Question:
Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:
Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:
Updated On: Aug 9, 2024
- 23
- 26
- 24
- 48
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct option is (C): 24.
Was this answer helpful?
0
0
Top Questions on Algebra
- The sum of the squares of the roots of $ |x - 2|^2 + |x - 2| - 2 = 0 $ and the squares of the roots of $ x^2 |x - 3| - 5 = 0 $, is:
Let $\alpha$ be a solution of $x^2 + x + 1 = 0$, and for some $a$ and $b$ in $\mathbb{R}$, $ \begin{bmatrix} 1 & 16 & 13 \\-1 & -1 & 2 \\-2 & -14 & -8 \end{bmatrix} \begin{bmatrix} 4 \\a \\b \end{bmatrix} = \begin{bmatrix} 0 \\0 \\0 \end{bmatrix}. $ If $\frac{4}{\alpha^4} + \frac{m} {\alpha^a} + \frac{n}{\alpha^b} = 3$, then $m + n$ is equal to _____.
- The number of solutions of the equation \[ 9\sqrt{x} - 9\sqrt{x} + 2 = 2x - 7\sqrt{x} + 3 = 0 \] is:
- Let \( f : \mathbb{R} \setminus \{0\} \to (-\infty, 1) \) be a polynomial of degree 2, satisfying \( f(x)f\left( \frac{1}{x} \right) = f(x) + f\left( \frac{1}{x} \right) \). If \( f(K) = -2K \), then the sum of squares of all possible values of \( K \) is:
If the set of all values of \( a \), for which the equation \( 5x^3 - 15x - a = 0 \) has three distinct real roots, is the interval \( (\alpha, \beta) \), then \( \beta - 2\alpha \) is equal to
View More Questions
Questions Asked in XAT exam
- Arya, a graduate from a reputable institute, got a job in an IT company but became bored after a year. Her best friend S, who worked at the same company, joined a top-tier B-school for an MBA, which tempted Arya to pursue the same path. Her friend assured her that an MBA would boost her career prospects and salary. Arya started preparing for an MBA while continuing her job, but the challenge of balancing preparation with work made her consider leaving the job.
- XAT - 2025
- Analytical Decision Making
- There’s a community 30 km outside of the main city. Mr. S started a grocery business in the community after winning the bid by offering way above the rent initially drafted by the community council. The community council, led by Mr. D, agreed to the offer with a performance review every three years. Mr. S also agreed to provide an additional 15% of his grocery sales to the council, banking on the prospect of selling in higher volumes. After setting up his business, Mr. S noticed that SUV owners in the community usually bought goods in bulk from the city once a week and used his store primarily for daily necessities and occasional big purchases like mixer grinders.
- XAT - 2025
- Analytical Decision Making
- Four reviewers (R1, R2, R3, R4) are in charge of reviewing products from companies A, B, C, and D. Each reviewer provides a rating between 1 and 5 for the products. Due to a technical glitch, the original ratings were deleted, and only the averages calculated for each product (A, B, C, D) and each reviewer (R1, R2, R3, R4) were saved. The data available is as follows:Tasks:
A B C D Average 3 4 4 ? 4 3 ? 5 ? 4 ? 3 3 ? 4 ? ? ? ? 4.25 4 4 4 4.25
1. What are the missing values in the table?
2. How were the missing values calculated?
3.Verify the correctness of the given averages for both rows and columns. - In an office with 8 employees, the average rating of all employees is 30. The average rating of the top five employees is 38, and the average rating of the bottom three employees is 25. Which of the following is not possible?
- XAT - 2025
- Average
- An iron beam made with rare materials has its market price dependent on the square of its length. The beam broke into two pieces in the ratio of 4 : 9. If it is sold as two separate pieces, what would be the percentage profit or loss compared to its original value?
- XAT - 2025
- Profit and Loss
View More Questions