List of top Mathematics Questions asked in CUET (UG)

If $ A $ is a $ 2 \times 2 $ matrix and $ |A| = 4 $, then $ |A^{-1}| $ is:

Given: The least-squares straight line is \(y = a + b(x - 2022)\).
 

Year (x)20202021202220232024
Profit (Rs. '000) (y)23452

The probability distribution of a random variable X is given by

X012
P(X)\(1 - 7a^2\)\(\tfrac{1}{2}a + \tfrac{1}{4}\)\(a^2\)


If \(a > 0\), then \(P(0 < X \leq 2)\) is equal to

Let A = $\begin{bmatrix} 1 & 2 & 1 \\ 1 & 3 & 2 \\ 2 & 4 & 1 \end{bmatrix}$ and Mij, Aij respectively denote the minor, co-factor of an element aij of matrix A, then which of the following are true?
(A) M22 = -1
(B) A23 = 0
(C) A32 = 3
(D) M23 = 1
(E) M32 = -3
Choose the correct answer from the options given below:

If A is any event associated with sample space and if E1, E2, E3 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) \(P(A|E_i) = \frac{P(E_i|A)P(E_i)}{\sum_{j=1}^{3} P(E_i|A)P(E_j)}, \; i=1,2,3\) 

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The probability distribution of the random variable X is given by

X0123
P(X)0.2k2k2k

Find the variance of the random variable \(X\).

Given: \(y = a + b(x - 2022)\) is the least-squares straight-line trend.

Year (x)20202021202220232024
Profit (Rs. '000) (y)23452
Which of the following is NOT a basic requirement of the linear programming problem (LPP)?
Which of the following statements are correct in reference to the linear programming problem (LPP):
Maximize Z = 5x + 2y
subject to the following constraints
3x + 5y \(\le\) 15,
5x + 2y \(\le\) 10,
x \(\ge\) 0, y \(\ge\) 0.
(A) The LPP has a unique optimal solution at (2, 0) only.
(B) The feasible region is bounded with corner points (0, 0), (2, 0), (20/19, 45/19) and (0, 3).
(C) The optimal value is unique, but there are an infinite number of optimal solutions.
(D) The feasible region is unbounded.
Choose the correct answer from the options given below:
A person wishes to purchase a house for Rupess 39,65,000 with a down payment of Rupees 5,00,000 and balance in equal monthly installments (EMI) for 25 years. If bank charges 6% per annum compounded monthly, then EMI on reducing balance payment method is:
[Given \((1.005)^{300} = 4.465\)]
A person invested Rupees 10000 in a stock of a company for 6 years. The value of his investment at the end of each year is given in the following table:
\begin{tabular}{|c|c|c|c|c|c|} \hline 2018 & 2019 & 2020 & 2021 & 2022 & 2023
\hline Rupees 11000 & Rupees 11500 & Rupees 13000 & Rupees 11800 & Rupees 12200 & Rupees 14000
\hline \end{tabular}
The compound annual growth rate (CAGR) of his investment is:
Given \((1.4)^{1/6} \approx 1.058\)
The original value of an asset minus the accumulated depreciation at a given date is known as
A sofa set costing Rupees 36000 has a useful life of 10 years. If the annual depreciation is Rupees 3000, then the scrap value by linear method is:
Which of the following are correct about the Sinking Fund?
(A) It is a fixed term account.
(B) It is a set-up for a particular upcoming expense.
(C) A fixed amount at regular intervals is deposited in the Sinking Fund.
(D) It can be used in any emergency.
Choose the correct answer from the options given below:
Which of the following is not a component of the time series?
If a 95% confidence interval for a population mean was reported to be 132 to 160 and sample standard deviation s = 50, then the size of the sample in the study is:
(Given \(Z_{0.025}\) = 1.96)
An annuity in which the periodic payment begin on a fixed date and continue forever is called

Match List-I with List-II

List-IList-II
(A) An observed set of population selected for analysis(I) Parameter
(B) A specific characteristic of the population(II) Hypothesis
(C) A specific characteristic of the sample(III) Statistic
(D) A statement made about a population parameter for testing(IV) Sample
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:
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:
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%?
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:
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?
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: