List of practice Questions

If the system of linear equations
7x +11y + αz = 13
5x + 4y + 7z = β
175x + 194y + 57z = 361
has infinitely many solutions, then α + β + 2 is equal to:

Let $ m $ and $ n $ be the numbers of real roots of the quadratic equations $ x^2 - 12x + [x] + 31 = 0 $ and $ x^2 - 5|x+2| - 4 = 0 $, respectively, where $ [x] $ denotes the greatest integer less than or equal to $ x $. Then $ m^2 + mn + n^2 $ is equal to ___________.

Find the number of integral values of x which satisfy the inequality x₂–10x+19<6.

If the system of equations αx + y + z = 5, x + 2y + 3z = 4, x + 3y +5z = β has infinitely many solutions, then the ordered pair (α, β) is equal to:

The boolean expression (~(p ∧q)) ∨q is equivalent to:

If the system of linear equations
2x + 3y – z = –2
x + y + z = 4
x – y + |λ|z = 4λ – 4
where λ ∈ R, has no solution, then

The system of linear equations $\lambda x+2y+2z=5$ $2\lambda x+3y+5z=8$ $4x+\lambda y+6z=10$ has :

let $\lambda\neq 0$ be in r.If $\alpha$ and $\beta$ are the roots of the equation, then x²-x+2$\lambda$=0 and $\alpha$ and $\gamma$ are the roots of the equation, 3x²-10x+27$\lambda$=0,then $\frac{\beta\gamma}{\lambda}=?$