Mathematics - Online Test
Q1. If f(x) be any function which assumes only positive values and f’ (x) exists then f’ (x) is equal to
Answer : Option B
Explaination / Solution:
Q2. In the following case, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. 4x + 8y + z – 8 = 0 and y + z – 4 = 0
Answer : Option D
Explaination / Solution:
We have, 4x + 8y + z – 8 = 0 and y + z – 4 = 0. Let be the angle between the planes, then
Q3. is equal to
Answer : Option C
Explaination / Solution:
We have for a complex number x+iy the argument or amplitude is a value of satisfying
Q4. Find the equation of a curve passing through the point (0, 0) and whose differential equation is y′ = sin x.
Answer : Option A
Explaination / Solution:
Q5.
Find the number of terms in the expansion of
Answer : Option A
Explaination / Solution:
Q6. If A , B , C be any three sets such that A∪B=A∪C and A∩B=A∩C , then
Answer : Option C
Explaination / Solution:
Q7. is equal to
Answer : Option C
Explaination / Solution:
Q8. An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy classthan by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit?
Answer : Option A
Explaination / Solution:
Let number of executive class tickets = x
And number of economy class tickets = y
Therefore , the above L.P.P. is given as :
Minimise , Z = 1000x +600y , subject to the constraints : x + y ≤ 200, 4x - y ≤ 0, x ≥ 20,x,y ≥ 0.,
Corner points | Z =1000x +600 y |
C(20 ,80 ) | 68000
|
B (40,160) | 136000 |
D(20,180 ) | 12800 |
Here Z = 136000 is maximum.
i.e. 40 tickets of executive class and 160 tickets of economy class; Maximum profit = Rs 136000 .
Q9. The solution set of 6x − 1 > 5 is :
Answer : Option A
Explaination / Solution:
Hence the solution set is
Q10. If three positive numbers a, b, c are in G. P. then log a, log b, log c are in
Answer : Option A
Explaination / Solution:
