List of top Questions asked in CUET (PG)- 2026

Let E, F and G be events such that $P(E|G) = 0.05$ and $P(F|G) = 0.05$ which of the following statement must be true?

If $P(E) = \frac{1}{3}$, $P(F) = \frac{2}{5}$ and $P(E \cup F) - P(E \cap F) = \frac{1}{5}$ then $P(E \cup F)$ is equal to

Which of the following statements are correct?
A. Ogive curves are used to obtain median

B. Histogram are used to obtain mode

C. Boxplots are used to determine mean

D. Pie charts are used to determine quantile

Choose the correct answer from the options given below

If A and B are two non-mutually exclusive events such that $P(A|B)=P(B|A)$ then

Which of the following differential equation is satisfied by $y_{1}(x)=e^{x}$, $y_{2}(x)=x~e^{x}$ and $y_{3}=e^{2x}?$

Let E and F be two events, if $P(E|F)=0.5$, $P(E|\overline{F})=0.6$ and $P(F)=0.6$ then $P(E)$ equals

The integrating factor for the differential equation $x~log_{e}x~dy = (2~log_{e}x - y) dx$ is

If $P(E)=\frac{1}{3}$, $P(F)=\frac{1}{5}$ and $P(E\cup F)=\frac{1}{2}$ then $P(E|\overline{F})+P(F|\overline{E})$ is equal to

Let $AX=B$ be a system of n-linear equations in n unknowns then

Solution of differential equation $(x^{2}+y^{2})dx-2xy~dy=0,$ where c is constant, is

If A and B are symmetric matrices of same order then
A. AB is symmetric iff $AB=BA$

B. $AB+BA$ is skew symmetric matrix

C. AB-BA is symmetric matrix

D. $(A+B)^{n}$ is symmetric for all $n \in N$

Choose the correct answer from the options given below

Let $A=\begin{bmatrix}2& 1& -2\\ 1& 1& -1\\ 1& 0& 2\end{bmatrix}$ and if $B=|A|adj(A)$ Then $|B|$ is equal to

If A is an invertible symmetric matrix then
A. $(A^{-1})^{T}=A^{-1}$

B. adj $A=(adj~A)^{T}$

C. $A^{-1}$ is skew-symmetric

D. $|A|=0$

Choose the correct answer from the options given below

The eigen vectors of the matrix $A=\begin{bmatrix}5 & 4\\ 1& 2\end{bmatrix}$ is

The value of $\lim_{x\rightarrow1}\frac{\int_{2 \log_{e}x}^{3\log_{e} x} e^{t} \, dt}{x-1}$ equals

The value of integral $\int_{0}^{1}\int_{x}^{1}\frac{1}{1+y^{2}}\cdot dydx$ is equal to

If $f(x)=\begin{cases}\frac{\log_{e}(1+\frac{x}{a})-\log_{e}(1-\frac{x}{b})}{x}& if~x\ne0\\k& if~x=0\end{cases}$ is continuous at $x=0$, then value of $k$ is:

The area of region in the first quadrant that is bounded by $y=\sqrt{x}$, $y=2-x$ and x-axis is

Integral $\int_{0}^{2}\int_{y^{2}}^{y+2} dxdy$ equals

In the Taylor series expansion of function $f(x)=e^{x^{2}-x}$, coefficient of $x^{3}$ is

Match List I with List - II. List - I & List - II
A. $x$ where $f(x)=9x(x-1)^{2}$ attains maximum & I. $e$

B. $x$ where $f(x)=\frac{1}{x}e^{-\frac{1}{2}(\log_{e}x-2)^{2}}$ attains maximum & II. $\frac{2}{3}$

C. $x$ where $f(x)=x^{2}(1-x)^{6}$ attains maximum & III. $\frac{1}{3}$

D. $x$ where $f(x)=x^{2}e^{-3x}$ attains maximum & IV. $\frac{1}{4}$

The function $f(x)=\int_{e^{x}}^{e^{2x}} t \log_{e}t \, dt$ has an absolute minima at $x=0$ and a local maxima at $x=$

The function $f(x)=|x^{2}+x-6|$ is not differentiable at $x=a$ and $x=b$ then $(b-a)^{2}$ equals

If $f(1)=1$ and $f^{\prime}(1)=-1$, then the value of $\frac{d}{dx}[\frac{f(x^{3})}{x~f(x^{2})}]$ at $x=1$ is equal to

The Sum $\sum_{r=1}^{20}(r^{2}+1)\times r!$ is equal to