List of top Mathematics Questions asked in CUET (UG)

For a matrix $ A $ of order $ 3 \times 3 $, which of the following is true?
If $ A $ is a $ 2 \times 2 $ matrix and $ |A| = 4 $, then $ |A^{-1}| $ is:
The angle between vectors $ \mathbf{a} = \hat{i} + \hat{j} - 2\hat{k} $ and $ \mathbf{b} = 3\hat{i} - \hat{j} + 2\hat{k} $ is:
The feasible region is bounded by the inequalities: \[ 3x + y \geq 90, \quad x + 4y \geq 100, \quad 2x + y \leq 180, \quad x, y \geq 0 \] If the objective function is $ Z = px + qy $ and $ Z $ is maximized at points $ (6, 18) $ and $ (0, 30) $, then the relationship between $ p $ and $ q $ is:
Direction cosines of a vector perpendicular to $ \mathbf{a} = \hat{i} + 2\hat{j} + 3\hat{k} $ and $ \mathbf{b} = 2\hat{i} - \hat{j} + \hat{k} $ are:
If vectors $ \mathbf{u}, \mathbf{v}, $ and $ \mathbf{w} $ satisfy $ \mathbf{u} + \mathbf{v} + \mathbf{w} = 0 $, and $ \mathbf{u} $ and $ \mathbf{v} $ are unit vectors, while $ |\mathbf{w}| = \sqrt{3} $, then the angle between $ \mathbf{v} $ and $ \mathbf{w} $ is:
Corner points of a feasible bounded region are \((0, 10)\), \((4, 2)\), \((3, 7)\) and \((10, 6)\). Maximum value 50 of objective function \(z = ax + by\) occurs at two points \((0, 10)\) and \((10, 6)\). The value of \(a\) and \(b\) are:
If $ A $ is a square matrix such that $ \text{adj}(\text{adj}(A)) = A $, then $ |A| $ is:
In a circle of radius 13 cm, a chord is at a distance of 12 cm from the center of the circle. Find the length (in cm) of the chord.
The general solution of the differential equation \( x\,dy + \left(y - e^x\right) dx = 0 \) is:
If $A$ is a square matrix of order 3 such that $|A| = 2$, then $|\operatorname{adj}(\operatorname{adj}(A))|$ is:
The derivative of \(\sin\left(\tan^{-1} e^{2x}\right)\) with respect to \(x\) is:
The vertices of a closed convex polygon representing the feasible region of the LPP with objective function \(z = 5x + 3y\) are \((0,0)\), \((3,1)\), \((1,3)\) and \((0,2)\). The maximum value of \(z\) is:
The general solution of the differential equation \( x\,dy + \left(y - e^x\right) dx = 0 \) is:
If A and B are square matrices of order 3 such that \(|A| = -1\), \(|B| = 3\) then \(|3AB|\) is:
If \(B\) is a non-singular \(4 \times 4\) matrix and \(A\) is its adjoint such that \(|A| = 125\), then \(|B|\) is:
The minimum value of \(\left(x^2 + \frac{250}{x}\right)\) is:
PQ and RS are common tangents to two circles intersecting at A and B. A and B, when produced on both sides, meet the tangents PQ and RS at X and Y, respectively. If \(AB = 3\) cm and \(XY = 5\) cm, then PQ is:
An amount becomes 5 times its original value in 25 years. What is the rate of simple interest per annum?
The function $f(x) = \begin{vmatrix} x^{2} & x \\ 3 & 1 \end{vmatrix}, x \in \mathbb{R}$ has:
If $A$ is a non-singular square matrix of order 3 and $|A^{-1}| = 24$, then the value of $|2A(\operatorname{adj}(3A))|$ is:
If $A$ is a square matrix of order 3 and $A \cdot (\operatorname{Adj}(A)) = 10I$, then the value of $\frac{1}{25} |\operatorname{adj}(A)|$ is:

For a $3 \times 3$ matrix $A$, if $A(\operatorname{adj} A) = \begin{bmatrix} 99 & 0 & 0 \\0 & 99 & 0 \\0 & 0 & 99 \end{bmatrix}$, then $\det(A)$ is equal to:

A person wants to invest at least ₹20,000 in plan A and ₹30,000 in plan B. The return rates are 9% and 10% respectively. He wants the total investment to be ₹80,000 and investment in A should not exceed investment in B. Which of the following is the correct LPP model (maximize return $ Z $)?

The absolute maximum value of $y = x^{3} - 3x + 2$, for $0 \leq x \leq 2$, is: