List of top Questions asked in CUET (UG)- 2023

The function \(f(x)=sinx+cosx,0\leq x\leq 2\pi \) is :

The interval in which the \(f(x) = sinx-cosx, 0 ≤ x ≤ 2π\) is strictly decreasing is :

The absolute maximum value of the function f(x)=sinx + cosx, x \(\in\)[0, \(\pi\)] is:

The area of the region \(\{(x, y) : x^2 + y^2 \leq 2ax, y^2 > ax, x \geq 0, y \geq 0\} \text{ where } a > 0\) , is :

The difference between length and breadth of a rectangle is 15m. If the perimeter of rectangle is 162 m, then the area of the rectangle (in m²) is

The integral \(\int_0^1x(1-x)^n dx\) is equal to :

In △ABC, BD is the internal bisector of ∠B meeting AC at D. If CD = 7 cm and AC = 10.5 cm, then AB : BC is

The diameter of the driving wheel of a bus is 140 m. How many revolutions per minute must the wheel make in order to keep a speed of 66 km/h?

₹4200 are divided among ‘P’, ‘Q’, ‘R’ and ‘S’ in such a way that the shares of ‘P’ and ‘Q’. ‘Q’ and ‘R’ as well ‘R’ and ‘S’ are in the ratios of 2:3, 4:5 and 6:7 respectively, the share of ‘P’ is :

The value of the integral \(\int\frac{1-\sin x}{\cos^2 x}dx\) is :

The value of k for which the matrix \(\begin{pmatrix} 0 & 2 & 4 \\ 2 & 0 & 5 \\ -3 & 5 & 0 \end{pmatrix}\) is a symmetric matrix is given by :

The equation of plane which cuts equal intercepts of unit length on the coordinate axes is:

Objective function \(z=30x-30y \) is subject to which combination of constraints, with feasible solution shown in the figure.

(A)\(x \geq 0, \quad y \geq 0, \quad x \leq 15\)
(B)\(y \leq 20, \quad x + y \leq 30\)
(C)\(x + y \leq 30, \quad x + y \leq 15, \quad 2x - y \leq 5\)
(D)\(2x + y \leq 30, \quad x + y \leq 15, \quad x > 15\)
(E)\(3x + y \leq 30, \quad x + 3y \leq 15, \quad y \geq 20\)
Choose the correct answer from the options given below:
 

The random variable X has a probability distribution P(X) of the following form, where k is some number.

Then P(x≤2) is:

A man goes uphill with an average speed of 24 km/h and comes down with an average speed of 36 km/h. The distance travelled in both cases being the same. The average speed for the entire journey is:

Let \(\begin{vmatrix}3x&-7\\1&4\end{vmatrix}=\begin{vmatrix}3&2\\ 4&x\end{vmatrix}\), then value of x is:

By investing ₹4650 in a \(7 \frac{1}{2} \%\)% stock, a person obtains an income of ₹300. The market price of the stock is:

The feasible region of an LPP is shown in the figure below.
If \( z=3x+9y\), then the minimum value of \(z\) occurs at :

A 10 m long, 4 m high and 24 cm thick wall is to be built using bricks having dimensions 25 cm × 12 cm × 8 cm. Number of bricks required is :

A vehicle whose cost is ₹7,00,000 will depreciate to scrap value of ₹1,50,000 in 5 years. Using linear method of depreciation, the book value of the vehicle at the end of the third year is :

The value of C in Rolles's theorem for the function \(f(x)=e^xsinx,x\epsilon[0,\pi]\),is :

The sum of order and degree of the differential equation\[\frac{\{1+(\frac{dy}{dx})^2\}^\frac{5}{2}}{\frac{d^2y}{dx^2}}=p\]is:

If \(\frac{d}{dx}(2\frac{d^2y}{dx^2})^3= 7\), then the sum of order and degree of the differential equation is:

A metallic sphere of radius 8 cm is melted to form a cone with radius same as that of sphere. What is the height of the cone (in cm) ?