List of top Questions asked in CUET (UG)

If \(\begin{bmatrix}        x+4 & 2x & 2x           \\[0.3em]        2x & x+4           & 2x\\[0.3em]        2x   & 2x & x+4      \end{bmatrix}=\lambda(4-x)^2\),then value of \(\lambda \) is

The value of det\((A^2-2A)\),If \(A=\begin{pmatrix}      1 & 3  \\[0.3em]    2  &1  \end{pmatrix}\),is

for which value of \(\lambda\) is the function ,\(f(x) = \begin{cases} \lambda(x^2-2x) & \text{if } x \leq 0 \\ 4x+1& \text{if } x > 0 \end{cases}\) continuous at \(x=0 ?\)

The value of \(K\),If \(\begin{bmatrix}    1 & K & 3          \\[0.3em]        3 & K   & -2 \\[0.3em]  2  & 3 & -1      \end{bmatrix}=33\),is :

If \(A=\begin{pmatrix}     1 & -2 & 3  \\[0.3em]   4 & 2 &5 \end{pmatrix}\) and \(A=\begin{pmatrix}     1 & 3   \\[0.3em]   4 & 5  \\[0.3em]   2&1 \end{pmatrix}\)and \(BA=(b_{ij})\),then \(b_{21}+b_{32}=\)

If \(\begin{bmatrix}      1 & 2  \\[0.3em]    3  &4  \end{bmatrix}\)\(\begin{bmatrix}      3& 1  \\[0.3em]    2  &5  \end{bmatrix}\)\(=\begin{bmatrix}      7 & 11  \\[0.3em]    K&23  \end{bmatrix}\),then the value of k is

If \(f(x)=e^x\) and \(g(x)=log_{e}{x}=lnx  \) then \((gof)(x) \) is

The value of \(sin^{-1} [cos(sin^{-1}\frac {\sqrt{3}}{2})]\) is:

\(2\tan^{-1} \frac12+\tan^{-1}\frac 17=\tan^{-1}x\), then the value of \(x\) is:

The region R on the set \(A=\{x \in Z:0\leq x\leq 12\}\) , given by \(R=\{(a,b):|a-b|\)  is a multiple of 4 \(\}\)  is :

The area of the region bounded by the curve \( 2y=3x-6\), y-axis and the line y=2 and y = −3 is :

The feasible region of an LPP is shown in the figure below.
If \( z=3x+9y\), then the minimum value of \(z\) occurs at :

The integrating factor of differential equation \(\frac{dy}{dx}+y=\frac{1+y}{x}\) is:

The value of objective function is maximum under linear constraints is

The sum of the order and degree of differential equation \(2x^3\left(\frac{d^2y}{dx^2}\right)^4 + \frac{d^3y}{dx^3}+y=0\) is :

A pair of dice is thrown 3 times. If getting a doublet is considered a success, then the probability of two successes is :

Match List - I with List - II.

List - I	List -II
(A) \(P(\overline{A} \cap B)\)	(I)\(P(A)+P(B)\)
(B)\(P(A\cap \overline B)\)	(II)\(P(A)+P(B)-2P(A\cap B)\)
(C) \(P[(A\cap \overline B) \cup (\overline A \cap B)]\)	(III)\(P(B)-P(A\cap B)\)
(D)\(P(A\cup B)+ P(A\cap B)]\)	(IV)\(P(B)-P(A\cap B)\)

Choose the correct answer from the options given below:

If \(|A|=3\)  and \(A^{-1}=\begin{bmatrix}        3 &-1 \\[0.3em]        \frac{-5}{3} & \frac{2}{3}    \\[0.3em]     \end{bmatrix}\) then adj \(A\) is 

If \(A\)=\( \begin{vmatrix}  3  & 1  \\[0.1em]   -1 & 2  \end{vmatrix}\) then \(A^2-5A=\)

The value of \(\int_1^4|x-1|dx \)  is :

Equation of normal to curve \(y=x+\frac12sin2x\) at \(x=-\frac{\Pi}{2}\) is:

A particle is moving along the curve \(y=\frac34x^4+3\). The point on the curve at which y-coordinate is changing thrice as fast as the x coordinate, is :

\(\begin{vmatrix} 2x  & 3  \\[0.1em]   5x & x  \end{vmatrix}\)=\(\begin{vmatrix}  16  & 3  \\[0.1em]   5 & 2  \end{vmatrix}\) the value of \(x\) is

The Matrix \(M = \begin{bmatrix}        0 & 1 & -1           \\[0.3em]        -1  & 0           &1 \\[0.3em]       1          & -1 & 0     \end{bmatrix}\)is
(A) Symmetric matrix 
(B) Square matrix 
(C) Diagonal matrix
(D) Skew-symmetric matrix
(E) Scalar matrix
Choose the correct answer from the options given below: