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

The area of the region bounded by |x| + |y| = 1, x ≥ 0 y ≥ 0 is :

If the present value of a perpetuity of ₹600 payable at the end of every six months is ₹18000, then the rate of interest is:

A shopkeeper sold \(\frac23\) of his stock of rice at a profit of \( 5\%\) and the remaining stock at a loss of \(2\%\). If his total profit was \( ₹\)\( 1000\), then the cost price of the whole stock of rice is:

If \(x=3at^2\), \(y=3at^4\) then \(\frac{dy}{dx}\) is:

The effective rate equivalent to a nominal rate of 8% per annum compounded semi-annually is:

A motor boat covers 16 km in 2 hours downstream and 14 km in 2 hours upstream. The speed of the motor boat is:

The tangent to the parabola, x² = 2y at the point \((1,\frac{1}{2})\) makes with the x-axis an angle of :

If A is a non-identity invertible symmetric matrix, then \(A^{-1}\) is:

The direction ratios of the line perpendicular to the lines \(\frac{x-7}{-6}= \frac{y+17}{4}= \frac{z-6}{2} \space and \space \frac {x+5}{6}=\frac{y+3}{3}=\frac{z-4}{-6}\) are proportional to:

Let\[f(x)=\begin{cases} 2x-1, x<1\\ 1, x=1 \\ x^2,x>1 \end{cases}\]then at x = 1

The function f(x) = \(|x - 1|\) is

The points of discontinuity of the function \(f\) defined by \(f(x) = \begin{cases} x+2 & x≤1 \\ x-2 &1<x<2\\ 0& x≥2\end{cases}\) are:

he trend line for the sales (in lakhs) is given by \(y_c=84+12(x-2017).\) The estimated sale for theyear \(2024 \) is :

The ratio of speeds of a motor boat and that of current of water is 35:6. The boat goes against the current in 6 hours 50 minutes. The time taken by boat to come back is :

In a certain code, COMPUTER is coded as ETUPMOCR. How is INACTIVE written in the same code?

The function f(x) - x³ , x ∈ R has :

The quantity of water that must be added to 36 litres of milk at 2 ½ litres for ₹120 so as to have mixture worth ₹36 for a litre is:

If A is a square matrix of order 3 and |A|=5, then |adj(adjA)| is:

If \(y=x^3\log x, then\ \frac{d^2y}{dx^2}\) is:

The money needed to invest now, so as to get ₹7500 at the beginning of each month forever (starting from the current month) if the money is worth 9% per annuum compounded monthly is.

If, A = \(\begin{bmatrix}a& d& l\\[0.3em]b& e& m\\[0.3em]c& f& n\\[0.3em] \end{bmatrix}\)and B = \(\begin{bmatrix}l& m& n\\[0.3em]a& b& c\\[0.3em]d& e& f\\[0.3em]  \end{bmatrix}\), then

The value of \(\int_1^4|x-1|dx \)  is :

Match List I with List II

List I	List II
\(A.\ [1 + (\frac{dy}{dx})^2] = \frac{d^2y}{dx^2}\)	I. order 2, degree 3
\(B. \ (\frac{d^3y}{dx^2})^2 - 3\frac{d^2y}{dx^2} + 2(\frac{dy}{dx})^4 = y^4\)	II. order 2, degree 1
\(C. \ (\frac{dy}{dx})^2 + (\frac{d^2y}{dx^2})^3 = 0\)	III. order 1, degree 2
\(D.\ (\frac{dy}{dx})^2 + 6y^3 = 0\)	IV. order 3, degree 2

Choose the correct answer from the options given below:

The value of C which satisfies Rolle's Theorem for f(x) = sin⁴x + cos⁴x in \([0, \frac{π}{2}]\). Then C is:

For the problem max Z = ax + by, x≥0, y ≥0, which of the following is NOT a valid constraint to make it a linear programming problem?