1
JEE Main 2019 (Online) 9th January Morning Slot
MCQ (Single Correct Answer)
+4
-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 :
A
$$\left[ {\matrix{ { {{\sqrt 3 } \over 2}} & { - {1 \over 2}} \cr {{{ 1} \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right]$$
B
$$\left[ {\matrix{ {{1 \over 2}} & -{{{\sqrt 3 } \over 2}} \cr {{{\sqrt 3 } \over 2}} & {{{ - 1} \over 2}} \cr } } \right]$$
C
$$\left[ {\matrix{ {{{\sqrt 3 } \over 2}} & {{1 \over 2}} \cr -{{1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right]$$
D
$$\left[ {\matrix{ {{1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr {-{{\sqrt 3 } \over 2}} & {{{ 1} \over 2}} \cr } } \right]$$
2
JEE Main 2019 (Online) 9th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
The system of linear equations
x + y + z = 2
2x + 3y + 2z = 5
2x + 3y + (a2 – 1) z = a + 1 then
A
has infinitely many solutions for a = 4
B
has a unique solution for |a| = $$\sqrt3$$
C
is inconsistent when |a| = $$\sqrt3$$
D
is inconsistent when a = 4
3
JEE Main 2018 (Online) 16th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Let A = $$\left[ {\matrix{ 1 & 0 & 0 \cr 1 & 1 & 0 \cr 1 & 1 & 1 \cr } } \right]$$ and B = A20. Then the sum of the elements of the first column of B is :
A
210
B
211
C
231
D
251
4
JEE Main 2018 (Online) 16th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
The number of values of k for which the system of linear equations,
(k + 2)x + 10y = k
kx + (k +3)y = k -1
has no solution, is :
A
1
B
2
C
3
D
infinitely many
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