Mathematics - Online Test
Q1. A dice is tossed once and even number has come up. The chance that it is either 2 or 4 is
Answer : Option D
Explaination / Solution:
Total number of ways of getting even number is 3
Out of these 3 even number we have to get either 2 or 4 which can be done in 2 ways.
So required probability is 2/3
Q2. The lines intersect . The shortest distance between them is
Answer : Option C
Explaination / Solution:
Since the lines intersect.Hence they have a common point in them.hence the distance will be zero
Q3. 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.
Q4. The number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated is
Answer : Option B
Explaination / Solution:
4 flowers which are always together can be considered as one SET,
Therefore we have to arrange one SET ( 4 flowers ) and 4 other flowers into a garland.
Which means, 5 things to be arranged in a garland.
(5-1)!
And the SET of flowers can arrange themselves within each other in 4! ways.
Therefore
(5-1)!*(4!)
But, Garland, looked from front or behind does not matter. Therefore the clockwise and anti clockwise observation does not make difference.
Therefore
(5-1)! * (4!)/ 2
= 288.
Therefore we have to arrange one SET ( 4 flowers ) and 4 other flowers into a garland.
Which means, 5 things to be arranged in a garland.
(5-1)!
And the SET of flowers can arrange themselves within each other in 4! ways.
Therefore
(5-1)!*(4!)
But, Garland, looked from front or behind does not matter. Therefore the clockwise and anti clockwise observation does not make difference.
Therefore
(5-1)! * (4!)/ 2
= 288.
Q5. Vector equation of a plane that passes through the intersection of planes 
expressed in terms of a non – zero constant is
expressed in terms of a non – zero constant is
Answer : Option C
Explaination / Solution:
Vector equation of a plane that passes through the intersection of planes 
expressed in terms of a non – zero constant is given by: 
expressed in terms of a non – zero constant is given by:
Q6. General solution of is
Answer : Option B
Explaination / Solution:
Q7. The value of is
Answer : Option A
Explaination / Solution:
Q8. The coefficient of xn in the expansion of (1+x)(1−x)n is
Answer : Option C
Explaination / Solution:
Q9. If A and B be two sets such that n( A ) = 70 , n ( B ) = 60 , and n ( A ∪ B ) = 110 . Then n ( A ∩ B ) is equal to
Answer : Option D
Explaination / Solution:
Q10. is equal to
Answer : Option C
Explaination / Solution:
