Mathematics - Online Test
Q1. A differential equation of the form y' = F(x,y) is homogeneous if
Answer : Option C
Explaination / Solution:
A differential equation of the form y' = F(x,y) is homogeneous if F(x,y) is a homogeneous function of degree zero , so that we can convert it into variable separable form by y=vx.
Q2. A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red is
Answer : Option C
Explaination / Solution:
No Explaination.
Q3. If A , B and C are non – empty sets , then ( A – B ) ∪( B – A ) equals :
Answer : Option A
Explaination / Solution:
Q4. is equal to
Answer : Option D
Explaination / Solution:
Q5. The sum of first eight terms of a G.P. is 82 times the sum of first four terms. The common ratio of the G.P. is
Answer : Option A
Explaination / Solution:
Q6. In a group of students, mean weight of boys is 80 kg and mean weight of girls is 50kg.If the mean weight of all the students taken together is 60kg, then the ratio of the number of boys to that of the girls is
Answer : Option A
Explaination / Solution:
let the no. of boys be x and no. of girls be y
sum of weights of boys= 80x
sum of weights of girls = 50y
sum of weights of boys and girls together = 60(x + y)
hence, 80x + 50 y = 60x + 60y
which gives, 20x = 10 y
so, x:y = 1:2
Q7. For a real number x, let [x] denote the greatest integer less than or equal to x thenf (x) = is
Answer : Option B
Explaination / Solution:
Since [x−π] is an integer for all x∈R and tan nπ = 0 for all n∈I, therefore, F(x)= 0 for all x∈R.. So, f (X) is a constant and hence derivatives of f(x) of all order exist.
Q8.
The feasible region for a LPP is shown in Figure. Find the minimum value of Z = 11x + 7y.
Answer : Option C
Explaination / Solution:
Corner points | Z = 11x +7 y |
(0, 5 ) | 35 |
(0,3) | 21…………………(min.) |
(3,2 ) | 47 |
Hence the minimum value is 21
Q9. The domain of the function is
Answer : Option D
Explaination / Solution:
domain of the function is equals to {x R : g (x) ≠ 0 } = R – { x R : g (x) = 0 }.
Q10. 
is equal to
is equal to
Answer : Option A
Explaination / Solution:
The determinant of a lower triangular or an upper triangular matrix is equal to the product of the diagonal elements.
