List of top Mathematics Questions asked in LPUNEST

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 ____
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
If \[ y=\frac{1}{2}\sin^{-1}\!\left(\frac{2xy}{x^2+y^2}\right) \] and \(y<x\), then \[ \lim_{y\to 0} x = \]
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 \(\alpha\) be a root of the equation \(4x^2+2x-1=0\), then the other root is
If \[ \left|\frac{z_1-7z_2}{\,7-z_1\overline{z_2}\,}\right|=1 \quad \text{and} \quad |z_2|\neq 1, \text{ then } |z_1|\neq \]
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 \(\dfrac{a_6}{a_{21}}=\)
\(f:\mathbb{R}\rightarrow\mathbb{R}\) is a function defined by \[ f(x)=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}} \] Then \(f\) is
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:
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
The graph of the function \(y=f(x)\) is symmetrical about the line \(x=2\), then
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
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 \[ \frac{a^2}{z_2-z_3}+\frac{b^2}{z_3-z_1}+\frac{c^2}{z_1-z_2}= \]
The contrapositive of the statement “if \(2^2 = 5\), then I got first class” is
If \(A=\{x \mid x^2-5x+6=0\}\), \(B=\{2,4\}\), \(C=\{4,5\}\), then \(A \times (B \cap C)=\)
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 \(f(2)=\)
If the 2$^{\text{nd}}$, 5$^{\text{th}}$ and 9$^{\text{th}}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is
The ratio in which $\hat{i}+2\hat{j}+3\hat{k}$ divides the join of $-2\hat{i}+3\hat{j}+5\hat{k}$ and $7\hat{i}-\hat{k}$ is
The ratio of the coefficient of $x^{15}$ to the term independent of $x$ in the expansion of $\left(x^2+\dfrac{2}{x}\right)^{15}$ is
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) The eccentricity of the ellipse \[ \frac{x^2}{25} + \frac{y^2}{16} = 1 \] is \( \dfrac{3}{__} \).
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) There are 10 points in a plane out of which 6 are collinear. The number of straight lines formed by joining all these points is ____.
For the following question, enter the correct numerical value upto TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numeric value 5 will be written as 5.00 and 2.346 will be written as 2.35) If \( z \), \( iz \) and \( z+iz \) are the vertices of a triangle and if \( |z| = 4 \), then the area (in sq. units) of that triangle is ______.