CMAT Quadratic and Linear Equations Practice Questions With Solutions

If $x^2 = y + z , y^2 = z + x$ and $z^2 = x + y$ then the value of $\frac{1}{x + 1} + \frac{1}{y + 1} + \frac{1}{z + 1}$ is

Anand's income is ₹ 140 more than Biren's income and Chandu's income is ₹ 80 more than Deepak's. If the ratio of Anand's & Chandu's income is 2 : 3 and the ratio of Biren's and Deepak's income is 1 : 2 , then the incomes of Anand, Biren, Chandu and Deepak are respectively:

The graphs of ax + by = c, dx+ey = f will be,
(A) Parallel if the system has no solution.
(B) Coincident if the system has finite number of solutions.
(C) Intersecting if the system has two solutions
(D) Intersecting if the system has only one solution
Choose the correct answer from the options given below :

A vessel of 160 L is filled with milk and water. 70% of milk and 30% of water is taken out of the vessel. It is found out that the vessel is vacated by 55%, then the quantity of milk and water in the original mixture is

If the roots of the equation $px^{2} + x + r = 0$ are reciprocal to each other, then which one of the following is correct ?

Consider the following figure that shows the graph of the function F defined by
F(x) = | 2x | + 4 for all numbers x:

For which of the following functions G defined for all numbers x does the graph of G intersect the graph of F?

Given below are two statements :
Statement I: The ratio of the son's age to the father's age is 1 : 5. The product of their ages is 245. The ratio of the son's age to the father's age after 9 years will be 3 : 5.
Statement II: A milkman adds 30 litres of water to 70 litres of milk. After selling 1/5th of the total quantity, he adds water equal to the quantity he sold. The proportion of water to milk he sells now would be 28 : 72.
In the light of the above statements, choose the correct answer from the options given below.

Find the range of values of real number x for which the inequality (x + 2) (x + 5) > 40 holds

Anil travelled 300 km by bus and 200 km by taxi. For this, it took him 5 hours and 30 minutes. However if he travels 260 km by bus and 240 km by taxi then he takes 6 minutes more. The speed of the bus is ________ km/hour.

Given below are two statements:
Statement I : If the roots of a quadratic equation are 2 and 3, then the equation is $x^{2} - 5x- 6 = 0$
Statement II: If the roots of $4x^{2}+3kx + 9 = 0$ are real and distinct, then $k \leq - 4$ or $k \geq 4$
In the light of the above statements, choose the most appropriate answer from the options given below: