1
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

The number of values of $$\alpha$$ for which the system of equations :

x + y + z = $$\alpha$$

$$\alpha$$x + 2$$\alpha$$y + 3z = $$-$$1

x + 3$$\alpha$$y + 5z = 4

is inconsistent, is

A
0
B
1
C
2
D
3
2
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

Let S = {$$\sqrt{n}$$ : 1 $$\le$$ n $$\le$$ 50 and n is odd}.

Let a $$\in$$ S and $$A = \left[ {\matrix{ 1 & 0 & a \cr { - 1} & 1 & 0 \cr { - a} & 0 & 1 \cr } } \right]$$.

If $$\sum\limits_{a\, \in \,S}^{} {\det (adj\,A) = 100\lambda }$$, then $$\lambda$$ is equal to :

A
218
B
221
C
663
D
1717
3
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Consider the system of linear equations

$$-$$x + y + 2z = 0

3x $$-$$ ay + 5z = 1

2x $$-$$ 2y $$-$$ az = 7

Let S1 be the set of all a$$\in$$R for which the system is inconsistent and S2 be the set of all a$$\in$$R for which the system has infinitely many solutions. If n(S1) and n(S2) denote the number of elements in S1 and S2 respectively, then
A
n(S1) = 2, n(S2) = 2
B
n(S1) = 1, n(S2) = 0
C
n(S1) = 2, n(S2) = 0
D
n(S1) = 0, n(S2) = 2
4
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Let $${J_{n,m}} = \int\limits_0^{{1 \over 2}} {{{{x^n}} \over {{x^m} - 1}}dx}$$, $$\forall$$ n > m and n, m $$\in$$ N. Consider a matrix $$A = {[{a_{ij}}]_{3 \times 3}}$$ where $${a_{ij}} = \left\{ {\matrix{ {{j_{6 + i,3}} - {j_{i + 3,3}},} & {i \le j} \cr {0,} & {i > j} \cr } } \right.$$. Then $$\left| {adj{A^{ - 1}}} \right|$$ is :
A
(15)2 $$\times$$ 242
B
(15)2 $$\times$$ 234
C
(105)2 $$\times$$ 238
D
(105)2 $$\times$$ 236
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