Mathematics - Online Test
Q1. The distance of the point ( x , y , z ) from the XY –plane is
Answer : Option D
Explaination / Solution:
Let L be the foot of perpendicular segment from the point P (x,y,z) on XY plane
Now since L is the foot of perpendicular on XY plane so z coordinate will be zero so the point L will be (x,y,0)
then distance between these two will be = = |z|
Q2. If , then
Answer : Option A
Explaination / Solution:
If any row or column of a square matrix is 0 , then its product with itself is always a zero matrix.
Q3. In the function f (x) = is
Answer : Option D
Explaination / Solution:
Hence an increasing function.
Q4. If |z−2|=|z−6| then locus of z is given by :
Answer : Option D
Explaination / Solution:
We have any line of the form x=a constant is a line parallel to Y-axis.
Q5. If A ⊆B , then A∪B is equal to
Answer : Option D
Explaination / Solution:
A ⊆B refers to A set is contained in the Set B.So Set B is bigger.So union the sets will be B
Q6. 
then det. A is equal to
then det. A is equal to
Answer : Option A
Explaination / Solution:
Q7. The two consecutive terms in the expansion of , which have equal coefficients, are
Answer : Option A
Explaination / Solution:
Q8. The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of atleast 65 marks.
Answer : Option D
Explaination / Solution:
Let x be the mark obtained by Rohit in the third test.
Then
Hence Rohit should get a minimum of 60 marks to get an average of atleast 65 marks.
Q9. If(x)=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪sin[x][x]0,,[x]≠0,thenLtx→0f(x)[x]=0
Answer : Option A
Explaination / Solution:
Q10. In Corner point method for solving a linear programming problem one finds the feasible region of the linear programming problem ,determines its corner points and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case feasible region is unbounded, m is the minimum value of the objective function
Answer : Option D
Explaination / Solution:
In Corner point method for solving a linear programming problem one finds the feasible region of the linear programming problem ,determines its corner points and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case feasible region is unbounded, m is the minimum value of the objective function if the open half plane determined by ax + by < m has no point in common with the feasible region . Otherwise Z has no minimum point.
