Mathematics - Online Test
Q1. The coefficient of in the expansion of is
Answer : Option D
Explaination / Solution:
Q2. The equation 
has
has
Answer : Option D
Explaination / Solution:
No Explaination.
Q3. Find all pairs of consecutive odd natural numbers, both of which are larger than 10, such that their sum is less than 40.
Answer : Option B
Explaination / Solution:
Let the consecutive odd natural numbers be x and x+2.
According to the question , x>10 and
Now
Hence the maximum value of x is 17 and minimum value is 11.
So the possible pairs of odd natural numbers are ( 11 , 13 ) , ( 13 , 15 ) , ( 15 , 17 ) , ( 17 , 19 )
Q4. Let then for f to be continuous at x = 0, f (0) must be equal to
Answer : Option C
Explaination / Solution:
Q5. 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 maximum value of the objective function if
Answer : Option C
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 maximum 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 maximum value.
Q6. The number of numbers between n and which are divisible by n is
Answer : Option D
Explaination / Solution:
No Explaination.
Q7. The Mode of the following items is 0,1,6,7,2,3,7,6,6,2,6,0,5,6,0.
Answer : Option B
Explaination / Solution:
6 is the most frequent value here.
Q8. Let A = {a, b, c} then the range of the relation R = {(a, b), (a, c), (b, c)} defined on A is
Answer : Option B
Explaination / Solution:
Since the range is represented by the y- co ordinate of the ordered pair ( x , y ).Therefore, range of the given relation is { b , c }.
Q9. The line passing through ( 1, 1 ) and parallel to the line 2x – 3y + 5 = 0 is
Answer : Option D
Explaination / Solution:
The required line is parallel to the given line, hence it has same slope
Therefore the equation of the required line is 2x-3y+k=0
Since it passes through (1,1)
2(1) - 3(1) +k = 0
Therefore k=1
Hence the equation of the required line is 2x - 3y + 1=0
Q10. If the inverse of implication p→q is defined as ∼p→∼q , then the inverse of proposition (p∧∼q)→r is
Answer : Option C
Explaination / Solution:
as given the rule of inverse in question it becomes ∼(p∧∼q)→∼r
=(∼p∨q)→∼r
