List of top Mathematics Questions asked in CUET (UG)

If \[ \left| \begin{matrix} x+a & y & z \\ x & y+b & z \\ x & y & z+c \end{matrix} \right| = 2abc, \] where \(a,b,c\neq0\), then find the value of \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}. \]
If \[ f(x)=\left(\frac{1+\sin x}{1-\sin x}\right)^{\tan x}, \] then find \[ \lim_{x\to0}\frac{\ln f(x)}{x^2}. \]
Find the equation of the plane which passes through the point \[ (1,-2,3), \] contains the line of intersection of the planes \[ x+y+z=1 \] and \[ 2x-y+3z=4, \] and is perpendicular to the plane \[ x-2y+2z+5=0. \]
Evaluate: \[ \int \dfrac{x^2+1}{x^4+1}\,dx \]
If \[ y = \left(\dfrac{x+1}{x-1}\right)^x, \] then find \(\dfrac{dy}{dx}\).
If \[ \left| \begin{matrix} x+a & y & z \\ x & y+b & z \\ x & y & z+c \end{matrix} \right| = abc, \] where \(a,b,c\neq0\), then find the value of \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}. \]
Let \(A\) be a non-singular \(3\times3\) matrix satisfying \[ A^3-6A^2+11A-6I=O. \] If \[ B=A^2-5A+7I, \] then find \(\det(B)\) given that \(\det(A)=6\).
If \( A \) is a square matrix of order \(3\) and \( |A|=-3 \), then the value of \( |2AA^T| \) is:
If \( A \) is a square matrix of order \(3\) such that \( |2(\operatorname{adj}A)|=288 \), then the value of \( |A| \) is:
If \( B \) is a non-singular \(4\times4\) matrix and \( A \) is its adjoint such that \( |A|=125 \), then \( |B| \) is:
The value of \( \cos\left(\frac{\pi}{6}-\cos^{-1}\left(-\frac{\sqrt3}{2}\right)\right) \) is equal to:
The value of \( \cot^{-1}\left[2\cos\left(2\sin^{-1}\frac{1}{2}\right)\right] \) is:

If \[ R=\{(x,y)\mid x,y\in \mathbb{R},\ x^2+y^2=1\} \] is a relation in \(\mathbb{R}\), then \(R\) is: 

If \[ R=\{(x,y)\mid x,y\in \mathbb{R},\ x^2+y^2=1\} \] is a relation in \(\mathbb{R}\), then \(R\) is: 

Match the following integrals in Column I with their corresponding results in Column II: 


 

Column IColumn II
A. \[ \displaystyle \int \frac{dx}{x^2-a^2} \]I. \[ \displaystyle \frac{1}{2a}\log\left|\frac{a+x}{a-x}\right|+C \]
B. \[ \displaystyle \int \frac{dx}{a^2-x^2} \]II. \[ \displaystyle \log\left|x+\sqrt{x^2-a^2}\right|+C \]
C. \[ \displaystyle \int \frac{dx}{\sqrt{x^2-a^2}} \]III. \[ \displaystyle \frac{1}{2a}\log\left|\frac{x-a}{x+a}\right|+C \]
D. \[ \displaystyle \int \frac{dx}{\sqrt{a^2-x^2}} \]IV. \[ \displaystyle \sin^{-1}\frac{x}{a}+C \]
Line through \((1,2,3)\) parallel to \(\hat{i}+2\hat{j}+3\hat{k}\):
Distance between \(A(1,2,3)\) and \(B(4,6,3)\):
If \(\vec{a}=2\hat{i}+\hat{j}\), \(\vec{b}=\hat{i}+3\hat{j}\), then \(\vec{a}\cdot\vec{b}=\)
For \(y = x^3 - 3x^2 + 2\), slope at \(x=2\):
Evaluate: \[ \int_{0}^{1} \frac{1}{1+x^2}\,dx \]
Evaluate: \[ \int \frac{1}{x^2 + 4x + 5}\,dx \]
Solve: \[ \frac{dy}{dx} + y = e^x, \qquad y(0)=2 \]
Solve: \[ \frac{dy}{dx} = y\tan x \]
Evaluate: \( \int_0^1 (2x+1) dx \)
Differentiate: \( y = x^2\sin x \)