1
WB JEE 2018
+1
-0.25 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
2
WB JEE 2018
+1
-0.25 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
3
WB JEE 2018
+2
-0.5 The least positive integer n such that $${\left( {\matrix{ {\cos \pi /4} & {\sin \pi /4} \cr { - \sin {\pi \over 4}} & {\cos {\pi \over 4}} \cr } } \right)^n}$$ is an identity matrix of order 2 is
A
4
B
8
C
12
D
16
4
WB JEE 2017
+1
-0.25 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.
WB JEE Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
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