Quantitative Aptitude PYQs

if a - b = 5 and a² + b² = 73, then the value of ab is:

If a² + b² + c² = 20 and ab + bc + ca = 10, then the value of (a + b + c)² is:

A rectangular parallelepiped tank has dimensions 4m x 3m x 2.5m. if it is filled with water and the cost of water is ₹25 per 1000 liters, what is the total cost to fill the tank? (1 m³ = 1000 liters)

Consider a triangle XYZ where the angle at vertex Y measures 90 degrees and M is the midpoint of hypotenuse XZ. What can be said | about point M?

Determine the volumetric measure of a cuboidal solid with a length of 12 centimeters, a breadth of 7 centimeters, and a height of 5 centimeters.

A circle has two chords, AB and CD, which are of equal length. subtend angles of x° and y° respectively at the center. Which of the following is true?

If \(\rm \sqrt{(x^2+10x+25)}+\sqrt{(x^2-6x+9)}=10\) find the value of x.

A student claims that the sum of two irrational numbers is always irrational. Which of the following pair of numbers disproves this |claim ?

Two triangles are similar if their corresponding sides are proportional. This is known as the:

If a price is reduced by 10% and then again reduced by 20%, what is the overall percentage decrease? 

A satellite dish is aligned so that it forms an angle x with the horizontal. It is known that cos x = -3/5 and x lies in the third quadrant. What is the sine of half the elevation angle ( / 2), assuming precision is necessary for signal locking?

Which of the following is both rational and an integer?

Two numbers are in ratio 4:5. If the sum is 81, find the numbers.

A, B, C share a profit of ₹4800 in the ratio 3:4:5. If C's share is reduced by ₹400, and the remainder is equally divided between A and B, what will be A's final share ?

A student scores an average of 70 in four subjects. What should he score in the fifth subject to have an average of 75?

A cuboidal block of metal is melted and recast into 12 identical cubes. If the original block had dimensions 24 cm × 6 cm × 6 cm, what is the edge of each cube?

Two tangents are drawn from an external point P to a circle, touching at points A and B. If the distance from P to the center O is 13 cm, and radius is 5 cm, what is the length of tangent PA?

If triangle ABC is congruent to triangle FED, which of the following is true?

A chord PQ of a circle is equal to its radius. The angle subtended by this chord at a point on the major arc is:

A positive number exceeds its square root by 132. Find the number given that it is also a multiple of 12.