List of top Mathematics Questions on Algebra asked in JEE Main

Let \( S = \{\theta \in (-2\pi, 2\pi): \cos \theta + 1 = \sqrt{3} \sin \theta\} \). Then \( \sum_{\theta \in S} \theta \) is equal to:

If \(\alpha\) and \(\beta\) are the roots of the equation \(z^2 - \sqrt{6}i z - 3 = 0\), then find \(\alpha^8 + \beta^8\).

The line \(x - y = 4\) is a chord of the circle \((x - 4)^2 + (y + 3)^2 = 9\), which cuts the circle at points Q & R. If \(P(\alpha, \beta)\) lies on the circle such that \(PQ = PR\), then find \((6\alpha + 8\beta)^2\).

Let \(x = 9\) be a directrix of an ellipse centred at \((0, 0)\) and having eccentricity \(\frac{1}{3}\). If focus at \((\alpha, 0)\) (\(\alpha<0\)), then locus of the mid-point of the chord passing through the focus \((\alpha, 0)\) is

An ellipse has directrix \(x = 9\) & eccentricity \(= \frac{1}{3}\). If one of its focus is \((\alpha,0)\), \(\alpha<0\), then locus of the mid-point of the chord passing through \(P(\alpha,0)\) is

A 3rd order square matrix M satisfies \( M \begin{pmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 2 & 1 \end{pmatrix} = \begin{pmatrix} 0 & 0 & 0 \\ 1 & 1 & 0 \\ 0 & 2 & 1 \end{pmatrix} \) and \( M \begin{pmatrix} 0 & -1 \\ 1 & 2 \\ 2 & 1 \end{pmatrix} = \begin{pmatrix} 1 & 1 \\ 2 & 1 \end{pmatrix} \). If \( M \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \\ 7 \end{pmatrix} \), then \( x + y + z \) is:

Let \( f(n) = \begin{vmatrix} n & -1 & -5 \\ -2n^2 & 3(2k+1) & 2k+1 \\ -3n^3 & 3k(2k+1) & 3k(k+2)+1 \end{vmatrix} \). If \( \sum_{n=1}^{k} f(n) = 98 \), then find \( k \).

If the sum of the first 10 terms of the series \( \frac{1}{1 + 4 \cdot 1^4} + \frac{2}{1 + 4 \cdot 2^4} + \frac{3}{1 + 4 \cdot 3^4} + \dots \) is \( \frac{m}{n} \) (where m, n are coprime), then (m + n) is:

If \( \alpha, \beta \) are the roots of the equation \( x^2 - 4x + p = 0 \) and \( \gamma, \delta \) are the roots of the equation \( x^2 - x + q = 0 \). When \( \alpha, \beta, \gamma, \delta \) form a G.P. with positive common ratio, then the value of \( (p + q) \) equals:

Let \( A_1, A_2, A_3, \dots, A_9 \) be 9 AM’s between 49 and 149. Then the mean of \( A_1, A_2, A_3 \) and \( A_9 \) is:

A bag contains 5 red balls, 6 blue balls and 4 black balls (balls of same colour are considered to be distinct). The number of ways in which 8 balls can be selected if at least two balls of each colour is there, is:

Sum of \( 1 + \dfrac{1}{2}(1^2 + 2^2) + \dfrac{1}{3}(1^2 + 2^2 + 3^2) + \dots \) up to 10 terms is

The sum of all possible values of \( \theta \in [0, 2\pi] \), for which the system of equations:
\( x \cos 3\theta - 8y - 12z = 0 \)
\( x \cos 2\theta + 3y + 3z = 0 \)
\( x \sin \theta + y + 3z = 0 \)
has a non-trivial solution, is equal to:

In the expansion of \( \left( \frac{1}{x^3} - x^4 \right)^n \), if the sum of the coefficients of \( x^7 \) and \( x^{14} \) is zero, then find \( n \):

Let \( S_n \) be the sum of the first \( n \) terms of an A.P. If \( S_n = 3n^2 + 5n \), then the sum of the squares of the first 10 terms of the given A.P. is:

The value of the sum of r / (4 + r⁴) for r = 1 to 10 is:

The coefficient of x² in the binomial expansion of (2x² + 1/x)¹⁰ is:

Let A1, A2, A3, ..., A49 be 49 arithmetic means between 49 and 149. Then the mean of A1, A25, A47 and A49 is:

Let \( A = \{2, 3\ \) and \( B = \{5, 6\} \). Then, the number of relations from \( A \times B \) to \( A \times B \) are:

Let the direction cosines of two lines satisfy the equations : \( 4l + m - n = 0 \) and \( 2mn + 5nl + 3lm = 0 \). Then the cosine of the acute angle between these lines is :

Find the value of \[ \frac{6}{3^{26}} + 10\cdot\frac{1}{3^{25}} + 10\cdot\frac{2}{3^{24}} + \cdots + 10\cdot\frac{2^{24}}{3^{1}} : \]

Given \(\frac{1}{\alpha} - \frac{1}{\beta} = \frac{1}{3}\) such that roots of the quadratic equation \(\lambda x^2 + (\lambda+1)x + 3 = 0\) are \(\alpha\) & \(\beta\), then sum of values of \(\lambda\) is equal to :

Consider the 10 observations 2, 3, 5, 10, 11, 13, 15, 21, a and b such that mean of observation is a and variance is 34.2. Then the mean deviation about median, is :