1
AIEEE 2011
+4
-1
The number of values of $$k$$ for which the linear equations
$$4x + ky + 2z = 0,kx + 4y + z = 0$$ and $$2x+2y+z=0$$ possess a non-zero solution is :
A
$$2$$
B
$$1$$
C
zero
D
$$3$$
2
AIEEE 2010
+4
-1
Let $$A$$ be a $$\,2 \times 2$$ matrix with non-zero entries and let $${A^2} = I,$$
where $$I$$ is $$2 \times 2$$ identity matrix. Define
$$Tr$$$$(A)=$$ sum of diagonal elements of $$A$$ and $$\left| A \right| =$$ determinant of matrix $$A$$.
Statement- 1: $$Tr$$$$(A)=0$$.
Statement- 2: $$\left| A \right| = 1$$ .
A
statement - 1 is true, statement - 2 is true; statement - 2 is not a correct explanation for statement - 1.
B
statement - 1 is true, statement - 2 is false.
C
statement - 1 is false, statement -2 is true
D
statement -1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement - 1.
3
AIEEE 2010
+4
-1
Consider the system of linear equations; $$\matrix{ {{x_1} + 2{x_2} + {x_3} = 3} \cr {2{x_1} + 3{x_2} + {x_3} = 3} \cr {3{x_1} + 5{x_2} + 2{x_3} = 1} \cr }$$\$
The system has :
A
exactly $$3$$ solutions
B
a unique solution
C
no solution
D
infinitenumber of solutions
4
AIEEE 2010
+4
-1
The number of $$3 \times 3$$ non-singular matrices, with four entries as $$1$$ and all other entries as $$0$$, is :
A
$$5$$
B
$$6$$
C
at least $$7$$
D
less than $$4$$
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