List of top Mathematics Questions asked in CUET (UG)

For the function \[ f(x)=ax+\frac{b}{x}, \qquad a>0,\; b>0, \] which of the following statements are correct?  

(A) Function \(f(x)\) is increasing on \[ \left(\sqrt{\frac{b}{a}},\,\infty\right) \] 

(B) Function \(f(x)\) is increasing on \[ (-\infty,\infty) \] 

(C) Function \(f(x)\) is decreasing on \[ \left(-\sqrt{\frac{b}{a}},\,\sqrt{\frac{b}{a}}\right) \] 

(D) Function \(f(x)\) is increasing on \[ \left(-\infty,\,-\sqrt{\frac{b}{a}}\right) \]

 The solution of the differential equation \[ (x-1)\frac{dx}{dy}+(y-2)=0, \] given that \(x=1\) when \(y=1\), represents a: 

A function \[ f(x)=12x^{4/3}-6x^{1/3}, \qquad x\in[-1,1] \] is given. Then, which of the following are TRUE?  

(A) \(f(x)\) has a critical point at \(x=\dfrac{1}{8}\) 
(B) Absolute maximum value of \(f(x)\) is \(18\) 
(C) Absolute maximum value of \(f(x)\) is \(6\) 
(D) Absolute minimum value of \(f(x)\) is \(-\dfrac{9}{4}\)

Water is leaking from the bottom of a conical funnel at the rate of \(0.15\pi\) cm³/s. If the radius of the base is 10 cm and the height is 20 cm, then the rate at which the water level is dropping when it is 5 cm from the top is: 

M is a square matrix of order 3. If \[ M(\operatorname{adj} M)= \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}, \] then the value of \[ |M+\operatorname{adj} M| \] is equal to: 

The order of the differential equation \[ \left(\frac{d^5y}{dx^5}\right)^2 + \frac{dy}{dx} + y^2 = 0 \] is: 

If \[ f(x)= \begin{cases} \dfrac{x-2}{|x-2|}+a, & x<2, \\[6pt] a+b, & x=2, \\[6pt] \dfrac{x-2}{|x-2|}+b, & x>2, \end{cases} \] is continuous at \(x=2\), then 

If \( P(A) = \frac{3}{5} \), \( P(\overline{B}) = \frac{4}{7} \), and \( P(A \cup B) = \frac{2}{3} \), which of the following are correct?  

(A) \( P(A \cap B) = \frac{17}{105} \) 
(B) \( P(A \mid B) = \frac{17}{45} \) 
(C) A and B are independent events 
(D) \( P(B \mid A) = \frac{17}{36} \)