List of top Mathematics Questions asked in CUET (UG)

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?

Which of the following are the assumptions underlying the use of t-distribution?
(A) The variance of population is known.
(B) The samples are drawn from a normally distributed population.
(C) Sample standard deviation is an unbiased estimate of the population variance.
(D) It depends on a parameter known as degree of freedom.
Choose the correct answer from the options given below:

Which of the following is not a component of the time series?

Which of the following are correct?
(A) Time series analysis does not help to understand the behavior of a variable in the past.
(B) Time series predict the future behavior of variable.
(C) Time series helps to plan future operations.
(D) The main aim of the time series analysis is to derive conclusions after arranging the time series in a systematic manner.

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

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:

The probability distribution of the random variable X is given by
\begin{tabular}{|l|l|l|l|l|} \hline X & 0 & 1 & 2 & 3 \\ \hline P(X) & 0.2 & k & 2k & 2k \\ \hline \end{tabular}
The variance of the random variable X 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 \(e^{\alpha y} + e^{\beta y} + \gamma x^2 + \delta \log|x| + C = 0\), 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

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

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?

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

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = \(0.007x^3 - 0.003x^2 + 15x + 400\). The marginal cost when 10 items are produced is:

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:

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

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

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:

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

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?

If A and B are any two events such that P(B) = P(A and B), then which of the following is correct