Mathematics - Online Test
Q1. Solve : 30x < 200, when x is a natural number :
Answer : Option C
Explaination / Solution:
Q2. If k be an integer, then is equal to
Answer : Option A
Explaination / Solution:
Q3. Maximise Z = 5x + 3y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0.
Answer : Option A
Explaination / Solution:
Objective function is Z = 5x + 3 y ……………………(1).
The given constraints are : 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0.
The corner points obtained by drawing the lines 3x+5y=15 and 5x+2y=10 are (0,0),(0,3), (2,0) and (20/19,45/19)
Corner points | Z = 5x + 3 y |
O(0 , 0 ) | 0 |
B ( 2 , 0 ) | 10 |
C( 0 , 3 ) | 9 |
D ( 20/19 , 45/19 ) | 235/19 ……………….(Max.) |
Here , Z = 235/19 is maximum at ( 20/19 , 45/19 ) .
Q4. If a∈R, then the roots of the equation tan x = a are in G.P for what values of a
Answer : Option C
Explaination / Solution:
Q5. If the mean of numbers 27,31,89,107,156 is 82 , then the mean of 130,126,68,50,1 is :
Answer : Option B
Explaination / Solution:
mean=130+126+68+50+15=3755=75
Q6. The minimum value of the function f(x) = x3 - 3x2 - 24x +
100 in the interval [-3. 3] is
Answer : Option B
Explaination / Solution:
Q7. The binary operation * defined on the set of integers as a∗b=|a−b|−1is
Answer : Option D
Explaination / Solution:
Here * is commutative as b*a = |b−a|−1=|a−b|−1=a∗b.
Because ,|−x|=|x|for all x∈R.
Q8. Solution set of the equation 
Answer : Option B
Explaination / Solution:
Q9. Two points ( a , 0 ) and ( 0 , b ) are joined by a straight line. Another point on this line is
Answer : Option A
Explaination / Solution:
The slope of the line joining the points (a,0) and (0,b) is [b-0]/[0-a] = -(b/a)
Hence the equation of the line is y = (-b/a)x +b
i.e; ay = -bx +ab
Substituting the x coordinate 3a in the place of x in the above equation we get y = -2b
Hence (3a,-2b) is another point on the line.
Q10. (p∧∼q)∧(∼p∨q) is
Answer : Option D
Explaination / Solution:
Since
F V F = F Since
Hence contracdiction
