Mathematics - Online Test
Q1. Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then R is
Answer : Option D
Explaination / Solution:
The relation R is not symmetric , (1,2) ∈R , but (2,1) ∉ R , (1,3) ∈R ,but (3,1) ∉ R , (3,2) ∈R, but (2,3) ∉R.
Q2. A determinant is unaltered , if
Answer : Option C
Explaination / Solution:
This is because of the elementary transformations of determinants . The value of determinant remains unaffected by applying elementary transformations.
Q3. The locus of the inequation xy ≥ 0 is
Answer : Option C
Explaination / Solution:
It is the set of all points either in the 1st quadrant or in the 3rd quadrant including the points on coordiate axis. This is because the inequality indicates that the points belong either to 1st or 3rd quadrant.
Q4. The statement p→(q→p) is equivalent to
Answer : Option D
Explaination / Solution:
| p | q | ||||
| T | T | T | T | T | T |
| T | F | T | T | T | T |
| F | T | F | T | T | T |
| F | F | T | F | T | T |
Hence they are equivalent
Q5.
dx is equal to
Answer : Option C
Explaination / Solution:
Q6. The scalar product of the vector with a unit vector along the sum of vectors is equal to one. Find the value of.
Answer : Option A
Explaination / Solution:
Let and
Therefore, a unit vector along
is given by:
Also, scalar product of with above unit vector is 1.
Therefore, a unit vector along
is given by:
Also, scalar product of with above unit vector is 1.
Q7. Which of the following is different from ?
Answer : Option B
Explaination / Solution:
therefore , none of these is the right option.
Q8. The focus of the parabola is
Answer : Option B
Explaination / Solution:
after completing the square we get,
Comparing the above equation with
focus is (0,-a)
putting x co-ordinate =0 we get x-4=0
=> x=4
and y co-ordinate =-a we get
=>y=4
hence (4,4) is the focus.
Q9.
If ( 1 + tan ) ( 1 + tan ) = 2, then + =
Answer : Option C
Explaination / Solution:
Q10. is equal to
Answer : Option D
Explaination / Solution:
