JEE Main 2022 (Online) 24th June Morning Shift | Matrices and Determinants Question 72 | Mathematics

PREVIOUS NEXT

JEE Main 2022 (Online) 24th June Morning Shift

MCQ (Single Correct Answer)

-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

JEE Main 2022 (Online) 24th June Morning Shift

MCQ (Single Correct Answer)

-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 :

218

221

663

1717

JEE Main 2021 (Online) 1st September Evening Shift

MCQ (Single Correct Answer)

-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

n(S₁) = 2, n(S₂) = 2

n(S₁) = 1, n(S₂) = 0

n(S₁) = 2, n(S₂) = 0

n(S₁) = 0, n(S₂) = 2

JEE Main 2021 (Online) 1st September Evening Shift

MCQ (Single Correct Answer)

-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 :

(15)² $$\times$$ 2⁴²

(15)² $$\times$$ 2³⁴

(105)² $$\times$$ 2³⁸

(105)² $$\times$$ 2³⁶

PREVIOUS NEXT