Mathematics - Online Test
Q1. 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:
Q2. is equal to
Answer : Option C
Explaination / Solution:
Q3. 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 .
Q4. The solution set of 6x − 1 > 5 is :
Answer : Option A
Explaination / Solution:
Hence the solution set is
Q5. 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:
Q6. Mean deviation from the mean for the observations – 1 , 0 ,4 is
Answer : Option C
Explaination / Solution:
mean=−1+0+43=3/3=1M.D=1n∣∣∑(Xi−X¯)∣∣=2+1+33=2
Q7. The function f (x) = | x | has
Answer : Option A
Explaination / Solution:
Q8.
The function
Answer : Option C
Explaination / Solution:
Because , here f( - x ) = - f( x).Therefore , the given function is an even function.
Q9. 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
Q10. If ( x , y ) are the coordinates of point in the plane , then 
represents
represents
Answer : Option C
Explaination / Solution:
The given determinant can be written as 2 
On expansion we get
2[3(8-y) - 4(5 - x) +1(5y - 8x)]
On simplifying the equation 2( - 4x+2y+4) = 0 represents a striaght line.
