List of top Mathematics Questions on Algebra asked in JEE Main

Let x be the number of 9 digit numbers formed by taking digits from first 9 natural numbers, where only one digit is repeated twice & y be the number of 9 digit numbers formed from first 9 natural numbers, such that exactly 2 digits repeated twice then

If $\vec{a}, \vec{b} \& \vec{c}$ are unit vectors such that $(\vec{a}-\vec{b})^2 + (\vec{b}-\vec{c})^2 + (\vec{c}-\vec{a})^2 = 9$. Find positive k if $|2\vec{a} + k\vec{b} + k\vec{c}| = 3$ :

Find possible no. of triplets (b, c, d), such that $x^2 + 2$ is divisor of $x^3 + bx^2 + cx + d$ & b, c, d $ \le $ 20 & b, c, d $ \in $ N :

In the binomial expansion of \[ (ax^2 + bx + c)(1 - 2x)^{26}, \] the coefficients of $x, x^2, x^3$ are $-56, 0$ and $0$ respectively. Then the value of $ (a + b + c) $ is:

If $ x^2 + x + 1 = 0 $, then evaluate \[ \left(x + \frac{1}{x}\right)^4 + \left(x^2 + \frac{1}{x^2}\right)^4 + \left(x^3 + \frac{1}{x^3}\right)^4 + \cdots + \left(x^{25} + \frac{1}{x^{25}}\right)^4. \]

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 range of the function $ f(x) = \sqrt{3 - x} + \sqrt{5 + x} $ is $[\alpha, \beta]$, then $ \alpha^2 + \beta^2 $ is equal to:

If all the words, with or without meaning, made using all the letters of the word ``RANCHI'' are arranged as in a dictionary, then the word at $560^{\text{th}}$ position is:

The number of integral terms in the binomial expansion of \[ \left(11^{\frac{1}{2}} + 17^{\frac{1}{8}}\right)^{1024} \] is:

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 $ b_1 = 3, b_2, b_3, \ldots $ be a geometric progression of increasing positive numbers. Let \[ \sum_{n=1}^{20} b_{3n} = 4\sum_{n=1}^{20} b_{3n-2}. \] Then, the sum of the first ten terms of the G.P. is:

If the system of linear equations : \[ x+y+z=4,\quad x+2y+3z=6,\quad 4x+5y+\lambda z=\mu \] has more than one solution, then the value of $ \lambda+\mu $ is equal to:

Two persons $A$ and $B$ alternately throw a pair of dice. $A$ wins if he throws a sum of $4$ before $B$ throws a sum of $9$, and $B$ wins if he throws a sum of $9$ before $A$ throws a sum of $4$. The probability that $A$ wins if $B$ makes the first throw is:

Let the value of $p$, such that the sum of the squares of the roots of the quadratic equation \[ x^2+(7-p)x+4=p \] has the least value, be $\alpha$, and the corresponding roots be $\beta$ and $\gamma$. Then $\alpha^3+\beta^3+\gamma^3$ equals \underline{\hspace{2cm}.}

Let $25^x+25^{-x},\ \dfrac{\alpha}{3},\ 20^{1+x}+20^{1-x}$, where $x,\alpha\in\mathbb{R}$, be the first three terms of an A.P. of increasing terms. For the least value of $\alpha$, the sum of its first $10$ terms 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

The sum of the series $ 2 \times 1 \times 20C_4 - 3 \times 2 \times 20C_5 + 4 \times 3 \times 20C_6 - 5 \times 4 \times 20C_7 + ... + 18 \times 17 \times 20C_{20}, \text{is equal to} $

The number of real roots of the equation $ x|x-2| + 3|x-3| + 1 = 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 _____.

$\text{The number of solutions of the equation}$$\left(\frac{9}{x}-\frac{9}{\sqrt{x}}+2\right)\left(\frac{2}{x}-\frac{7}{\sqrt{x}}+3\right)=0\mathrm \; {is:}$

If the equation $ a(b - c)x^2 + b(c - a)x + c(a - b) = 0 $ has equal roots, where $ a + c = 15 $ and $ b = \frac{36}{5} $, then $ a^2 + c^2 $ is equal to .

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: