1
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following statements in respect of square matrices A, B, C each of same order n :

1. AB = AC ⇒ B = C if A is non-singular

2. If BX = CX for every column matrix X having n rows then B = C

Which of the statements given above is/are correct ?  

A
1 only 
B
2 only 
C
Both 1 and 2
D
Neither 1 nor 2
2
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

The system of linear equations

x + 2y + z = 4, 2x + 4y + 2z = 8 and 3x + 6y + 3z = 10 has  

A
a unique solution 
B
infinite many solutions
C
no solution 
D
exactly three solutions
3
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
Let AX = B be a system of 3 linear equations with 3-unknowns. Let X1 and X2 be its two distinct solutions. If the combination aX1 + bX2 is a solution of AX = B; where a, b are real numbers, then which one of the following is correct ? 
A
a = b
B
a + b = 1
C
a + b = 0
D
a - b = 1
4
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is the sum of the roots of the equation $\left|\begin{array}{ccc} 0 & x-a & x-b \\ 0 & 0 & x-c \\ x+b & x+c & 1 \end{array}\right|=0 $ ?
A
a + b + c
B
a - b + c
C
a + b - c
D
a - b - c
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