List of top Mathematics Questions on Linear Equations

Evaluate the series \[ \frac{1}{25!}+\frac{1}{3!\,23!}+\frac{1}{5!\,21!}+\cdots \text{ up to 13 terms.} \]

Find the number of real solutions of \[ x|x-3|+|x-1|+3=0 \]

Find the sum of all real solutions of
$|x + 1|^2 - 4|x + 1| + 3 = 0$

Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.

The sum of a two-digit number and the number obtained by reversing the digits is 110. If the tens digit of the number is 6 more than the units digit, then find the number.

Solve the following pairs of linear equations : $3x - 5y = 4$, $9x = 2y + 7$

In linear equation $\frac{x}{3} + \frac{y}{2} = 6$ if $x = 9$ then the value of $y$ will be :

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 $(\alpha+\beta)$.

The value of \(k\) for which the system of linear equations \(\frac{x}{2} + \frac{y}{3} = 5\) and \(2x + ky = 7\) is inconsistent, is

Assertion (A) : \((\sqrt{3} + \sqrt{5})\) is an irrational number.
Reason (R) : Sum of the any two irrational numbers is always irrational.

If the pair of linear equations : \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) is consistent and dependent, then

If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has :

Determine graphically, the coordinates of vertices of a triangle whose equations are \(2x - 3y + 6 = 0\); \(2x + 3y - 18 = 0\) and \(x = 0\). Also, find the area of this triangle.

Draw the graph of the pair of linear equations $x - y + 2 = 0$ and $4x - y - 4 = 0$. Calculate the area of the triangle formed by the lines so drawn and the $x$-axis.

The system of linear equations \(px + qy = r\) and \(p_1x + q_1y = r_1\) has a unique solution, if :

The system of equations \(x = 2\) and \(x = 3\) has:

Solve the following system of equations graphically : \(x + 3y = 6\) and \(2x - 3y = 12\). Also, find the area of the triangle formed by the lines \(x + 3y = 6\), \(x = 0\) and \(y = 0\).

One of the supplementary angles exceeds the other by 120°. Express this as a system of linear equations and find the angles.

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: