1
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
Let $$A = \left( {\matrix{ {[x + 1]} & {[x + 2]} & {[x + 3]} \cr {[x]} & {[x + 3]} & {[x + 3]} \cr {[x]} & {[x + 2]} & {[x + 4]} \cr } } \right)$$, where [t] denotes the greatest integer less than or equal to t. If det(A) = 192, then the set of values of x is the interval :
A
[68, 69)
B
[62, 63)
C
[65, 66)
D
[60, 61)
2
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
Let A(a, 0), B(b, 2b + 1) and C(0, b), b $$\ne$$ 0, |b| $$\ne$$ 1, be points such that the area of triangle ABC is 1 sq. unit, then the sum of all possible values of a is :
A
$${{ - 2b} \over {b + 1}}$$
B
$${{2b} \over {b + 1}}$$
C
$${{2{b^2}} \over {b + 1}}$$
D
$${{ - 2{b^2}} \over {b + 1}}$$
3
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
Let [$$\lambda$$] be the greatest integer less than or equal to $$\lambda$$. The set of all values of $$\lambda$$ for which the system of linear equations
x + y + z = 4,
3x + 2y + 5z = 3,
9x + 4y + (28 + [$$\lambda$$])z = [$$\lambda$$] has a solution is :
A
R
B
($$-$$$$\infty$$, $$-$$9) $$\cup$$ ($$-$$9, $$\infty$$)
C
[$$-$$9, $$-$$8)
D
($$-$$$$\infty$$, $$-$$9) $$\cup$$ [$$-$$8, $$\infty$$)
4
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
If the matrix $$A = \left( {\matrix{ 0 & 2 \cr K & { - 1} \cr } } \right)$$ satisfies $$A({A^3} + 3I) = 2I$$, then the value of K is :
A
$${1 \over 2}$$
B
$$-$$$${1 \over 2}$$
C
$$-$$1
D
1
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