1
WB JEE 2017
+1
-0.25 Let $$A = \left( {\matrix{ {x + 2} & {3x} \cr 3 & {x + 2} \cr } } \right),\,B = \left( {\matrix{ x & 0 \cr 5 & {x + 2} \cr } } \right)$$. Then all solutions of the equation det (AB) = 0 is
A
1, $$-$$1, 0, 2
B
1, 4, 0, $$-$$2
C
1, $$-$$1, 4, 3
D
$$-$$1, 4, 0, 3
2
WB JEE 2017
+1
-0.25 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)
3
WB JEE 2017
+2
-0.5 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
$$\left( {\matrix{ 1 & n & {2n - 1} \cr 0 & {{{n + 1} \over 2}} & {{n^2}} \cr 0 & 0 & {{{n + 1} \over 2}} \cr } } \right)$$
4
WB JEE 2017
+2
-0.5 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
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
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