List of top Mathematics Questions asked in LPUNEST

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 \(\dfrac{a_6}{a_{21}}=\)
For \(x,y\in \mathbb{R}\), define a relation \(R\) by \(xRy\) if and only if \(x-y+\sqrt{2}\) is an irrational number. Then \(R\) is
If \[ \left|\frac{z_1-7z_2}{\,7-z_1\overline{z_2}\,}\right|=1 \quad \text{and} \quad |z_2|\neq 1, \text{ then } |z_1|\neq \]
\(f:\mathbb{R}\rightarrow\mathbb{R}\) is a function defined by \[ f(x)=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}} \] Then \(f\) is
A set \(A\) has 3 elements and another set \(B\) has 6 elements. Then
If the first term of an A.P. is \(2\) and the sum of first five terms is equal to one fourth of the sum of the next five terms, then the sum of the first \(30\) terms is
Consider the non-empty set consisting of children in a house. Consider a relation \(R\): \(xRy\) if \(x\) is brother of \(y\). The relation \(R\) is:
The graph of the function \(y=f(x)\) is symmetrical about the line \(x=2\), then
If \(A=\{x \mid x^2-5x+6=0\}\), \(B=\{2,4\}\), \(C=\{4,5\}\), then \(A \times (B \cap C)=\)
The vectors \(\overrightarrow{AB}=-3\hat{i}+4\hat{k}\) and \(\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\) are the sides of a triangle \(ABC\). The length of the median through \(A\) is
The contrapositive of the statement “if \(2^2 = 5\), then I got first class” is
If \(z_1, z_2, z_3\) are three distinct complex numbers and \(a,b,c\) are three positive real numbers such that \[ \frac{a}{|z_2-z_3|}=\frac{b}{|z_3-z_1|}=\frac{c}{|z_1-z_2|} \] then \[ \frac{a^2}{z_2-z_3}+\frac{b^2}{z_3-z_1}+\frac{c^2}{z_1-z_2}= \]
If the relation \(R: A \rightarrow B\) where \(A=\{1,2,3,4\}\), \(B=\{1,3,5\}\) is defined by \(R=\{(x,y): x<y,\; x\in A,\; y\in B\}\), then \(R\circ R^{-1}=\)
If \(2f(x)-3f\!\left(\dfrac{1}{x}\right)=x^2,\; x\neq 0\), then \(f(2)=\)