List of top Questions asked in LPUNEST

Rank the following animal groups from greater to least (left to right) in the number of described species: Mammalia (mammals), Aves (birds), Mollusca (clams, snails, etc.), and Insecta
Epithelium that appears layered due to the varying levels at which nuclei are found in cells, but in reality is not layered, is
Cell theory states I. All living cells must have a cell wall.
II. All living cells require glucose for survival.
III. The basic unit of life is a cell.
Lipids are water insoluble because lipid molecules are
Due to low atmospheric pressure, the rate of transpiration will be
A trace element essential for plant growth and radioactive isotope which is used in cancer therapy is known as
Quantasomes contain
\( z \) be a complex number satisfying \( |z-5i|\le 1 \) such that \( \arg z \) is minimum, then \( z = \)
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.) After inserting \(n\) A.M.’s between \(2\) and \(38\), the sum of the resulting progression is \(200\). The value of \(n\) 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 \(\alpha,\beta,\gamma\) 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 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 ____.

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 \[ \operatorname{tr}(A)+\operatorname{tr}\!\left(\frac{ABC}{2}\right) +\operatorname{tr}\!\left(\frac{A(BC)^2}{4}\right) +\operatorname{tr}\!\left(\frac{A(BC)^3}{8}\right)+\cdots = \_\_\_\_ \]

Quality of storing food using simple inorganic material belongs to plants which are
If \[ \left|\frac{z_1-7z_2}{\,7-z_1\overline{z_2}\,}\right|=1 \quad \text{and} \quad |z_2|\neq 1, \text{ then } |z_1|\neq \]
If \(\alpha\) be a root of the equation \(4x^2+2x-1=0\), then the other root is
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 \[ y=\frac{1}{2}\sin^{-1}\!\left(\frac{2xy}{x^2+y^2}\right) \] and \(y<x\), then \[ \lim_{y\to 0} x = \]
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
A set \(A\) has 3 elements and another set \(B\) has 6 elements. Then
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:
\(f:\mathbb{R}\rightarrow\mathbb{R}\) is a function defined by \[ f(x)=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}} \] Then \(f\) is
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