List of top Mathematics Questions on Linear Equations

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?

Nimra went to a bank to withdraw ₹2,000. She asked the cashier to give her ₹50 and ₹100 notes only and she got 30 notes in all. How many notes of ₹50 and ₹100 respectively that she received?

The difference between two numbers is 24. If one number is 2 times the second. Then the two numbers will be:

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

Let the system of linear equations
-x+2y-9z=7
-x+3y+72=9
-2x+y+5z=8
-3x+y+13z = λ
has a unique solution x=α, y=β, z=γ. Then the distance of the point (α, β, γ) from the plane 2x-2y+z=λ is

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?

The solution of \(7x ≡ 3(mod 5)\) is:

Two bags of iron ore weight 180 kg 250 gm and 270 kg 50 gm respectively. How much iron ore (in gm) must be taken out from the first bag and added to the second bag so that weight of the first bag may then be two-third of the second bag?

The pair of linear equations \(x+2y-5=0\) and \(3x+12y-10=0\) has

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)² is equal to

If f(x) = ax + b, where a and b are integers, f(-1) = -5 and f(3) = 3 then a and b are respectively

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

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

Let p, q, r be non-zero real numbers that are, respectively, the 10^th, 100^th and 1000^th terms of a harmonic progression. Consider the system of linear equations
x + y + z = 1
10x + 100y + 1000z = 0
qr x + pr y + pq z = 0
 

List-I		List-II
(I)	If \(\frac{q}{r}=10\), then the system of linear equations has	(P)	x = 0, \(y=\frac{10}{9},z=-\frac{1}{9}\) as a solution
(II)	If \(\frac{p}{r}≠100\), then the system of linear equations has	(Q)	\(x=\frac{10}{9},y=\frac{-1}{9},z=0\) as a solution
(III)	If \(\frac{p}{q}≠10,\) then the system of linear equations has	(R)	infinitely many solutions
(IV)	If \(\frac{p}{q}=10,\) then the system of linear equations has	(S)	no solution
		(T)	at least one solution

If in the equation \(x+3y=10\), the value of \(y\) is \(4\), then the value of \(x\) will be

The pair of equations y = 0 and y = -7 has

The value of k for which the pair of linear equations kx- y = 2 and 6x-2y = 3 has a unique solution, 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

The number of solutions of the pair of linear equations x+2y=8 and 2x+4y-16 are

The pair of linear equations 2x+y-5-0 and 3x-2y-4=0 intersect at the point.

Five years ago. Ramu was thrice as old as Somu and ten years later, Ramu will be twice as old as Somu. Then the present ages of Ramu and Somu respectively are

A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Assuming that there is no slack in the string, the length of the string is