Mathematics - Online Test
Q1. The number of ways in which 6 “ + “ and 4 “ – “ signs can be arranged in a line such that no two “ – “ signs occur together is
Answer : Option C
Explaination / Solution:
Since all the plus signs are identical , we have number of ways in which 6 plus signs can be arranged=1.
Now we will have 7 empty slots between these 6 identical + signs
Hence number of possible places of - sign =7
Therefore number of ways in which the 4 minus sign can take any of the possible 7 places=
Q2. The equation of a plane through a point whose position vector is and perpendicular to the vector . is
Answer : Option C
Explaination / Solution:
In vector form The equation of a plane through a point whose position vector is and perpendicular to the vector . Is given by :
Q3. Find the particular solution of the differential equation , given that y = 0 and x = 0.
Answer : Option D
Explaination / Solution:
Q4. The number of solutions of the equation is
Answer : Option C
Explaination / Solution:
Q5. Find the middle term in the expansion of
Answer : Option C
Explaination / Solution:
Q6. If aN = { ax : x ∈ N } , then the set 3N ∩ 7N is
Answer : Option A
Explaination / Solution:
Q7. is equal to
Answer : Option D
Explaination / Solution:
Q8. The curves cut orthogonally when
Answer : Option C
Explaination / Solution:
Q9. Maximize Z = – x + 2y, subject to the constraints: x ≥ 3, x + y ≥ 5, x + 2y ≥ 6, y ≥ 0.
Answer : Option C
Explaination / Solution:
Objective function is Z = - x + 2 y ……………………(1).
The given constraints are : x ≥ 3, x + y ≥ 5, x + 2y ≥ 6, y ≥ 0.
Corner points | Z = - x + 2y |
D(6,0 ) | -6 |
A(4,1) | -2 |
B(3,2) | 1 |
Here , the open half plane has points in common with the feasible region .
Therefore , Z has no maximum value.
Q10. Solve the system of inequalities − 4x + 1 ≥ 0 , 3 − 4x < 0
Answer : Option C
Explaination / Solution:
Hence solution set is
which means no solution exist.
