List of top Questions asked in CUET (UG)

Which of the following are linear first order differential equations?
(A) $\frac{dy}{dx} + P(x)y = Q(x)$
(B) $\frac{dx}{dy} + P(y)x = Q(y)$
(C) $(x - y)\frac{dy}{dx} = x + 2y$
(D) $(1 + x^2)\frac{dy}{dx} + 2xy = 2$
Choose the correct answer from the options given below:

The solution of the differential equation $\log_e(\frac{dy}{dx}) = 3x + 4y$ is given by

The corner points of the feasible region associated with the LPP: Maximise Z = px + qy, p, q > 0 subject to 2x + y $\le$ 10, x + 3y $\le$ 15, x,y $\ge$ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then

Consider the LPP: Minimize Z = x + 2y subject to 2x + y $\ge$ 3, x + 2y $\ge$ 6, x, y $\ge$ 0. The optimal feasible solution occurs at

If P, Q and R are three singular matrices given by \(P = \begin{bmatrix} 2 & 3a \\ 4 & 3 \end{bmatrix}\), \(Q = \begin{bmatrix} b & 5 \\ 2a & 6 \end{bmatrix}\) and \(R = \begin{bmatrix} a^2 + b^2 - c & 1-c \\ c+1 & c \end{bmatrix}\), then the value of \((2a + 6b + 17c)\) is

Let A be a non-singular matrix of order 3 and \(|A| = 15\), then \(|\text{adj } A|\) is equal to

If \(A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}\), \(X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}\), \(B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}\) and \(AX = B\), then the value of the \(\alpha\) is

If X = 11 and Y = 3, then X mod Y = (X + aY) mod Y holds

The least non-negative remainder when \(3^{128}\) is divided by 7 is:

A tub contains 60 litres of milk. From this tub, 6 litres of milk was taken out and replaced with water. This whole process was repeated further two more times. How much milk is there in the tub now?

A person can row a boat in still water at the rate of 5 km/hr. It takes him 4 times as long to row upstream of a river as to row downstream to cover same distance in the same river. The speed of flow of the stream is

Two runners, Ajay and Vijay complete a 600 m race in 38 seconds and 48 seconds respectively. By how many meters will Ajay defeat Vijay?

Which of the following inequalities holds true?
(A) \(\sqrt{5} + \sqrt{3}>\sqrt{6} + \sqrt{2}\)
(B) If \(a>b\) and \(c<0\), then \(\frac{a}{c}<\frac{b}{c}\)
(C) \(\frac{1}{x^2}>\frac{1}{x}>1\), if \(0<x<1\)
(D) If a and b are positive integers and \(\frac{a-b}{6.25} = \frac{4}{2.5}\) then \(b>a\)
Choose the correct answer from the options given below:

If \(e^y = \log x\), then which of the following is true?

The slope of the normal to the curve y = \(2x^2\) at x = 1 is:

If \(\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C\), where C is constant of integration, then f(x) is

Let \(e^{\alpha y} + e^{\beta y} + \gamma x^2 + \delta \log|x| + C = 0\), where \(C \in \mathbb{R}\) be a particular solution of the differential equation \(x(e^{2y} - 1)dy + (x^2 - 1)e^y dx = 0\) and passes through the point (1, 1). The value of \((\alpha + \beta + \gamma + \delta - C)\) is

How many minimum number of times must a man toss a fair coin so that the probability of having at least one head is more than 90%?

Let F(Z) be the cumulative density function of the standard normal variate Z, then which of the following are correct?
(A) \(F(Z) = \int_{-\infty}^{Z} \frac{1}{\sqrt{2\pi}} e^{-z^2/2} dz, -\infty < Z <\infty\)
(B) \(F(-Z) = 1 - F(Z)\)
(C) \(F(0) = 0\)
(D) \(F(\infty) = 1\)
Choose the correct answer from the options given below:

What is the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on 1 face?

For the given 5 values, 15, 18, 21, 27, 39; the three year moving averages are: