CUET Mathematics 2024 16 May Shift 1 PYQs

The corner points of the feasible region determined by $x+y \leq 8, 2 x+y \geq 8, x \geq 0, y \geq 0$ are $A(0,8), B(4,0)$ and $C(8,0)$. If the objective function $Z=a x+$ by has its maximum value on the line segment $A B$, then the relation between $a$ and $b$ is :

If $t=e^{2 x}$ and $y=\log _{e} t^{2}$, then $\frac{d^{2} y}{d x^{2}}$ is :

An objective function $Z=a x+b y$ is maximum at points $(8,2)$ and $(4,6)$. If $a \geq 0$ and $b \geq 0$ and $a b=25$, then the maximum value of the function is equal to :

The area of the region bounded by the lines $x+2 y=12, x=2, x=6$ and $x$-axis is :

A die is rolled thrice. What is the probability of getting a number greater than $4$ in the first and the second throw of dice and a number less than $4$ in the third throw ?

$\int \dfrac{\pi}{x^{n+1}-x} d x=$

The value of $\int_{0}^{1} \frac{a-b x^{2}}{\left(a+b x^{2}\right)^{2}} d x$ is :

The second order derivative of which of the following functions is $5^{\mathrm{x}}$ ?

The degree of the differential equation $\left(1-\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}=k \frac{d^{2} y}{d x^{2}}$ is :

If $A$ and $B$ are symmetric matrices of the same order, then $A B-B A$ is a :

If $A$ is a square matrix of order $4$ and $|A|=4$, then $|2 A|$ will be :

If $[\mathrm{A}]_{3 \times 2}[\mathrm{~B}]_{\mathrm{x} \times \mathrm{y}}=[\mathrm{C}]_{3 \times 1}$, then :

If a function $f(x)=x^{2}+b x+1$ is increasing in the interval $[1,2]$, then the least value of $b$ is :

Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be :

For the function $f(x) = 2x^3 - 9x^2 + 12x - 5$, $x \in [0, 3]$, match List-I with List-II : | List-I | List-II | | --- | --- | | A. Absolute maximum value | (I) $ 3 $ | | B. Absolute minimum value | (II) $ 0 $ | | C. Point of maxima | (III) $ -5 $ | | D. Point of minima | (IV) $ 4 $ |

For which one of the following purposes is CAGR (Compounded Annual Growth Rate) <b>not</b> used ?

A flower vase costs ₹ $36,000$. With an annual depreciation of ₹ $2,000$, its cost will be ₹ $6,000$ in $_____$ years.

Arun's speed of swimming in still water is $5 \mathrm{~km} / \mathrm{hr}$. He swims between two points in a river and returns back to the same starting point. He took $20$ minutes more to cover the distance upstream than downstream. If the speed of the stream is $2 \mathrm{~km} / \mathrm{hr}$, then the distance between the two points is :

If $\mathrm{e}^{\mathrm{y}}=\mathrm{x}^{\mathrm{x}}$, then which of the following is true ?

The probability of a shooter hitting a target is $\frac34$. How many minimum number of times must he fire so that the probability of hitting the target at least once is more than $90 \%$ ?

Ms. Sheela creates a fund of ₹ $1,00,000$ for providing scholarships to needy children. The scholarship is provided in the beginning of the year. This fund earns an interest of $r \%$ per annum. If the scholarship amount is taken as ₹ $8,000$, then $r=$

A person wants to invest an amount of ₹ $75,000$. He has two options A and B yielding $8 \%$ and $9 \%$ return respectively on the invested amount. He plans to invest at least ₹ $15,000$ in Plan A and at least ₹ $25,000$ in Plan B. Also he wants that his investment in Plan A is less than or equal to his investment in Plan B. Which of the following options describes the given LPP to maximize the return (where $x$ and $y$ are investments in Plan A and Plan B respectively) ?

