List of top Mathematics Questions on Linear Equations asked in JEE Main

Consider a geometric sequence $729,\,81,\,9,\,1,\ldots$ If $P_n$ denotes the product of first $n$ terms of the G.P. such that \[ \sum_{n=1}^{40} (P_n)^{\frac{1}{n}}=\frac{3^{\alpha}-1}{2\times 3^{\beta}}, \] then find the value of $(\alpha+\beta)$.

Let $f(x)$ be a differentiable function satisfying \[ f(x)=e^x+\int_0^1 (y+xe^x)f(y)\,dy \] Find $f(0)+e$, where $e$ is Napier's constant.

Let $5000<N<9000$ and $N$ has digits from the set $\{0,1,2,5,9\}$. If digits can be repeated, then find the number of such numbers $N$ which are divisible by $3$.

Let $f(x)$ be a differentiable function satisfying \[ f(x)=e^x+\int_0^1 (y+xe^x)f(y)\,dy \] Find $f(0)+e$, where $e$ is Napier's constant.

The system of linear equations \[ \begin{cases} x + y + z = 6 \\ 2x + 5y + az = 36 \\ x + 2y + 3z = b \end{cases} \] has:

If the system of linear equations: \[ x + y + 2z = 6, \] \[ 2x + 3y + az = a + 1, \] \[ -x - 3y + bz = 2b, \] where $ a, b \in \mathbb{R} $, has infinitely many solutions, then $ 7a + 3b $ is equal to:

If $ 5f(x) + 4f\left(\frac{1}{x}\right) = x^2 - 2 $, for all $ x \neq 0 $, and $ y = 9x^2f(x) $, then $ y $ is strictly increasing in:

Consider the system of linear equations
x + y + z = 5,
x + 2y + λ²z = 9,
x + 3y + λz = μ,
where λ, μ ∈ ℝ.Then, which of the following statement is NOT correct?

If for z=α+iβ, |z+2|=z+4(1+i), then α +β and αβ are the roots of the equation

Consider the following system of equations
$\alpha x + 2y + z = 1$
$2\alpha x + 3y + z = 1$
$3x + \alpha y + 2z = b$
For some $\alpha,\beta∈R$ then which of the following is NOT correct?

Let α, β, γ be the three roots of the equation x³+bx+c=0. If βγ =1=-α, then b³+2c³-3α³-6β³-8γ³ is equal to

If the equation of the plane containing the line x+2y+3z-4=0=2x+y-z+5 and perpendicular to the plane $\vec{r}=(\vec{i}-\vec{j})+\lambda(\vec{i}+\vec{j}+\vec{k})+\mu(\vec{i}-2\vec{j}+3\vec{k})$ is ax+by+cz=4, then (a-b+c) is equal to

Let S be the set of all values of θ Ε [-π, π] for which the system of linear equations
x+y+√3z=0
-x+(tanθ)y+ √7z=0
x+y+(tanθ)z = 0 has non-trivial solution.
Then 120/π ∑θ_θ∈s is equal to

If the system of equations
2x + y - z = 5
2x -5y + λz = μ
x + 2y - 5z = 7
has infinitely many solutions, then (λ + μ)² + (λ - μ)²is equal to

Let the system of linear equations
$-x + 2y - 9z = 7$,
$-x + 3y + 72 = 9$,
$-2x + y + 5z = 8$,
$-3x + y + 13z = \lambda$
has a unique solution $x = \alpha, y = \beta, z = \gamma$. Then the distance of the point $(\alpha, \beta, \gamma)$ from the plane $2x - 2y + z = \lambda$ is:

Let the system of linear equations
x + y + az = 2
3x + y + z = 4
x + 2z = 1
have a unique solution (x*, y*, z*). If (α, x*), (y*, α) and (x*, –y*) are collinear points, then the sum of absolute values of all possible values of α is

Let the system of linear equations 4x + λy + 2z = 0 ; 2x - y + z = 0 ; μx + 2y + 3z = 0, λ, μ ∈ R has a non-trivial solution. Then which of the following is true ?

If the system of equations $kx + y + 2z = 1$, $3x - y - 2z = 2$, $-2x - 2y - 4z = 3$ has infinitely many solutions, then k is equal to ________