Mathematics - Online Test
Q1.
The area between the hyperbola , then x – axis and the ordinates at a and b with a > b is :
Answer : Option C
Explaination / Solution:
Required area :
= = = =
= = = =
Q2. If k be an integer, then is equal to
Answer : Option C
Explaination / Solution:
Q3. The solution set for ( x + 3 ) + 4 > − 2x + 5:
Answer : Option B
Explaination / Solution:
Q4. Minimize Z = x + 2y subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0.
Answer : Option A
Explaination / Solution:
Objective function is Z = x + 2 y ……………………(1).
The given constraints are : 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0 .
Corner points | Z = x + 2y |
A(0 ,3 ) | 6…………………..(Minimum) |
B(6,0) | 6………………………(Minimum) |
Here , Z = 18 is minimum at ( 0, 3 ) and ( 6 , 0 ) .
Minimum Z = 6 at all the points on the line segment joining the points (6, 0) and (0, 3).
Q5. The sum of first four terms of an A. P. is 56 and sum of last four terms is 112. If the first term is 11, then the number of terms is
Answer : Option B
Explaination / Solution:
Q6. If the mean of the squares of first n natural numbers be 11, then n is equal to
Answer : Option C
Explaination / Solution:
Q7. Given the relation R = {(1, 2), (2, 3)} on the set {1, 2, 3}, the minimum number of ordered pairs which when added to R make it an equivalence relation is =
Answer : Option B
Explaination / Solution:
To make the relation an equivalence relation , the following ordered pairs are required (1,1),(2,2),(3,3)(2,1)(3,2)(1,3),(3,1).
Q8. 
Answer : Option C
Explaination / Solution:
Q9. The area of the triangle whose sides are along the lines x = 0 , y = 0 and 4x + 5y = 20 is
Answer : Option B
Explaination / Solution:
The equation 4x + 5y = 20 can be written as + = 1
This implies the intercepts cut by this line on the X and Y axes are 5 and 4 respectively.
Hence the area of the triangle is 1/2 [ 5 x 4] = 10 square units
Q10. Which of the following statement is a tautology
Answer : Option B
Explaination / Solution:
Since
Hence tautology
