Mathematics - Online Test
Q1. The product of three consecutive natural numbers is divisible by
Answer : Option D
Explaination / Solution:
By replacing n by 1 we get 6.
Q2. The letters of the word ‘ MALENKOV ‘are arranged in all possible ways. The chance that there are exactly four letters between M and E is
Answer : Option D
Explaination / Solution:
No Explaination.
Q3. A sphere through three non – collinear points A, B, and C is smallest when its centre is
Answer : Option B
Explaination / Solution:
No Explaination.
Q4. Two matrices A and B are multiplicative inverse of each other only if
Answer : Option C
Explaination / Solution:
If AB = BA = I , then A and B are inverse of each other. i.e. A is invers of B and B is inverse of A.
Q5. The number of ways, in which a student can select one or more questions out of 12 each having an alternative, is
Answer : Option B
Explaination / Solution:
Since a student can solve each question in 3 different ways - either he can attempt the first alternative ,or the second alternative or he can leave it unanswered.
Hence number of ways in which a student can attempt one or more of the 12 given questions =
Now we can consider a case that the student leave all the 12 given questions unanswered.
The number of ways, in which a student can select one or more questions out of 12 each having an alternative=
Q6. is equal to
Answer : Option C
Explaination / Solution:
ddx(log|x|)=1|x|x|x|=x|x|2=xx2=1x
Q7. The matrix 
has three distinct eigenvalues and one of its eigenvectors is 
Which one of the following can be another eigenvector of A?
has three distinct eigenvalues and one of its eigenvectors is Which one of the following can be another eigenvector of A?
Answer : Option C
Explaination / Solution:
By the properties of Eigen values and Eigen vectors, another eigen vector of A is 
The eigen vectors corresponding to distinct eigen values of a real symmetric matrix are
orthogonal i.e., pair wise dot product is zero
Q8. In the following case, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. 2x – y + 3z – 1 = 0 and 2x – y + 3z + 3 = 0
Answer : Option B
Explaination / Solution:
We have ,
2x – y + 3z – 1 = 0 and 2x – y + 3z + 3 = 0 . Here ,
Therefore , the given planes are parallel.
2x – y + 3z – 1 = 0 and 2x – y + 3z + 3 = 0 . Here ,
Therefore , the given planes are parallel.
Q9. is
Answer : Option B
Explaination / Solution:
Q10. Differential equation of the family of ellipses having foci on y-axis and centre at origin is
Answer : Option A
Explaination / Solution:
