List of top Mathematics Questions asked in LPUNEST

If \[ \Delta= \begin{vmatrix} f(x) & f\!\left(\dfrac{1}{x}\right)+f(x)\\ 1 & f\!\left(\dfrac{1}{x}\right) \end{vmatrix} =0 \] where \(f(x)\) is a polynomial and \(f(2)=17\), then \(f(5)=\) ?
If \[ \sum_{r=1}^{n} a_r = \frac{n(n+1)(n+2)}{6}\quad \forall\, n \ge 1, \] then \[ \lim_{n\to\infty}\sum_{r=1}^{n}\frac{1}{a_r} = \]
Value of \[ \sum_{k=1}^{\infty}\sum_{r=0}^{k}\frac{1}{3^{k}}\binom{k}{r} \] is:
If \(x,y,z\) are in A.P. with common difference \(d\) and the rank of the matrix \[ \begin{pmatrix} 4 & 5 & x \\ 5 & 6 & y\\ 6 & k & z \end{pmatrix} \] is \(2\), then the values of \(k,d\) are:
If 8 G.M.’s inserted between 2 and 3 then product of all 8 G.M.’s is
\(f:\mathbb{R}-\{0\}\rightarrow\mathbb{R}\) given by \[ f(x)=\frac{1}{x}-\frac{2}{e^{2x}-1} \] can be made continuous at \(x=0\) by defining \(f(0)\) as:
If \(z\) represents point on circle \(|z|=2\) then locus of \(z+\frac1z\) is
The quadratic equation \(8\sec^2x-6\sec x+1=0\) has
The minimum number of elements that must be added to the relation \(R=\{(1,2),(2,3)\}\) on the set \(\{1,2,3\}\) so that it becomes an equivalence relation is
If \(X = \{\,8^n - 7n - 1 \mid n \in \mathbb{N}\,\}\) and \(Y = \{\,49(n-1) \mid n \in \mathbb{N}\,\}\), then
If \[ \left| \begin{array}{ccc} x^{n} & x^{n+2} & x^{n+3} \\ y^{n} & y^{n+2} & y^{n+3} \\ z^{n} & z^{n+2} & z^{n+3} \end{array} \right| =(x-y)(y-z)(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \] then \(n\) is equal to:
Let \(R=\{(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6)\}\) be a relation on the set \(A=\{3,6,9,12\}\). The relation is
Let \(S=\{x\in \mathbb{R}\mid x\ge 0 \text{ and } 2|\sqrt{x}-3|+\sqrt{x}(\sqrt{x}-6)+6=0\}\), then \(S=\)
If \(A=(a_{ij})_{4\times 4}\) such that \[ a_{ij}= \begin{cases} 2 & \text{if } i=j\\ 0 & \text{if } i\neq j \end{cases} \] then \[ \left\{\dfrac{\det(\operatorname{adj}(\operatorname{adj}A))}{7}\right\} \] is (where \(\{\ \}\) represents fractional part function)
If \(x\neq 0,\; y\neq 0,\; z\neq 0\) and \[ \left| \begin{array}{ccc} 1+x & 1 & 1 \\ 1+y & 1+2y & 1 \\ 1+z & 1+z & 1+3z \end{array} \right|=0, \] then \(x^{-1}+y^{-1}+z^{-1}=\)
If \(A=\{(x,y)\mid x^2+y^2\le 4;\; x,y\in \mathbb{R}\}\) and \(B=\{(x,y)\mid x^2+y^2\ge 9;\; x,y\in \mathbb{R}\}\), then
For the following question, enter the correct numerical value up to TWO decimal places. (If the numerical value has more than two decimal places, round-off the value to TWO decimal places.) After inserting \(n\) A.M.’s between \(2\) and \(38\), the sum of the resulting progression is \(200\). The value of \(n\) is _____
\( z \) be a complex number satisfying \( |z-5i|\le 1 \) such that \( \arg z \) is minimum, then \( z = \)
For the following question, enter the correct numerical value up to TWO decimal places. (If the numerical value has more than two decimal places, round-off the value to TWO decimal places.) If 7 times of the 7th term of an A.P. is equal to 11 times of its 11th term, then the 18th term of the A.P. is ____.
If \( p,q,r \) are positive and are in A.P., the roots of the equation \( px^2+qx+r=0 \) are all real for
For the following question, enter the correct numerical value up to TWO decimal places. (If the numerical value has more than two decimal places, round-off the value to TWO decimal places.) If \(\alpha,\beta,\gamma\) and \(a,b,c\) are complex numbers such that \[ \frac{\alpha}{a}+\frac{\beta}{b}+\frac{\gamma}{c}=1+i \quad \text{and} \quad \frac{a}{\alpha}+\frac{b}{\beta}+\frac{c}{\gamma}=0, \] then the value of \[ \frac{\alpha^2}{a^2}+\frac{\beta^2}{b^2}+\frac{\gamma^2}{c^2}=____.\, i \]
For the following question, enter the correct numerical value up to TWO decimal places. (If the numerical value has more than two decimal places, round-off the value to TWO decimal places.) If \(\alpha,\beta \in \mathbb{C}\) are the distinct roots of the equation \(x^2-x+1=0\), then the value of \(\alpha^{101}+\beta^{107}\) is ____

For the following question, enter the correct numerical value up to TWO decimal places. (If the numerical value has more than two decimal places, round-off the value to TWO decimal places.) If \[ A=\begin{pmatrix}2&1\\[2pt]1&1\end{pmatrix},\; B=\begin{pmatrix}3&4\\[2pt]1&3\end{pmatrix},\; C=\begin{pmatrix}3&-4\\[2pt]-2&3\end{pmatrix}, \] then the value of \[ \operatorname{tr}(A)+\operatorname{tr}\!\left(\frac{ABC}{2}\right) +\operatorname{tr}\!\left(\frac{A(BC)^2}{4}\right) +\operatorname{tr}\!\left(\frac{A(BC)^3}{8}\right)+\cdots = \_\_\_\_ \]

Let \(a_1,a_2,a_3,\ldots\) be the terms of an A.P. If \[ \frac{a_1+a_2+\cdots+a_p}{a_1+a_2+\cdots+a_q}=\frac{p^2}{q^2}\quad (p\neq q), \] then \(\dfrac{a_6}{a_{21}}=\)
If \[ y=\frac{1}{2}\sin^{-1}\!\left(\frac{2xy}{x^2+y^2}\right) \] and \(y<x\), then \[ \lim_{y\to 0} x = \]