XAT Functions Practice Questions With Solutions

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XAT Functions Practice Questions with Solutions

Functions are a mathematical concept, and are an integral part of the Quantitative Ability section of the XAT exam. The XAT Functions Practice Questions with Solutions are a great resource to help students in mastering their problem solving skills and score well in the quantitative ability section of the Xavier Aptitude Test. Practising problems on functions on a regular basis is very important, as this section of the XAT exam has many challenging questions. These questions test the candidate’s ability to solve critical mathematical problems. Therefore, it is advised for students to practise at least 10 problems based on functions every week.

The Quantitative Ability section, overall, has 28 questions in the XAT exam paper. The important topics included in functions are the basics of functions, function definition, compositions, odd functions, even functions, functional equations, domain & range finding, maxima & minima with functions, and graphical questions on functions. Practising the XAT Functions Practice Questions with Solutions regularly will help students in understanding the format of the questions asked, improving their accuracy while solving function-based problems, and managing time better during the exam. It will also enhance their confidence, which is necessary for solving mathematical questions with ease and achieving success in the XAT exam.

XAT Quantitative Ability & Data Interpretation Functions Practice Questions

Verbal and Logical Ability Decision Making General Knowledge

Question 1.

Consider the equation $\log_5(x - 2) = 2 \log_{25}(2x - 4)$ , where x is a real number.
For how many different values of x does the given equation hold?

Infinitely many

Question 2.

The roots of the polynomial $P(x) = 2x^3 - 11x^2 + 17x - 6$ are the radii of three concentric circles.
The ratio of their area, when arranged from the largest to the smallest, is:

6:2:1

9:4:1

16:6:3

36:16:1

None of the remaining options is correct.

Question 3.

Given $A = |x + 3| + | x - 2 | - | 2x -8|$ . The maximum value of $|A|$ is:

111

$\infty$

Question 4.

ABC is a triangle and the coordinates of A, B and C are (a, b-2c), (a, b+4c) and (-2a,3c) respectively where a, b and c are positive numbers.
The area of the triangle ABC is:

6abc

9abc

6bc

9ac

None of the above

Question 5.

Consider $a_{n+1} =\frac{1}{1+\frac{1}{a_{n}}}$ for $n = 1,2, ....., 2008, 2009$ where $a_{1} = 1$ . Find the value of $a_{1}a_{2} + a_{2}a_{3} + a_{3}a_{4} + ... + a_{2008}a_{2009}$ .

$\frac{2009}{1000}$

$\frac{2009}{2008}$

$\frac{2008}{2009}$

$\frac{6000}{2009}$

$\frac{2008}{6000}$

Question 6.

Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?

None of the above

Question 7.

The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is 2.

256

Question 8.

Consider the real-valued function $f(x)=\frac{\log{(3x-7)}}{\sqrt{2x^{2}-7x+6}}$ Find the domain of f(x).

$(\frac{7}{3},\infty)$

$R-\left\{\frac{7}{3}\right\}$

$R-\left\{\frac{3}{2},2\right\}$

$R-\left\{\frac{3}{2},2,\frac{7}{3}\right\}$

$(-\infty,\frac{7}{3})$

Question 9.

Let $f(x) = \frac{x^2 + 1}{x^2 - 1}$ if $x \neq 1, -1,$ and 1 if x = 1, -1. Let $g(x) = \frac{x + 1}{x - 1}$ if $x \neq 1,$ and 3 if x = 1.
What is the minimum possible values of $\frac{f(x)}{g(x)}$ ?

$\frac{1}{2}$

-1

$\frac{1}{4}$

$\frac{1}{3}$

Question 10.

The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The points B and C are somewhere between A and D on the pole. From a point E, located on the ground at a certain distance from D, the points A, B and C are at angles of 60, 45 and 30 degrees respectively. What is AB : BC : CD?

$(3 + \sqrt 3) : (1 + \sqrt 3) : 1$

$(3 - \sqrt 3) : 1 : (\sqrt 3 - 1)$

1 : 1 : 1

$(3 - \sqrt 3) : (\sqrt 3 - 1) : 1$

$(\sqrt 3 - 1) : 1 : (3 - \sqrt 3)$

Question 1.

Consider the four variables A, B, C and D and a function Z of these variables, $Z = 15A^2 - 3B^4 + C + 0.5D$ It is given that A, B, C and D must be non-negative integers and thatall of the following relationships must hold:
i) $2A + B \leq 2$
ii) $4A + 2B + C \leq 12$
iii) $3A + 4B + D \leq 15$
If Z needs to be maximised, then what value must D take?

Question 2.

Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:

Question 3.

If $x^2 + x + 1 = 0$ , then $x^{2018} + x^{2019}$ equals which of the following:

$x+1$

$x$

$-x$

$x-1$

Question 4.

We have two unknown positive integers m and n, whose product is less than 100.

Which of the two statements above, alone or in combination shall be sufficient to determine the numbers m and n?

Each statement alone is suﬃcient to answer the question.

Both statements taken together are suﬃcient to answer the question, but neither statement alone is suﬃcient.

Statement 2 alone is suﬃcient, but statement 1 alone is not suﬃcient to answer the question.

Statements 1 and 2 together are not suﬃcient, and additional data is needed to answer the question.

Statement 1 alone is suﬃcient, but statement 2 alone is not suﬃcient to answer the question.

Question 5.

Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?

The common root is 29.

The smallest among the roots is 1.

One of the roots is 5.

Product of the roots of the other equation is 5.

All of the above are possible, but none are definitely correct.

Question 6.

X and Y are the digits at the unit's place of the numbers (408X) and (789Y) where X ≠ Y. However, the digits at the unit's place of the numbers $(408X)^{63}$ and $(789Y)^{85}$ are the same. What will be the possible value(s) of (X + Y)?

None of the above

Question 7.

If $2 \leq |x - 1| \times |y + 3| \leq 5$ and both $x$ and $y$ are negative integers, find the number of possible combinations of $x$ and $y$ .

Question 8.

If $x$ and $y$ are real numbers, the least possible value of the expression $4(x - 2)^{2} + 4(y - 3)^{2} - 2(x - 3)^{2}$ is :

- 8

- 4

- 2

Question 9.

If f(x) = ax + b, a and b are positive real numbers and if f(f(x)) = 9x + 8, then the value of a + b is:

None of the above

Question 10.

If 5° $\leq$ x° $\leq$ 15°, then the value of sin 30° + cos x° - sin x° will be :

Between -1 and -0.5 inclusive

Between -0.5 and 0 inclusive

Between 0 and 0.5 exclusive

between 0.5 and 1 inclusive

None of the above

XAT Functions Practice Questions With Solutions

XAT Functions Practice Questions with Solutions

XAT Quantitative Ability & Data Interpretation Functions Practice Questions

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

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