List of top Mathematics Questions asked in CUET (UG)

Differentiate: \( y = x^2\sin x \)

The principal value of \( \tan^{-1}(1) \) is:

The feasible region of a linear programming problem is always:

Solve: \( \frac{dy}{dx}=3x^2 \)

If \( f(x)= \begin{cases x^2+k, & x\leq 1 \\ 2x+1, & x>1 \end{cases} \) is continuous at \( x=1 \), then the value of \( k \) is:}

A bag contains 5 red balls and 3 blue balls. Two balls are drawn at random without replacement. The probability that both are red is:

Let \( A = \{1,2,3\} \) and \( B = \{2,4,6\} \). A function \( f : A \to B \) is defined by \( f(x)=2x \). The function is:

Consider the function \( f(x) = -2x^3 - 9x^2 - 12x + 5 \). Then, which of the following is/are correct?

If \(\vec{a}\) and \(\vec{b}\) are unit vectors, then the angle between \(\vec{a}\) and \(\vec{b}\) for \( \sqrt{3}\vec{a} - \vec{b} \) to be a unit vector is given by :

A card is picked at random from a pack of 52 playing cards. Given that the picked card is a king, the probability of this card to be a card of spade is:

A certain type of fish has a 4/5 probability of surviving in a pond, while another fish has a 2/5 probability of survival. What is the probability that exactly one of them survives?

The value of \( \int_0^2 |x - 2| dx = \)

The integral \( \int e^x \left(\tan^{-1}x + \frac{1}{1+x^2}\right) dx \) is equal to

The value of the integral \( I = \int_{-3}^3 (x^3 - x) dx \) is

The integral \( \int \frac{2+x^4}{1+x^2} dx \) is equal to

If \( f(x) = x^5 - 5x^3 + 5x^2 - 1 \), then the number of critical points of \( f(x) \) is:

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:

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