CMAT Algebra — practice questions
85 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CMAT Algebra in the app →The sample space of a single throw of a fair six-faced die isIf a fair coin is tossed once, the probability of getting a HEAD isA fair die is rolled. The probability of getting an ODD number isTwo fair dice are rolled. The probability that the SUM of the numbers showing is 7 isFor any two events $A$ and $B$, the probability of $A \cup B$ (A or B) is given byA card is drawn from a well-shuffled standard deck of 52 cards. The probability of drawing a KING isA fair die is rolled. The probability of getting a PRIME number isThree fair coins are tossed simultaneously. The probability of getting EXACTLY two heads isA card is drawn from a standard deck of 52. The probability that it is a KING or a QUEEN isIf $P(A) = 0.4$ and $P(B) = 0.5$ and $P(A \cap B) = 0.2$, then $P(A \cup B)$ isWhat is the probability that a randomly drawn card from a 52-card deck is a FACE CARD (King, Queen, or Jack)?Two events $A$ and $B$ are MUTUALLY EXCLUSIVE ifTwo fair coins are tossed. The probability of getting AT LEAST ONE head isIf the probability that a student passes a CAT mock test is $0.6$, what is the probability that the student FAIf x² + y² = 25 and xy = 12, then (x + y)² =If x + 1/x = 3, find x² + 1/x².If a + b = 7 and ab = 12, find a² + b².Expand (x + y)³.Solve: |2x − 5| = 3.An equation of the form ax + by + c = 0, with a and b not both zero, is a linear equation in:Substituting x = 1 and y = 1 in 2x + 3y = 5 gives 5, so this pair of values is:Each solution of a linear equation in two variables corresponds to:Two lines drawn in a plane can intersect, be coincident, or be:If the two lines of a pair of linear equations intersect at one point, the pair has:A pair of linear equations that has no solution is called:A pair of linear equations whose lines coincide has:A pair of equations which are equivalent, with infinitely many common solutions, is called:Akhila's rides and games gave x - 2y = 0 and 3x + 4y = 20. The lines meet at:From that solution, the number of rides Akhila had on the Giant Wheel was:Romila paid 9 for 2 pencils and 3 erasers; Sonali paid 18 for 4 pencils and 6 erasers. Their lines are:Two rails are x + 2y - 4 = 0 and 2x + 4y - 12 = 0. Do they cross?For x + 3y = 6 and 2x - 3y = 12, the common point is:If a1/a2 is not equal to b1/b2, the two lines are:If a1/a2 = b1/b2 = c1/c2, the two lines are:If a1/a2 = b1/b2 but this differs from c1/c2, the two lines are:A pair of linear equations that has a solution is called:A coach buys 3 bats and 6 balls for 3,900 and later 1 bat and 3 balls for 1,300. This is a situation of:2 kg apples with 1 kg grapes cost 160, and 4 kg apples with 2 kg grapes cost 300. The unknowns here are:Putting x = 0 in the equation 3x + 4y = 20 gives y equal to:Choosing y = 2 in 3x + 4y = 20 was preferred because it gives x as:The graphical representation of a linear equation in two variables is:The distance between two points in a plane is worked out using which theorem?Since distance can never be negative, the distance formula takes:The distance between the points (4, 6) and (6, 8) is:The distance between the points (2, 3) and (4, 1) is:The distance between the points (0, 0) and (36, 15) is:The distance of the point (6, 4) from the point (minus 5, minus 3) comes to:The distance of any point P from the origin uses which coordinates?The points (3, 2), (minus 2, minus 3) and (2, 3) form which kind of triangle?The points (1, 7), (4, 2), (minus 1, minus 1) and (minus 4, 4) are the vertices of a:Ashima, Bharti and Camella sit at (3, 1), (6, 4) and (8, 6). Are they in a line?The relation satisfied by every point equidistant from (7, 1) and (3, 5) is:The graph of that relation is the:The point on the y-axis equidistant from (6, 5) and (minus 4, 3) is:The formula giving the point dividing a segment in a given ratio is the:The point dividing the join of (4, minus 3) and (8, 5) in the ratio 3 to 1 is:A midpoint divides a line segment in which ratio?Because of that, the midpoint of the join of two points is found by:The area of the triangle with vertices (1, minus 1), (minus 4, 6) and (minus 3, minus 5) is:The area of the triangle with vertices (5, 2), (4, 7) and (7, minus 4) is:When the area formula gives a negative value for a triangle, you should:If three points give an area of zero, what does that show?The points (1, 5), (2, 3) and (minus 2, minus 11) are examined to check whether they are:An equation p(x) = 0 where p is a polynomial of degree 2 is called a:The standard form of such an equation is written as:In that standard form, the one restriction placed on the coefficient a is that it is:The scholar credited with deriving the quadratic formula around 1025 CE was:The expression b squared minus 4ac is called the equation's:If that expression is greater than zero, the equation has:If that expression equals zero, the equation has:If that expression is less than zero, the equation has:For the equation 2x squared minus 5x plus 3 equals 0, the discriminant is:Because that discriminant is positive, the equation 2x squared minus 5x plus 3 equals 0 has:The roots of 2x squared minus 5x plus 3 equals 0 are:For the equation 6x squared minus x minus 2 equals 0, the discriminant is:The roots of 6x squared minus x minus 2 equals 0 are:For the equation x squared plus 4x minus 5 equals 0, the discriminant is:The roots of x squared plus 4x minus 5 equals 0 are:A method that rewrites the equation so one side becomes a perfect square is called:The values of x that satisfy a quadratic equation are called its:The roots of a quadratic equation are the same as the zeroes of the corresponding:A number of toys problem leads to 2x squared plus x minus 300 equals 0. Its discriminant is:Because 2401 is the square of 49, that equation has roots that are:Which two methods of solving quadratic equations are worked through in the examples?Before applying any solving method, an equation must first be written in its: