List of top Quantitative Ability Questions asked in XAT

Suppose \(S\) and \(T\) are sets of vectors, where \(S = \{(1,0,0), (0, 0, -5), (0, 3, 4)\}\) and \(T = \{(5, 2, 3), (5, -3, 4)\}\), then:

The horizontal distance of a kite from the boy flying it is 30 m and 50 m of cord is out from the roll. If the wind moves the kite horizontally at the rate of 5 km per hour directly away from the boy, how fast is the cord being released?

Set of real numbers 'x, y', satisfying the inequations \(x - 3y \geq 0\), \(x + y \geq -2\) and \(3x - y \leq -2\) is:

\(ABCD\) is a trapezium, such that \(AB\), \(DC\) are parallel and \(BC\) is perpendicular to them. If \(\angle DAB = 45^{\circ}\), \(BC = 2\) cm and \(CD = 3\) cm, then \(AB = ?\)

Suppose the function \(f\) satisfies the equation \(f(x+y) = f(x)f(y)\) for all \(x\) and \(y\). Here \(f(x) = 1 + xg(x)\), where \(\displaystyle\lim_{x \to 0} g(x) = T\), and \(T\) is a positive integer. If \(f^{n}(x) = kf(x)\), where \(f^{n}(x)\) denotes the \(n\)th derivative of \(f\), then \(k\) is equal to:

What is the sum of the first 100 terms which are common to both the progressions \(17, 21, 25, \ldots\) and \(16, 21, 26, \ldots\)?

If the roots of the equation \(\dfrac{x+a}{x+a+c} + \dfrac{x+b}{x+b+c} = 1\) are equal in magnitude but opposite in sign, then:

Two people agree to meet on January 9, 2005 between 6:00 P.M. and 7:00 P.M., with the understanding that each will wait no longer than 20 minutes for the other. What is the probability that they will meet?

Steel Express runs between Tatanagar and Howrah and has five stoppages in between. Find the number of different kinds of one-way second class tickets that Indian Railways will have to print to service all types of passengers who might travel by Steel Express.

The expression \(\dfrac{x^2 - 2x + a^2 + b^2}{x^2 + 2x + a^2 + b^2}\) lies between:

If \(x > 8\) and \(y > -4\), then which one of the following is always true?

The length of the sides of a triangle are \(x + 1\), \(9 - x\) and \(5x - 3\). The number of values of x for which the triangle is isosceles is:

If \(R = \{(1,1), (2,2), (1,2), (2,1), (3,3)\}\) and \(S = \{(1,1), (2,2), (2,3), (3,2), (3,3)\}\) are two relations on the set \(X = \{1, 2, 3\}\), the incorrect statement is:

An equilateral triangle is formed by joining the midpoints of the sides of a given equilateral triangle. A third equilateral triangle is formed inside the second equilateral triangle in the same way, and so on. If this process continues indefinitely, then the sum of the areas of all such triangles, when the side of the first triangle is 16 cm, is:

For \(n = 1, 2, 3, \ldots\), let \(T_n = 1^3 + 2^3 + \cdots + n^3\). Which one of the following statements is correct?

An operation \( \$ \) is defined as follows. For any two positive integers \(x\) and \(y\),
\[ x \$ y = \sqrt{ \sqrt{\dfrac{x}{y}} + \sqrt{\dfrac{y}{x}} } \]
Which of the following is an integer?

If \(a\), \(b\) and \(c\) are three real numbers, then which of the following is NOT true?

If \(f(x) = \cos(x)\) then the 50th derivative of \(f(x)\) is:

How many numbers between 1 and 1000 (both excluded) are both squares and cubes?

The curve \(y = 4x^2\) and \(y^2 = 2x\) meet at the origin O and at a point P, forming a loop. The straight line OP divides the loop into two parts. What is the ratio of the areas of the two parts of the loop?

If \(S_n\) denotes the sum of the first \(n\) terms of an Arithmetic Progression, and \(S_1 : S_4 = 1 : 10\), then the ratio of the first term to the fourth term is:

The sides of a rhombus ABCD measure 2 cm each, and the difference between two of its angles is \(90^{\circ}\). Then the area of the rhombus is:

In an examination, the average marks obtained by students who passed was \(x\%\), while the average of those who failed was \(y\%\). The average marks of all the students taking the exam was \(z\%\). Find, in terms of \(x\), \(y\) and \(z\), the percentage of students taking the exam who failed.

Three circles A, B and C have a common centre O. A is the inner circle, B is the middle circle, and C is the outer circle. P is a point on the outer circle C, and the radius OP cuts the inner circle at X and the middle circle at Y, such that \(OX = XY = YP\). The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circles is:

Last year, Mr Basu bought two scooters. This year, he sold both of them for Rs 30,000 each. On one scooter, he earned a profit of 20%, and on the other, he made a loss of 20%. What was his net profit or loss?