Mathematics - Online Test
Q1. 
f (x) is
f (x) is
Answer : Option B
Explaination / Solution:
At x=1,
L.H.L.1
R.H.L.2
L.H.L. R.H.L.
Therefore function is not continuous at x=1 which is why it is not derivable at x=1
Q2. A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods F1 and F2 are available. Food F1 costs Rs 4 per unit food and F2 costs Rs 6 per unit. One unit of food F1 contains 3 units of vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.
Answer : Option B
Explaination / Solution:
Let number of units of food F1 = x
And number of units of food F2 = y
Therefore , the above L.P.P. is given as :
Minimise , Z = 4x +6y , subject to the constraints : 3 x + 6y ≥ 80, 4x + 3y ≥ 100, x,y ≥ 0.,
Corner points | Z =4x +6 y |
B(80/3 , 0 ) | 320/3 |
D(24,4/3 ) | 104…………………(Min.) |
A(0,100/3) | 200 |
Corner points Z =4x +6 y B(80/3 , 0 ) 320/3 D(24,4/3 ) 104…………………(Min.) A(0,100/3) 200 Here Z = 104 is minimum. i.e. Minimum cost = Rs 104.
Q3. The solution set for :
Answer : Option B
Explaination / Solution:
Q4. An A.P. consists of n (odd) terms and its middle term is m. Then the sum of the A.P. is
Answer : Option D
Explaination / Solution:
Q5. The point on the curve where tangent makes an angle of with the X – axis is
Answer : Option A
Explaination / Solution:
Q6. For a symmetrical distribution and . The median of the data is
Answer : Option D
Explaination / Solution:
For symmetric distribution,
Q7. The function f:R→R given by f(x)= cosx∀x∈R is :
Answer : Option C
Explaination / Solution:
f (0) = cos 0 = 1 ,and f (2π) =cos (2π)= 1. So , different elements in R may have the same image . Hence , f is not an injective function .Also, range of f(x) is not equal to its co-domain . So, f is not surjective.
Q8. 
then B is given by
then B is given by
Answer : Option A
Explaination / Solution:
Q9. The image of the point ( -1 , 2 ) in the origin is
Answer : Option A
Explaination / Solution:
when a point M which is in the 2nd quadrant is reflected in the origin, its image is formed in the 4th quadrant whose coordinates are (x,-y)
Hence the image of the point (1,-2) is (1,-2)
Q10. Logical equivalent proposition to the proposition ∼(p∨q) is
Answer : Option B
Explaination / Solution:
∼(p∨q)≡∼p∧∼q De Morgan's law
