List of top Mathematics Questions asked in LPUNEST

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) An envelope is known to have come from either `LONDON` OR `CLIFTON`. On the postal card only two successive letters `ON` are visible. The probability that the envelope comes from LONDON is \( \dfrac{12}{__} \).
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 ____.
Two vertices of a triangle are $(5,-1)$ and $(-2,3)$. If the origin is the orthocentre of this triangle, then the coordinates of the third vertex of that triangle are
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 ______.
If $y=y(x)$ is the solution of the differential equation \[ x\frac{dy}{dx}+2y=x^2 \] satisfying $y(1)=1$, then $y\!\left(\dfrac{1}{2}\right)$ is equal to:
Let $f$ be a polynomial function such that $f'(x)=f(x)\,f''(x)$ for all $x\in\mathbb{R}$. Then:
The minimum distance of a point on the curve $y=x^2-4$ from the origin is
Evaluate: \[ \int \frac{dx}{\cos x+\sqrt{3}\sin x} \]
If \[ \int \frac{1}{(x+100)\sqrt{x+99}}\,dx = f(x)+c \] then $f(x)=$
Evaluate: \[ \int_{0}^{\pi} \frac{x\sin x}{1+\cos^2 x}\,dx \]
$1^3 - 2^3 + 3^3 - 4^3 + \cdots + 9^3 =$
A square matrix (non-singular) satisfies $A^2 - A + 2I = 0$. Then $A^{-1}=$
Consider the following statements \[ P:\ \text{Suman is brilliant} \] \[ Q:\ \text{Suman is rich} \] \[ R:\ \text{Suman is honest} \] The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as:
10 men and 6 women are to be seated in a row so that no two women sit together. The number of ways they can be seated is
If $R$ is an equivalence relation on a set $A$, then $R \circ R$ is
Evaluate the limit: \[ \lim_{x \to \infty} \left(\frac{x^2 + 5x + 3}{x^2 + x + 2}\right)^x \]
Universal set, \[ U = \{x \mid x^5 - 6x^4 + 11x^3 - 6x^2 = 0\} \] \[ A = \{x \mid x^2 - 5x + 6 = 0\} \] \[ B = \{x \mid x^2 - 3x + 2 = 0\} \] What is $(A \cap B)$ equal to?
If one root of the quadratic equation $ax^2+bx+c=0$ is $3-4i$, then $31a+b+c=$
If \[ A(\alpha)= \begin{pmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{pmatrix} \] then $A(\alpha)\,A(\beta)=$