Mathematics - Online Test
Q1. The area bounded by the parabola and the line x + y = 3 is
Answer : Option B
Explaination / Solution:
Q2. Let L be the set of all lines in a plane and R be the relation on L defined as R = {(L1, L2): L1 is perpendicular to L2}. Then R is
Answer : Option B
Explaination / Solution:
The relation R is symmetric only , because if L1 is perpendicular to L2 ,then L2 is also perpendicular to L1,but no other cases that is reflexive and transitive is not possible.
Q3. 
Answer : Option D
Explaination / Solution:
Q4. The equations of the lines through ( - 1 , - 1 ) and making angles of with the line x + y = 0 are
Answer : Option D
Explaination / Solution:
The lines x+1=0 and y+1=0 are perpendicular to each other.
The slope of the line x+y =0 is -1
Hence the angle made by this line with respect to X axis is 450
In other words the angle made by this line with x+1=0 is 450
Clearly the other line with which it can make 450 is y+1=0
Q5. If x = 5 and y = - 2 , then x – 2y = 9 . The contrapositive of this proposition is
Answer : Option D
Explaination / Solution:
p: x = 5 and y = - 2 , q : x – 2y = 9
The contrapositive of
Hence If x – 2y 9 , then x 5 or y - 2
Q6. dx is equal to
Answer : Option C
Explaination / Solution:
∫log(1−x)dx−∫logx dx⇒(x−1)log(1−x)+1−xlnx+C
Q7. Find the value of x for which is a unit vector
Answer : Option D
Explaination / Solution:
As x is a unit vector ,
therefore,
therefore,
Q8. is equal to
Answer : Option C
Explaination / Solution:
Q9. The equations x = a cos + b sin , and , 0 2 represent
Answer : Option D
Explaination / Solution:
x = a cos + b sin , and
putting the value of x and y in x2+y2
we get a2+b2
=> x2+y2 =a2+b2
which is quadratic in nature,
coefficient of x2 = coefficient of y2
and no term involving xy
hence its locus represents a circle
Q10. If f (x) = x then f ‘ (1 ) is equal to
Answer : Option B
Explaination / Solution:
