JEE Main 2019 (Online) 8th April Morning Slot | Matrices and Determinants Question 178 | Mathematics

JEE Main 2019 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

Let $$A = \left( {\matrix{ {\cos \alpha } & { - \sin \alpha } \cr {\sin \alpha } & {\cos \alpha } \cr } } \right)$$, ($$\alpha $$ $$ \in $$ R)
such that $${A^{32}} = \left( {\matrix{ 0 & { - 1} \cr 1 & 0 \cr } } \right)$$ then a value of $$\alpha $$ is

$${\pi \over {16}}$$

$${\pi \over {32}}$$

$${\pi \over {64}}$$

JEE Main 2019 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

The greatest value of c $$ \in $$ R for which the system of linear equations
x – cy – cz = 0
cx – y + cz = 0
cx + cy – z = 0
has a non-trivial solution, is :

-1

1/2

JEE Main 2019 (Online) 12th January Evening Slot

MCQ (Single Correct Answer)

-1

If A = $$\left[ {\matrix{ 1 & {\sin \theta } & 1 \cr { - \sin \theta } & 1 & {\sin \theta } \cr { - 1} & { - \sin \theta } & 1 \cr } } \right]$$;

then for all $$\theta $$ $$ \in $$ $$\left( {{{3\pi } \over 4},{{5\pi } \over 4}} \right)$$, det (A) lies in the interval :

$$\left( {{3 \over 2},3} \right]$$

$$\left( {0,{3 \over 2}} \right]$$

$$\left[ {{5 \over 2},4} \right)$$

$$\left( {1,{5 \over 2}} \right]$$

JEE Main 2019 (Online) 12th January Evening Slot

MCQ (Single Correct Answer)

-1

The set of all values of $$\lambda $$ for which the system of linear equations
x – 2y – 2z = $$\lambda $$x
x + 2y + z = $$\lambda $$y
– x – y = $$\lambda $$z
has a non-trivial solutions :

is an empty set

contains more than two elements

is a singleton

contains exactly two elements

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