Mathematics - Online Test
Q1. is satisfied by ,
Answer : Option C
Explaination / Solution:
if ,
i.e. if ,
i.e. if ,
Q2. The line 3x – 4y = 0
Answer : Option A
Explaination / Solution:
After completing the square,we get
so center is (0,0) and radius is 5 units.
As the normal should pass through the centre of the circle, center should satisfy the equation of normal
so 3x – 4y = 0 is the equation of normal as (0,0) satisfy this equation.
Q3. where
Answer : Option A
Explaination / Solution:
is valid only if , i.e. if
Q4. The solution of tan 2 θ tan θ = 1 is
Answer : Option D
Explaination / Solution:
Q5. The sum of the terms in the nth bracket of the series 1 + (2+3+4) + (5+6+7+8+9) ….is
Answer : Option D
Explaination / Solution:
replace n = 1 we get the first term and n = 2 we get the sum of first two terms....
Q6. 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
Q7. 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
Q8. 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.
Q9. 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.
Q10. 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: 