by Naveen Neredimalli
Wed 29 May 2024 05:41 PM
21

Check out the Top 20 Functions and Graphs Questions for CAT 2024 preparation. Questions related to functions and graphs are quite common in the quantitative aptitude section of CAT and require a strong understanding of mathematical concepts and problem-solving skills.

Download PDF is designed to help you enhance your proficiency in solving CAT Quant questions related to functions and graphs. Practising these top 20 questions will strengthen your grasp of fundamental concepts and develop strategies to tackle complex problems efficiently. Each question in this PDF is carefully curated to reflect the diverse range of topics and difficulty levels you may encounter in the CAT exam. These CAT questions will test your analytical reasoning and mathematical abilities, from essential functions to advanced graphical representations.

Let $$f(x)$$ be a quadratic polynomial in $$x$$ such that $$f(x) \geq 0$$ for all real numbers $$x$$. If f(2) = 0 and f( 4) = 6, then f(-2) is equal to

correct answer:-**2**

Suppose for all integers x, there are two functions f and g such that $$f(x) + f (x - 1) - 1 = 0$$ and $$g(x ) = x^{2}$$. If $$f\left(x^{2} - x \right) = 5$$, then the value of the sum f(g(5)) + g(f(5)) is

correct answer:-**12**

The number of real-valued solutions of the equation $$2^{x}+2^{-x}=2-(x-2)^{2}$$ is:

correct answer:-**4**

Let $$f(x)=x^{2}+ax+b$$ and $$g(x)=f(x+1)-f(x-1)$$. If $$f(x)\geq0$$ for all real x, and $$g(20)=72$$. then the smallest possible value of b is

correct answer:-**2**

For any real number x, let [x] be the largest integer less than or equal to x. If $$\sum_{n=1}^N \left[\frac{1}{5} + \frac{n}{25}\right] = 25$$ then N is

correct answer:-**44**

The area of the quadrilateral bounded by the Y-axis, the line x = 5, and the lines $$\mid x-y\mid-\mid x-5\mid=2$$, is

correct answer:-**45**

In how many ways can a pair of integers (x , a) be chosen such that $$x^{2}-2\mid x\mid+\mid a-2\mid=0$$ ?

correct answer:-**4**

Let S be the set of all points (x, y) in the x-y plane such that $$\mid x \mid + \mid y \mid \leq 2$$ and $$\mid x \mid \geq 1.$$ Then, the area, in square units, of the region represented by S equals

correct answer:-**2**

For any positive integer n, let f(n) = n(n + 1) if n is even, and f(n) = n + 3 if n is odd. If m is a positive integer such that 8f(m + 1) - f(m) = 2, then m equals

correct answer:-**10**

In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by

correct answer:-**2**

The area, in sq. units, enclosed by the lines $$x=2,y=\mid x-2\mid+4$$, the X-axis and the Y-axis is equal to

correct answer:-**1**

Let r be a real number and $$f(x) = \begin{cases}2x -r & ifx \geq r\\ r &ifx; < r\end{cases}$$. Then, the equation $$f(x) = f(f(x))$$ holds for all real values of $$x$$ where

correct answer:-**2**

If $$f(5+x)=f(5-x)$$ for every real x, and $$f(x)=0$$ has four distinct real roots, then the sum of these roots is

correct answer:-**4**

The number of the real roots of the equation $$2 \cos (x(x + 1)) = 2^x + 2^{-x}$$ is

correct answer:-**2**

The area of the region satisfying the inequalities $$\mid x\mid-y\leq1,y\geq0$$ and $$y\leq1$$ is

correct answer:-**3**

If $$f(x+y)=f(x)f(y)$$ and $$f(5)=4$$, then $$f(10)-f(-10)$$ is equal to

correct answer:-**3**

Let $$0 \leq a \leq x \leq 100$$ and $$f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid$$. Then the maximum value of f(x) becomes 100 when a is equal to

correct answer:-**3**

Suppose f(x, y) is a real-valued function such that f(3x + 2y, 2x - 5y) = 19x, for all real numbers x and y. The value of x for which f(x, 2x) = 27, is

correct answer:-**3**

If $$f(x)=x^{2}-7x$$ and $$g(x)=x+3$$, then the minimum value of $$f(g(x))-3x$$ is:

correct answer:-**4**

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