Mathematics - Online Test
Q1. In the Cartesian form two linesand are coplanar if
Answer : Option D
Explaination / Solution:
In the Cartesian form two linesand are coplanar if
Q2. Forming a differential equation representing the given family of curves by eliminating arbitrary constants a and b fromyields the differential equation
Answer : Option B
Explaination / Solution:
Q3. The value of is
Answer : Option D
Explaination / Solution:
Q4.
If the coefficients of 2nd ,3rd and 4th terms in the expansion of are in A.P. then
Answer : Option B
Explaination / Solution:
Q5. If Q = { x : = 1/y , where y ∈ N } , then
Answer : Option D
Explaination / Solution:
N is set of natural number,so
x = 1/y
when y=1 then x=1
so
1 Q
Q6. is equal to
Answer : Option D
Explaination / Solution:
Q7. A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximize his profit?
Answer : Option D
Explaination / Solution:
Let number of pedestal lamps manufactured = x
And number of wooden shades manufactured = y
Therefore , the above L.P.P. is given as :
Maximise , Z = 5x +3y , subject to the constraints : 2x +y ≤ 12 and. 3x +2y ≤ 20 , x, y ≥ 0.
Corner points | Z =5x +3 y |
O( 0 , 0 ) | 0 |
D(6,0 ) | 30 |
A(0,10) | 30 |
B(4,4) | 32…………………(Max.) |
Here Z = 32 is maximum.
i.e 30 packages of screws A and 20 packages of screws B; Maximum profit = Rs 410.
i.e. 4 Pedestal lamps and 4 wooden shades; Maximum profit = Rs 32 .
Q8. The solution set for | 3x − 2 | ≤ 1/2
Answer : Option D
Explaination / Solution:
Q9. If the numbers a, b, c, d, e form an A.P. then the value of a – 4b + 6 c – 4 d + e is
Answer : Option D
Explaination / Solution:
Q10. An edge of a variable cube is increasing at the rate of 3cm/sec.Find the rate at which the volume of the cube is increasing when the edge is 10cm long
Answer : Option D
Explaination / Solution:
