CBSE 12TH MATHEMATICS - Online Test

Answer : Option B
Explaination / Solution:

Conditions for the partition sub-sets to be an equivalence relation:

(i) The partition sub-sets must be disjoint i.e.their is no common elements between them

(ii) Their union must be equal to the main set (super-set)

Here the set A={1,2,3,4,5,6},the partition sub-sets {1,3},{2,4,5},{6} are pairwise disjoint and their union i.e. {1,3} U {2,4,5} U {6} = {1,2,3,4,5,6} = A,which is the condition for  the partition sub-sets to be an equivalence relation of the set A.

Answer : Option B
Explaination / Solution:

Answer : Option B
Explaination / Solution:

ddx(∫f(x)dx)=f(x)

Answer : Option A
Explaination / Solution:

Addition of two vectors i.e. vector addition is associative. i.e. 

Answer : Option C
Explaination / Solution:

As the probability of any event always lies between 0 and 1. Therefore , 0 ≤ P (E|F) ≤ 1.

Answer : Option B
Explaination / Solution:

Answer : Option D
Explaination / Solution:

Case 1 Let c be a real number which is not equal to any integer. for all real numbers close to c the value of the function is equal to [c]; i.e., limx→cf(x)=limx→c[x]=[c]. Also f(c)=[c]and hence the function is continuous at all real numbers not equal to integers.

Case 2 Let c be an integer. Then we can find a sufficiently small real number r>0 such that [c−r]=c−1whereas[c+r]=c

This, in terms of limits mean that limx→c−f(x)=c−1,limx→c+f(x)=c

Since these limits cannot be equal to each other for any c, the function is discontinuous at every integral point.

Answer : Option C
Explaination / Solution:

The general solution of differential equation contains arbitrary constants equal to the order of differential equaition.

Answer : Option A
Explaination / Solution:

Shortest distance between r⃗ =a1→+λb2→andr⃗ =a1→+μb2→
is given by :

Answer : Option B
Explaination / Solution:

The product of any matrix with itself can be found only when it is a square matrix.i.e. m=n.