If \(\displaystyle\lim _{n \rightarrow \infty}\left(\sqrt{n^2-n-1}+n \alpha+\beta\right)=0 \) then \(8(\alpha+\beta)\) is equal to :
- 4
- $-8$
-4
- 8
The Correct Option is C
Solution and Explanation
Top Questions on linear inequalities
- Solve the system of equations: \[ x + y = 10 \] \[ 3x - y = 5 \]
- MHT CET - 2025
- Mathematics
- linear inequalities
- Solve the system of equations: \[ x + y = 5 \] \[ 2x - y = 4 \]
- MHT CET - 2025
- Mathematics
- linear inequalities
- The sum of the ages of a father and his son is 60 years. The father is three times as old as the son. What is the son's age?
- MHT CET - 2025
- Mathematics
- linear inequalities
- If \[ A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix} \] and \[ A^{-1} = \frac{1}{2} \begin{bmatrix} 1 & -1 & 1 \\ -8 & 6 & 2c \\ 5 & -3 & 1 \end{bmatrix}, \] then the values of \( a \) and \( c \) are respectively:
- MHT CET - 2024
- Mathematics
- linear inequalities
- If \( AX = B \), where \[ A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}, \quad B = \begin{bmatrix} 4 \\ 0 \\ 2 \end{bmatrix}, \] then \( 2x + y - z \) is:
- MHT CET - 2024
- Mathematics
- linear inequalities
Questions Asked in JEE Main exam
- The system of linear equations
$x + y + z = 6$
$2x + 5y + az = 36$
$x + 2y + 3z = b$
has- JEE Main - 2026
- Matrices and Determinants
- The displacement of a particle executing simple harmonic motion with time period \(T\) is expressed as \[ x(t)=A\sin\omega t, \] where \(A\) is the amplitude of oscillation. If the maximum value of the potential energy of the oscillator is found at \[ t=\frac{T}{2\beta}, \] then the value of \(\beta\) is ________.
- JEE Main - 2026
- Waves and Oscillations
- A complex number 'z' satisfy both \(|z-6|=5\) & \(|z+2-6i|=5\) simultaneously. Find the value of \(z^3 + 3z^2 - 15z + 141\).
- JEE Main - 2026
- Algebra
In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$)
- JEE Main - 2026
- Rotational Mechanics
Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).
- JEE Main - 2026
- Rotational motion
Concepts Used:
Linear Inequalities
The expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’ are called linear inequalities. These values could be numerical or algebraic or a combination of both expressions. A system of linear inequalities in two variables involves at least two linear inequalities in the identical variables. After solving linear inequality we get an ordered pair. So generally, in a system, the solution to all inequalities and the graph of the linear inequality is the graph representing all solutions of the system.
How to Solve Inequalities in Maths?
Follow the below steps to solve all types of inequalities:
- At the vert first, write the inequality as an equation.
- Solve the provided equation for one or more values.
- Now, display all the values obtained in the number line.
- Use open circles to show the excluded values on the number line.
- Find the interim.
- At the moment, take any random value from the interval and substitute it in the inequality equation to check whether the values reassure the inequality equation.
- Intervals that reassure the inequality equation are the solutions of the given inequality equation.