1
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The linear system of equations

$$\left. \matrix{ 8x - 3y - 5z = 0 \hfill \cr 5x - 8y + 3z = 0 \hfill \cr 3x + 5y - 8z = 0 \hfill \cr} \right\}$$ has
A
only zero solution
B
only finite number of non-zero solutions
C
no non-zero solution
D
infinitely many non-zero solutions.
2
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let P be the set of all non-singular matrices of order 3 over R and Q be the set of all orthogonal matrices of order 3 over R. Then,
A
P is proper subset of Q
B
Q is proper subset of P
C
Neither P is proper subset of Q nor Q is proper subset of P
D
P $$ \cap $$ Q = $$\phi$$, the void set
3
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let $$A = \left( {\matrix{ {x + 2} & {3x} \cr 3 & {x + 2} \cr } } \right),\,B = \left( {\matrix{ x & 0 \cr 5 & {x + 2} \cr } } \right)$$. Then all solutions of the equation det (AB) = 0 is
A
1, $$-$$1, 0, 2
B
1, 4, 0, $$-$$2
C
1, $$-$$1, 4, 3
D
$$-$$1, 4, 0, 3
4
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The value of det A, where $$A\, = \left( {\matrix{ 1 & {\cos \theta } & 0 \cr { - \cos \theta } & 1 & {\cos \theta } \cr { - 1} & { - \cos \theta } & 1 \cr } } \right)$$, lies
A
in the closed interval [1, 2]
B
in the closed interval [0, 1]
C
in the open interval (0, 1)
D
in the open interval (1, 2)
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