1
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)
2
WB JEE 2017
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$A = \left( {\matrix{ 1 & 1 & 1 \cr 0 & 1 & 1 \cr 0 & 0 & 1 \cr } } \right)$$. Then, for positive integer n, An is
A
$$\left( {\matrix{ 1 & n & {{n^2}} \cr 0 & {{n^2}} & n \cr 0 & 0 & n \cr } } \right)$$
B
$$\left( {\matrix{ 1 & 1 & {n\left( {{{n + 1} \over 2}} \right)} \cr 0 & 1 & n \cr 0 & 0 & 1 \cr } } \right)$$
C
$$\left( {\matrix{ 1 & {{n^2}} & n \cr 0 & n & {{n^2}} \cr 0 & 0 & {{n^2}} \cr } } \right)$$
D
$$\left( {\matrix{ 1 & n & {2n - 1} \cr 0 & {{{n + 1} \over 2}} & {{n^2}} \cr 0 & 0 & {{{n + 1} \over 2}} \cr } } \right)$$
3
WB JEE 2017
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let a, b, c be such that b(a + c) $$ \ne $$ 0. If $$\left| {\matrix{ a & {a + 1} & {a - 1} \cr { - b} & {b + 1} & {b - 1} \cr c & {c - 1} & {c + 1} \cr } } \right| + \left| {\matrix{ {a + 1} & {b + 1} & {c - 1} \cr {a - 1} & {b - 1} & {c + 1} \cr {{{( - 1)}^{n + 2}}a} & {{{( - 1)}^{n + 1}}b} & {{{( - 1)}^n}c} \cr } } \right| = 0$$, then the value of n is
A
any integer
B
zero
C
any even integer
D
any odd integer
WB JEE Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12