In a $700 \mathrm{~m}$ race, Amit reaches the finish point in $20$ seconds and Rahul reaches in $25$ seconds. Amit beats Rahul by a distance of :

For the given five values $12,15,18,24,36$; the three-year moving averages are :

The corner points of the feasible region for an L.P.P. are $(0,10),(5,5),(5,15)$ and $(0,30)$. If the objective function is $Z=\alpha x+\beta y, \alpha, \beta>0$, the condition on $\alpha$ and $\beta$ so that maximum of $Z$ occurs at corner points $(5,5)$ and $(0,20)$ is :

The solution set of the inequality $|3 x| \geq|6-3 x|$ is :

If the matrix $\left[\begin{array}{rrr}0 & -1 & 3 x \\ 1 & y & -5 \\ -6 & 5 & 0\end{array}\right]$ is skew-symmetric, then the value of $5 x-y$ is:

A company is selling a certain commodity $x$. The demand function for the commodity is linear. The company can sell $2000$ units when the price is ₹$8$ per unit and it can sell $3000$ units when the price is ₹$4$ per unit. The Marginal revenue at $x=5$ is:

If the lengths of the three sides of a trapezium other than the base are $10 \mathrm{~cm}$ each, then the maximum area of the trapezium is:

Three defective bulbs are mixed with $8$ good ones. If three bulbs are drawn one by one with replacement, the probabilities of getting exactly $1$ defective, more than $2$ defective, no defective and more than $1$ defective respectively are:

If $\mathrm{A}=\left[\begin{array}{ll}2 & 4 \\ 4 & 3\end{array}\right], \mathrm{X}=\left[\begin{array}{l}\mathrm{n} \\ 1\end{array}\right], \mathrm{B}=\left[\begin{array}{c}8 \\ 11\end{array}\right]$ and $A X=B$, then the value of $n$ will be :

The equation of the tangent to the curve $\mathrm{x}^{\frac{5}{2}}+\mathrm{y}^{\frac{5}{2}}=33$ at the point $(1,4)$ is :

| $ X $ | -2 | -1 | 0 | 1 | 2 | | --- | --- | --- | --- | --- | --- | | $ P(X) $ | $ 0.2 $ | $ 0.1 $ | $ 0.3 $ | $ 0.2 $ | $0.2$ | The variance of $X$ will be :

A Multinational company creates a sinking fund by setting a sum of ₹ $12,000$ annually for $10$ years to pay off a bond issue of ₹ $72,000$. If the fund accumulates at $5 \%$ per annum compound interest, then the surplus after paying for bond is : (Use $\left.(1.05)^{10} \approx 1.6\right)$

The least non-negative remainder when $3^{51}$ is divided by $7$ is :

If $\left[\begin{array}{cc}5 x+8 & 7 \\ y+3 & 10 x+12\end{array}\right]=\left[\begin{array}{cc}2 & 3 y+1 \\ 5 & 0\end{array}\right]$, then the value of $5 x+3 y$ is equal to :

There are $6$ cards numbered $1$ to $6$, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two cards drawn. Then $\mathrm{P}(\mathrm{X}>3)$ is :

Which of the following are components of a time series ? (A) Irregular component (B) Cyclical component (C) Chronological Component (D) Trend Component Choose the <b>correct</b> answer from the options given below :

The following data is from a simple random sample : $15,23, x, 37,19,32$ If the point estimate of the population mean is $23$, then the value of $x$ is :

For an investment, if the nominal rate of interest is $10 \%$ compounded half yearly, then the effective rate of interest is :

A mixture contains apple juice and water in the ratio $10: \mathrm{x}$. When $36$ litres of the mixture and $9$ litres of water are mixed, the ratio of apple juice and water becomes $5: 4$. The value of $x$ is :

For $I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, if $X$ and $Y$ are square matrices of order $2$ such that $X Y=X$ and $Y X=Y$, then $\left(\mathrm{Y}^{2}+2 \mathrm{Y}\right)$ equals to :

A coin is tossed K times. If the probability of getting $3$ heads is equal to the probability of getting $7$ heads, then the probability of getting $8$ tails is :

If $95 \%$ confidence interval for the population mean was reported to be $160$ to $170$ and $\sigma=25$, then size of the sample used in this study is: (Given $\mathrm{Z}_{0.025}=1.96$ )

Two pipes A and B together can fill a tank in $40$ minutes. Pipe A is twice as fast as pipe B. Pipe A alone can fill the tank in :