CBSE 12TH MATHEMATICS - Online Test
Q1. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are 
externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.
externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.
Answer : Option C
Explaination / Solution:
Q2. The value of is
Answer : Option D
Explaination / Solution:
Q3. is equal to
Answer : Option C
Explaination / Solution:
=
Q4. 
Answer : Option D
Explaination / Solution:
symmetric matrix ,since A’ = A . therefore ,
Q5. In the Cartesian form two linesand are coplanar if
Answer : Option D
Explaination / Solution:
In the Cartesian form two linesand are coplanar if
Q6. 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:
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. 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:
Q9. The area of the region bounded by y = and y = 1 is
Answer : Option A
Explaination / Solution:
∣∣∣∫01[(x−1)−(1−x)]dx∣∣∣=1
Q10. Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Then R is
Answer : Option A
Explaination / Solution:
Consider any a ,b , c A .
- Since both a and a must be either even or odd, so (a , a) R R is reflexive.
- Let (a ,b) R both a and b must be either even or odd, both b and a must be either even or odd, ( b ,a) R .Thus , (a ,b) R ( b ,a) R R is symmetric.
- Let (a ,b) R and (b ,c) R both a and b must be either even or odd, also ,both b and c must be either even or odd, all elements a, b and c must be either even or odd, ( a ,c) R . Thus , (a ,b) R ( b ,c) R (a ,c) R R is transitive.
