Home
Class 12
MATHS
Statement-1 If AuuB=AuuC and AnnB=AnnC, ...

Statement-1 If `AuuB=AuuC` and `AnnB=AnnC`, then B = C.
Statement-2 `Auu(BnnC)=(AuuB)nn(AuuC)`

Text Solution

Verified by Experts

The correct Answer is:
a
We have, `B=Buu(AnnB)`
`=Buu(AnnC)" "[Because AnnB = AnnC]`
`=(AuuC)nn(BuuC)" "[because AuuB = AuuC]`
`=(AnnB)uuC`
`=(AnnC)uuC" "[Because AnnB = AnnC]`
= C
Hence, Statement-1 is true, Statement-2 is true, Statement-2 is correct explanation of Statement-2.
Promotional Banner

Similar Questions

Explore conceptually related problems

Statement-1 P(A)nnP(B)=P(AnnB) , where P(A) is power set of set A. Statement-2 P(A)uuP(B)=P(AuuB) .

Statement-1 If A is any event and P(B)=1 , then A and B are independent Statement-2 P(AcapB)=P(A)cdotP(B), if A and B are independent

Statement-1 If U is universal set and B = U - A, then n(B) = n(U) - n(A) . Statement-2 For any three arbitrary sets A, B and C, if C = A - B, then n(C ) = n(A) - n(B).

Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A^2=""I . Statement 1: If A!=I and A!=""-I , then det A""=-1 . Statement 2: If A!=I and A!=""-I , then t r(A)!=0 . (1) Statement 1 is false, Statement ( 2) (3)-2( 4) is true (6) Statement 1 is true, Statement ( 7) (8)-2( 9) (10) is true, Statement ( 11) (12)-2( 13) is a correct explanation for Statement 1 (15) Statement 1 is true, Statement ( 16) (17)-2( 18) (19) is true; Statement ( 20) (21)-2( 22) is not a correct explanation for Statement 1. (24) Statement 1 is true, Statement ( 25) (26)-2( 27) is false.

Statement-1 For a singular matrix A , if AB = AC rArr B = C Statement-2 If abs(A) = 0, then A^(-1) does not exist.

Statement-1 A is singular matrix of order nxxn, then adj A is singular. Statement -2 abs(adj A) = abs(A)^(n-1)

A fair die is thrown twice. Let (a, b) denote the outcome in which the first throw shows 'a' and the second throw shows 'b' . Let A and B be the following events : A={(a,b): a is even}, B={(a,b): b is even} Statement-1: If C={(a,b): a+b is odd}, then P(A cap B cap C)=(1)/(8) Statement-2: If D={(a,b): a+b is even}, then P(A cap B cap D// A cup B)=(1)/(3)

Statement-1 (Assertion) and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement-1 if A and B are two square matrices of order nxxn which satisfy AB= A and BA = B, then (A+B) ^(7) = 2^(6) (A+B) Statement- 2 A and B are unit matrices.

Statement-1 If A and B be the event in a sample space, such that P(A)=0.3 and P(B)=0.2, then P(Acapoverline(B)) cannot be found. Statement-2 P(Auuoverline(B))=P(A)+P(overline(B))-P(Acapoverline(B))

Let A and B are symmetric matrices of order 3. Statement -1 A (BA) and (AB) A are symmetric matrices. Statement-2 AB is symmetric matrix, if matrix multiplication of A with B is commutative.