List of top Mathematics Questions asked in CUET (UG)

A motorboat can travel in still water at the speed 15 km/h, while the speed of the current is 3 km/h. Time taken by boat to go 36 km upstream is:

A mixture contains milk and water in the ratio 8 ∶ x. If 3 liters of water is added in 33 liters of mixture, the ratio of milk and water becomes 2 ∶ 1, then value of x is:

The Value of tan⁻¹ [2sin{2cos⁻¹ (\(\frac {\sqrt 3}{2}\))}].

Corner points of the feasible region for an LPP, are (0, 2), (3, 0), (6, 0) and (6, 8). If z = 2x + 3y is the objective function of LPP then max. (z)-min.(z) is equal to:

If $\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \frac{\pi}{2}$, then ________.

Let $A = \begin{bmatrix} \cos^2 x & \sin^2 x \\ \sin^2 x & \cos^2 x \end{bmatrix}$ and $B = \begin{bmatrix} \sin^2 x & \cos^2 x \\ \cos^2 x & \sin^2 x \end{bmatrix}$. Then the determinant of the matrix $A+B$ is ________.

The general solution of the differential equation $\frac{dy}{dx}+\frac{x}{y}=0$ is ________.

The solution of the differential equation $\frac{dx}{dy}+Px=Q$, where P and Q are constants or functions of y, is given by ________.

Let $[x^{r}]$ denotes the greatest integer of $x^{r}$ and $|x|$ denotes the modulus of x. Then $\lim_{x\rightarrow0}\frac{\sum_{r=1}^{100}[x^{r}]}{1+|x|}$ is ________.

The equation of the tangent to the curve given by $x=a \sin^{3}t$, $y=b \cos^{3}t$ at a point where $t = \frac{\pi}{2}$ is ________.

If $f(x)=ax^{2}+6x+5$ attains its maximum value at $x=1$, then the value of a is ________.

The equation of the circle passing through the foci of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ and having centre at (0, 3) is ________.

The area of the region bounded by the line $y=4$ and the curve $y=x^{2}$ is ________.

The equation $ax+by+c=0$ represents a straight line ________.

A card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either Ace or a King?

Let $E_{1}$ and $E_{2}$ be two independent events. If $P(E_{1}' \cap E_{2}) = \frac{2}{15}$ and $P(E_{1} \cap E_{2}') = \frac{1}{6}$, then $P(E_{1})$ is ________.

If $a = \frac{2 \sin \theta}{1 + \cos \theta + \sin \theta}$, then $\frac{1 + \sin \theta - \cos \theta}{1 + \sin \theta}$ is ________.

The value of k for which the system $x+ky+3z=0$, $4x+3y+kz=0$, $2x+y+2z=0$ has non-trivial solution is:

The domain of the function defined by $f(x)=log_x 10$ is:

If $19^{th}$ term of a non-zero arithmetic progression (AP) is zero, then its ($49^{th}$ term) : ($29^{th}$ term) is ________.

Let P be any non-empty set containing p elements. Then, what is the number of relations on P?

Let det M denotes the determinant of the matrix M. Let A and B be $3 \times 3$ matrices with det A = 3 and det B = 4. Then the det (2AB) is ________.