1
JEE Main 2022 (Online) 27th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the system of linear equations
$$x + 2y + z = 2$$,
$$\alpha x + 3y - z = \alpha $$,
$$ - \alpha x + y + 2z = - \alpha $$
be inconsistent. Then $$\alpha$$ is equal to :

A
$${5 \over 2}$$
B
$$-$$$${5 \over 2}$$
C
$${7 \over 2}$$
D
$$-$$$${7 \over 2}$$
2
JEE Main 2022 (Online) 27th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$x = \sum\limits_{n = 0}^\infty {{a^n},y = \sum\limits_{n = 0}^\infty {{b^n},z = \sum\limits_{n = 0}^\infty {{c^n}} } } $$, where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc $$\ne$$ 0, then :

A
x, y, z are in A.P.
B
x, y, z are in G.P.
C
$${1 \over x}$$, $${1 \over y}$$, $${1 \over z}$$ are in A.P.
D
$${1 \over x}$$ + $${1 \over y}$$ + $${1 \over z}$$ = 1 $$-$$ (a + b + c)
3
JEE Main 2022 (Online) 27th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let $${{dy} \over {dx}} = {{ax - by + a} \over {bx + cy + a}}$$, where a, b, c are constants, represent a circle passing through the point (2, 5). Then the shortest distance of the point (11, 6) from this circle is :

A
10
B
8
C
7
D
5
4
JEE Main 2022 (Online) 27th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let a be an integer such that $$\mathop {\lim }\limits_{x \to 7} {{18 - [1 - x]} \over {[x - 3a]}}$$ exists, where [t] is greatest integer $$\le$$ t. Then a is equal to :

A
$$-$$6
B
$$-$$2
C
2
D
6
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