List of top Mathematics Questions asked in CUET (UG)

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

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

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:

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

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

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:

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:

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

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

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 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?

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

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

The corner points of the feasible region of the LPP: Minimize \( Z = -50x + 20y \) subject to \( 2x - y \geq -5 \), \( 3x + y \geq 3 \), \( 2x - 3y \leq 12 \), and \( x, y \geq 0 \) are:

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

A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than 9, given that the black die resulted in a 5 is

If A is any event associated with sample space and if E\textsubscript{1}, E\textsubscript{2}, E\textsubscript{3} are mutually exclusive and exhaustive events. Then which of the following are true?
(A) $P(A) = P(E_1)P(E_1|A) + P(E_2)P(E_2|A) + P(E_3)P(E_3|A)$
(B) $P(A) = P(A|E_1)P(E_1) + P(A|E_2)P(E_2) + P(A|E_3)P(E_3)$
(C) $P(E_i|A) = \frac{P(A|E_i)P(E_i){\sum_{j=1}^{3} P(A|E_j)P(E_j)}, i=1,2,3$}
(D) $P(A|E_i) = \frac{P(E_i|A)P(E_i){\sum_{j=1}^{3} P(E_i|A)P(E_j)}, i=1,2,3$}
Choose the correct answer from the options given below: