1
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $${a_r} = {(\cos 2r\pi + i\sin 2r\pi )^{1/9}}$$,

then the value of $$\left| {\matrix{ {{a_1}} & {{a_2}} & {{a_3}} \cr {{a_4}} & {{a_5}} & {{a_6}} \cr {{a_7}} & {{a_8}} & {{a_9}} \cr } } \right|$$ is equal to
A
1
B
$$-$$ 1
C
0
D
2
2
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $${S_r} = \left| {\matrix{ {2r} & x & {n(n + 1)} \cr {6{r^2} - 1} & y & {{n^2}(2n + 3)} \cr {4{r^3} - 2nr} & z & {{n^3}(n + 1)} \cr } } \right|$$, then the value of

$$\sum\limits_{r = 1}^n {{S_r}} $$ is independent of
A
only x
B
only y
C
only n
D
x, y, z and n
3
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If the following three linear equations have a non-trivial solution, then

x + 4ay + az = 0

x + 3by + bz = 0

x + 2cy + cz = 0
A
a, b, c are in AP
B
a, b, c are in GP
C
a, b, c, are in HP
D
a + b + c = 0
4
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
On R, a relation $$\rho $$ is defined by x$$\rho $$y if and only if x $$-$$ y is zero or irrational. Then,
A
$$\rho $$ is equivalence relation
B
$$\rho $$ is reflexive but neither symmetric nor transitive
C
$$\rho $$ is reflexive and symmetric but not transitive
D
$$\rho $$ is symmetric and transitive but not reflexive
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