JEE Main 2021 (Online) 1st September Evening Shift | Matrices and Determinants Question 74 | Mathematics

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

JEE Main 2021 (Online) 31st August Evening Shift

MCQ (Single Correct Answer)

-1

If $$\alpha$$ + $$\beta$$ + $$\gamma$$ = 2$$\pi$$, then the system of equations

x + (cos $$\gamma$$)y + (cos $$\beta$$)z = 0

(cos $$\gamma$$)x + y + (cos $$\alpha$$)z = 0

(cos $$\beta$$)x + (cos $$\alpha$$)y + z = 0

has :

no solution

infinitely many solution

exactly two solutions

a unique solution

JEE Main 2021 (Online) 31st August Morning Shift

MCQ (Single Correct Answer)

-1

If the following system of linear equations

2x + y + z = 5

x $$-$$ y + z = 3

x + y + az = b

has no solution, then :

$$a = - {1 \over 3},b \ne {7 \over 3}$$

$$a \ne {1 \over 3},b = {7 \over 3}$$

$$a \ne - {1 \over 3},b = {7 \over 3}$$

$$a = {1 \over 3},b \ne {7 \over 3}$$