CBSE 12TH 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. 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:
Q4. 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 .
Q5. The function f (x) = | x | has
Answer : Option A
Explaination / Solution:
Q6.
The function
Answer : Option C
Explaination / Solution:
Because , here f( - x ) = - f( x).Therefore , the given function is an even function.
Q7. If A and B are invertible matrices of order 3 , then det(adj A) =
Answer : Option C
Explaination / Solution:
Let A be a non singular square matrix of order n then
det(adjA)=|A|n-1
here order is 3 so det(adj A)=|A|3-1=|A|2
Q8. The area bounded by the parabolas y= is equal to
Answer : Option A
Explaination / Solution:
