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

Choose the synonym of the word: APLOMB ____.

Choose the synonym of the word: CONCISE ____.

Solve: \[ \begin{vmatrix} x & 1\\ 2 & x \end{vmatrix}=0 \]

If \[ A= \begin{bmatrix} 2 & 3\\ 1 & 4 \end{bmatrix} \] then \(A^{-1}=\)

The total area of a parallelogram constructed with adjacent vector sides given by \( \vec{a} = \hat{i} - \hat{j} + 3\hat{k} \) and \( \vec{b} = 2\hat{i} - 7\hat{j} + \hat{k} \) is equal to:

If the three vectors \( \vec{a} = \hat{i} + \lambda\hat{j} + \hat{k} \), \( \vec{b} = \hat{j} + \hat{k} \), and \( \vec{c} = \hat{i} + \hat{j} \) are coplanar, find the exact value of the scalar constant \( \lambda \).

Find the shortest distance between the two skew lines whose vector equations are given by: \[ \vec{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \lambda(\hat{i} - 3hat{j} + 2\hat{k}) \] \[ \vec{r} = (4\hat{i} + 5\hat{j} + 6\hat{k}) + \mu(2\hat{i} + 3\hat{j} + \hat{k}) \]

Find the shortest distance between the two parallel lines given by the vector equations: \( \vec{r} = (\hat{i} + 2\hat{j} - 4\hat{k}) + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k}) \) and \( \vec{r} = (3\hat{i} + 3\hat{j} - 5\hat{k}) + \mu(2\hat{i} + 3\hat{j} + 6\hat{k}) \)

The value of the determinant \( \left| \begin{matrix} x+a & y & z \\ x & y+b & z \\ x & y & z+c \end{matrix} \right| = abc \), where \( a, b, c \neq 0 \). The value of the expression \( \frac{x}{a} + \frac{y}{b} + \frac{z}{c} \) is:

If the system of equations \[ x-3y+5z=3 \] \[ x-2y+4z=4 \] \[ 2x-7y+\lambda z=5 \] has infinite number of solutions, then the value of \(\lambda\) is:

At what angle are the hands of a clock inclined at \(15\) minutes past \(5\)?

A unit vector perpendicular to the vectors \[ \hat i-\hat j \] and \[ \hat i+\hat j \] is:

Let \[ \vec{a}=2\hat{i}-\hat{j}+\hat{k}, \qquad \vec{b}=\hat{i}+2\hat{j}-\hat{k}, \] and \[ \vec{c}=\lambda\hat{i}+\mu\hat{j}+3\hat{k}. \] If \[ [\vec{a}\ \vec{b}\ \vec{c}]=0 \] and \[ \vec{c}\cdot(\vec{a}+\vec{b})=10, \] then find the value of \(\lambda+\mu\).

The value of \( \lambda \) for which the following system of equations has unique solution: \[ \lambda x+3y-z=1 \] \[ x+2y+z=2 \] \[ -\lambda x+y+2z=-1 \] are:

If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), then:

Evaluate: \( \begin{vmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{vmatrix} \)

If \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \), then \( A^{-1} \) is:

If \( X + Y = \begin{pmatrix} 5 & 3 \\ 0 & 7 \end{pmatrix} \) and \( X - Y = \begin{pmatrix} 7 & 1 2 & 3 \end{pmatrix} \). Then X and Y are

Match the grammar terms:

If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, then $\text{adj}(A)$ is:

In the given analogy, choose the word which will replace the question mark: \[ \text{NEGI : MVTR :: SING : ?} \]

The female reproductive part of a flower is:

Assertion (A): In RNA, thymine is replaced by uracil.
Reason (R): Uracil pairs with adenine during base pairing.