1
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
2
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
3
WB JEE 2018
MCQ (Single Correct Answer)
+2
-0.5
Change Language
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
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.
WB JEE Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12