Mathematics - Online Test
Q1. The number of spheres of a given radius r and touching the coordinate axes is
Answer : Option A
Explaination / Solution:
No Explaination.
Q2. From the matrix equation AB = AC we can conclude B = C, provided
Answer : Option D
Explaination / Solution:
Here , only non- singular matrices obey cancellation laws.
Q3. Find a particular solution of = 1; y =0 when x =2
Answer : Option A
Explaination / Solution:
Here y =0 when x =2
Hence
Q4. The smallest positive integer n for which is
Answer : Option D
Explaination / Solution:
By inspection we have the smallest positive integer such that is n=4.
Q5. The coefficient of in the expansion of is
Answer : Option A
Explaination / Solution:
Q6. Let A and B be subsets of a set X , Then which of the following is correct
Answer : Option A
Explaination / Solution:
Q7. The normal to the curve x = a (cosθ+θsinθ),y = a (sinθ−θcosθ)at any point θ is such that
Answer : Option A
Explaination / Solution:
Equation of normal at θisxcosθ+ysinθ−a=0.So,normal is at a fixed distance a from the origin.
Q8. The area of the smaller portion of the circle cut off by the line x = 1 is
Answer : Option A
Explaination / Solution:
Q9. is equal to
Answer : Option D
Explaination / Solution:
Q10. Minimize Z = 5x + 10 y subject to x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x, y ≥ 0
Answer : Option D
Explaination / Solution:
Objective function is Z = 5x + 10 y ……………………(1).
The given constraints are : x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x, y ≥ 0 .
The corner points are obtained by drawing the lines x+2y =120, x+y = 60 and x-2y = 0. The points so obtained are (60,30),(120,0), (60,0) and (40,20)
Corner points | Z = 5x + 10y |
D(60 ,30 ) | 600 |
A(120,0) | 600 |
B(60,0) | 300……………………..(Min.) |
C(40,20) | 400 |
Here , Z = 300 is minimum at ( 60, 0 ).
