List of top Quantitative Ability and Data Interpretation Questions on Algebra

If \( a_1, a_2, \dots, a_8 \) are the roots of the equation \( x^8 + x^7 + \dots + x + 1 = 0 \), then the value of \( a_1^{2025} + a_2^{2025} + \dots + a_8^{2025} \) is
Which of the following numbers is divisible by \( 3^{10} + 2 \)?
Let \( f(x) = a^2x^2 + 2bx + c \) where, a \( \neq \) 0, b, c are real numbers and x is a real variable then
Let P(x) be a quadratic polynomial such that \( \begin{vmatrix} P(0) & P(1) \\ P(0) & P(2) \end{vmatrix} = 0 \). Let P(0) = 2 and P(1) + P(2) + P(3) = 14. Then P(4) equals
If \( 8x^2 - 2kx + k = 0 \) is a quadratic equation in x, such that one of its roots is p times the other, and p, k are positive real numbers, then k equals
If the sum of the first 21 terms of the sequence \( \ln \frac{a}{b}, \ln \frac{a^2}{b^3}, \ln \frac{a^3}{b^5}, \dots \) is \( \ln \frac{a^m}{b^n} \), then the value of \( m + n \) is ________
If \( \log_3(x^2 - 1) \), \( \log_3(2x^2 + 1) \) and \( \log_3(6x^2 + 3) \) are the first three terms of an arithmetic progression, then the sum of the next three terms of the progression is ________
English exam and Math exam were conducted separately for a class of 120 students. The number of students who did not appear for the English exam is twice the number of students who did not appear for the Math exam. The number of students who passed the Math exam is twice the number of students who appeared but failed the English exam. If the number of students who passed the English exam is twice the number of students who appeared but failed the Math exam, then the number of students who appeared but failed the English exam is ________
If \( A = \begin{bmatrix} 2 & n \\ 1 & 4 \end{bmatrix} \) such that \( A^3 = 27 \begin{bmatrix} 4 & q \\ p & r \end{bmatrix} \), then \( p + q + r \) equals ________
If the polynomial \( ax^2 + bx + 5 \) leaves a remainder 3 when divided by \( x - 1 \), and a remainder 2 when divided by \( x + 1 \), then \( 2b - 4a \) equals ________