore, the unit vector perpendicular to both the vectors
and
is given by:
Therefore, the unit vector perpendicular to both the vectors
and
is given by:
Q6. If then the value of the integral dx is equal to
Answer : Option D
Explaination / Solution:
Q7. tan−114+tan−129=
Answer : Option D
Explaination / Solution:
Q8. locus of the point of intersection of the lines x = sec θ + tan θ and y = sec θ – tan θ is
Answer : Option A
Explaination / Solution:
After solving the equations we will get x+y = 2sec θ which represents a linear equation.
Q9. The values of (0 < < ) satisfying are
Answer : Option A
Explaination / Solution:
Hence the values of betwwen 0 and 360 are [when n=1,n=2]
Q10. The smallest positive integer for which The statement is true for
Answer : Option C
Explaination / Solution:
When n = 1 9<4 not valid. when n = 2 27<16 not true. when n = 3 81<64 is in correct. when n = 4 243<256, is true.
