Mathematics - Online Test
Q1. In Z , the set of integers , inverse of – 7 , w.r.t. ‘ * ‘ defined by a*b = a +b + 7 for all a,b∈Z ,is
Answer : Option B
Explaination / Solution:
If ‘ e ‘ is the identity ,then a*e = a ⇒a + e + 7 = a ⇒ e = - 7 . Also,inverse of e is e itself. Hence , inverse of -7 is -7.
Q2. 
then D is equal to
then D is equal to
Answer : Option D
Explaination / Solution:
Q3. The line x + y – 6 = 0 is the right bisector of the segment [PQ]. If P is the point ( 4, 3 ) , then the point Q is
Answer : Option B
Explaination / Solution:
Equation of the line which is perpendicular to the given line x + y = 6 is x - y + k = 0
Since it passes through the point (4,3)
4 - 3 + k = 0
Therefore k = -1
Hence the equation of the line segment PQ is x - y - 1 = 0
On solving these two lines we get x = 7/2 and y = 5/2
This point of intersection is the midpoint of the line segement PQ
That is = 7/2 Hence x = 3
Similarly = 5/2. Hence y = 2
Hence the coordiates of the point Q is (3,2)
Q4. Negation of the statement (p∧r)→(r∨q) is
Answer : Option A
Explaination / Solution:
(p∧r)∧(∼r∧∼q) since ∼(p→q)≡p∧∼q
Q5.
dx is equal to
Answer : Option B
Explaination / Solution:
∫1xdx=loge|x|+C
Q6. In triangle ABC, which of the following is not true?
Answer : Option B
Explaination / Solution:
(triangle law of vector addition) but
Q7. If 
are two collinear vectors, then which of the following are incorrect
are two collinear vectors, then which of the following are incorrect
Answer : Option A
Explaination / Solution:
If 
are two collinear vectors, then, they are parallel to the same line irrespective of their magnitudes and directions.
are two collinear vectors, then, they are parallel to the same line irrespective of their magnitudes and directions.
Q8. is equal to
Answer : Option B
Explaination / Solution:
=.because ,
Q9.
If x sin (a + y) = sin y, then is equal to
Answer : Option C
Explaination / Solution:
Q10. The equation of the normal to the parabola having slope 1 is
Answer : Option C
Explaination / Solution:
slope form of normal is y=mx-2am-am3
for the given parabola a = 2 and m = 1
therefore y = x -4 -2
i.e; x - y - 6 = 0
