WB JEE 2017 | Matrices and Determinants Question 59 | Mathematics

1

WB JEE 2017

MCQ (Single Correct Answer)

+1

-0.25

Let P be the set of all non-singular matrices of order 3 over R and Q be the set of all orthogonal matrices of order 3 over R. Then,

A

P is proper subset of Q

B

Q is proper subset of P

C

Neither P is proper subset of Q nor Q is proper subset of P

D

P $$ \cap $$ Q = $$\phi$$, the void set

2

WB JEE 2017

MCQ (Single Correct Answer)

+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

3

WB JEE 2017

MCQ (Single Correct Answer)

+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)

4

WB JEE 2017

MCQ (Single Correct Answer)

+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

$$\left( {\matrix{ 1 & n & {2n - 1} \cr 0 & {{{n + 1} \over 2}} & {{n^2}} \cr 0 & 0 & {{{n + 1} \over 2}} \cr } } \right)$$