List of top Questions asked in CUET (UG)- 2021

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

Which of the following sequences fits into the organic evolution theory proposed by Charles Darwin and Alfred Wallace?

Suppose we have block of 4 kilogram kept on a horizontal surface and we are applying a horizontal force of 10 newton. Let the coefficient of friction is 0.2. Find the force of friction. Assume that $g=10.$}

If the horizontal and vertical components of a force are negative, then that force is acting in between ________.

A ball is thrown upward at a speed of 28 meter per second. What is the speed of ball one second before reaching maximum height? (Given that $g = 10$ meter per second²)}

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

Which one of the following statements is correct for a moving body?

Let $\vec{\alpha} = \hat{i} + 2\hat{j} - \hat{k}$, $\vec{\beta} = 2\hat{i} - \hat{j} + 3\hat{k}$, and $\vec{\gamma} = 2\hat{i} + \hat{j} + 6\hat{k}$.If $\vec{\alpha}$ and $\vec{\beta}$ are both perpendicular to a vector $\vec{\delta}$ and $\vec{\delta} \cdot \vec{\gamma} = 10$, then the magnitude of $\vec{\delta}$ is: }

Let $\hat{a}, \hat{b}, \hat{c}$ be unit vectors such that $\hat{a}\times(\hat{b}\times\hat{c})=\frac{\sqrt{3}}{2}(\hat{b}+\hat{c})$. The angle between $\hat{a}$ and $\hat{c}$ is:

A bullet of mass m and velocity a is fired into a large block of wood of mass M. The final velocity of the system 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 ________.

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 ________.

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

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 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 ________.

Upon increase in pressure for dissociation of $N_{2}O_{4}$ into $NO_{2}$ equilibrium shift towards ________.

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?