CBSE 12TH MATHEMATICS - Online Test
Q1. A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity?
Answer : Option A
Explaination / Solution:
Let number of rackets made = x
And number of bats made = y
Therefore , the above L.P.P. is given as :
Maximise , Z = x +y , subject to the constraints : 1.5x +3y ≤ 42 and. 3x +y ≤ 24, i.e.0.5x + y ≤ 14 i.e. x +2y ≤ 28 and 3x +y ≤ 24 , x, y ≥ 0.
Corner points | Z = x + y |
O( 0 , 0 ) | 0 |
D(0,14 ) | 14 |
A(8,0) | 8 |
B(4,12) | 16…………………(Max.) |
Here Z = 16 is maximum. i.e Maximum number of rackets = 4 and number of bats = 12.
Here , profit function is P = 20x + 10y
Profit is maximum at x = 4 and y = 12 .
Therefore , maximum profit = 20(4) + 10 ( 12) = 200.i.e. Rs.200.
Q2. The line touches the curve at the point
Answer : Option C
Explaination / Solution:
Q3. The positive value of the parameter a for which the area of the figure bounded by y = sin ax , y = 0 , x = is 3 is equal to
Answer : Option B
Explaination / Solution:
Q4. Let A be the set of all students of a boys school. The relation R on A is given by R = {(a, b) : a is sister of b} is
Answer : Option A
Explaination / Solution:
Because , the relation is defined over the set A be the set of all students of a boys school.
Q5. If the entries in a 3 x 3 determinant are either 0 or 1 , then the greatest value of this determinant is :
Answer : Option C
Explaination / Solution:
Greatest value = 2 .
Q7. Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.
Answer : Option D
Explaination / Solution:
Let be a unit vector in XY plane,making angle 300 with positive X axis,so we have the vector as
is the required vector.
is the required vector.
Q8. is satisfied by ,
Answer : Option C
Explaination / Solution:
if ,
i.e. if ,
i.e. if ,
Q9. where
Answer : Option A
Explaination / Solution:
is valid only if , i.e. if
Q10. If A any square matrix then which of the following is not symmetric ?
Answer : Option A
Explaination / Solution:
For every square matrix (A – A’ ) is always skew – symmetric.
