1
JEE Main 2017 (Online) 8th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let A be any 3 $$ \times $$ 3 invertible matrix. Then which one of the following is not always true ?
A
adj (A) = $$\left| \right.$$A$$\left| \right.$$.A$$-$$1
B
adj (adj(A)) = $$\left| \right.$$A$$\left| \right.$$.A
C
adj (adj(A)) = $$\left| \right.$$A$$\left| \right.$$2.(adj(A))$$-$$1
D
adj (adj(A)) = $$\left| \, \right.$$A $$\left| \, \right.$$.(adj(A))$$-$$1
2
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$A = \left[ {\matrix{ 2 & { - 3} \cr { - 4} & 1 \cr } } \right]$$,

then adj(3A2 + 12A) is equal to
A
$$\left[ {\matrix{ {51} & {63} \cr {84} & {72} \cr } } \right]$$
B
$$\left[ {\matrix{ {51} & {84} \cr {63} & {72} \cr } } \right]$$
C
$$\left[ {\matrix{ {72} & {-63} \cr {-84} & {51} \cr } } \right]$$
D
$$\left[ {\matrix{ {72} & {-84} \cr {-63} & {51} \cr } } \right]$$
3
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
If S is the set of distinct values of 'b' for which the following system of linear equations

x + y + z = 1
x + ay + z = 1
ax + by + z = 0

has no solution, then S is :
A
an empty set
B
an infinite set
C
a finite set containing two or more elements
D
a singleton
4
JEE Main 2016 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If    A = $$\left[ {\matrix{ { - 4} & { - 1} \cr 3 & 1 \cr } } \right]$$,

then the determinant of the matrix (A2016 − 2A2015 − A2014) is :
A
2014
B
$$-$$ 175
C
2016
D
$$-$$ 25
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