1
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If n is even positive integer, then the condition that the greatest term in the expansion of (1 + x)n may also have the greatest coefficient, is
A
$${n \over {n + 2}} < x < {{n + 2} \over n}$$
B
$${n \over {n + 1}} < x < {{n + 1} \over n}$$
C
$${{n + 1} \over {n + 2}} < x < {{n + 2} \over {n + 1}}$$
D
$${{n + 2} \over {n + 3}} < x < {{n + 3} \over {n + 2}}$$
2
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $$\left| {\matrix{ { - 1} & 7 & 0 \cr 2 & 1 & { - 3} \cr 3 & 4 & 1 \cr } } \right| = A$$, then $$\left| {\matrix{ {13} & { - 11} & 5 \cr { - 7} & { - 1} & {25} \cr { - 21} & { - 3} & { - 15} \cr } } \right|$$ is
A
$${A^2}$$
B
$${A^2} - A + {I_3}$$
C
$${A^2} - 3A + {I_3}$$
D
$$3{A^2} + 5A - 4{I_3}$$
3
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
4
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
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