JEE Main 2019 (Online) 9th January Evening Slot | Matrices and Determinants Question 251 | Mathematics

If $$A = \left[ {\matrix{ {{e^t}} & {{e^{ - t}}\cos t} & {{e^{ - t}}\sin t} \cr {{e^t}} & { - {e^{ - t}}\cos t - {e^{ - t}}\sin t} & { - {e^{ - t}}\sin t + {e^{ - t}}co{\mathop{\rm s}\nolimits} t} \cr {{e^t}} & {2{e^{ - t}}\sin t} & { - 2{e^{ - t}}\cos t} \cr } } \right]$$

then A is :

invertible for all t$$ \in $$R.

invertible only if t $$=$$ $$\pi $$

not invertible for any t$$ \in $$R

invertible only if t $$=$$ $${\pi \over 2}$$.

JEE Main 2019 (Online) 9th January Morning Slot

MCQ (Single Correct Answer)

-1

If $$A = \left[ {\matrix{ {\cos \theta } & { - \sin \theta } \cr {\sin \theta } & {\cos \theta } \cr } } \right]$$, then the matrix A^–50 when $$\theta $$ = $$\pi \over 12$$, is equal to :

$$\left[ {\matrix{ { {{\sqrt 3 } \over 2}} & { - {1 \over 2}} \cr {{{ 1} \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right]$$

$$\left[ {\matrix{ {{1 \over 2}} & -{{{\sqrt 3 } \over 2}} \cr {{{\sqrt 3 } \over 2}} & {{{ - 1} \over 2}} \cr } } \right]$$

$$\left[ {\matrix{ {{{\sqrt 3 } \over 2}} & {{1 \over 2}} \cr -{{1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right]$$

$$\left[ {\matrix{ {{1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr {-{{\sqrt 3 } \over 2}} & {{{ 1} \over 2}} \cr } } \right]$$

JEE Main 2019 (Online) 9th January Morning Slot

MCQ (Single Correct Answer)

-1

The system of linear equations
x + y + z = 2
2x + 3y + 2z = 5
2x + 3y + (a² – 1) z = a + 1 then

has infinitely many solutions for a = 4

has a unique solution for |a| = $$\sqrt3$$

is inconsistent when |a| = $$\sqrt3$$

is inconsistent when a = 4