CUET Mathematics 2023 11 Aug Shift 1 PYQs

If $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} = 4x$, then $x =$

If $x = 2at, y = at^2$, where 'a' is a constant, then $\frac{d^2 y}{dx^2}$ at $x = 2$ is :

The variance of the number of heads in two tosses of a coin is :

The interval in which where the function $f(x) = x^3 - 3x^2 + 4x + 1, x \in R$ is increasing in, is :

The area bounded by the curve $y = x^2$ between $x = 0$ and $x = \pi$ in the first quadrant is :

The area of the triangle with vertices $(1,4), (2,7)$ and $(4,13)$ is :

If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}, I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $A^2 = 8A + kI$, the value of k is :

Let X & Y be 2 invertible square matrix, then which of the following is true (A) $(AB)^{-1} = A^{-1} B^{-1}$ (B) $(AB)^{-1} = B^{-1} A^{-1}$ (C) $(AB)' = A' B'$ (D) $(AB)' = B' A'$ Choose the answer from the options given below

The order and degree Of the differential equation $\frac{d^2 y}{dx^2} + 2 e^{-x} = 0$, respectively are

the general solution of the differential equation $(1 + y) dx - 2x dy = 0$ is :

If $v = \frac{4}{3} \pi r^3$, at what rate is cubic / unit sec is increasing when $r = 10$, and $\frac{dr}{dt} = 0.01$ ?

Objective function $Z = 200x + 500y$, subject to constraint, $x + 2y \geq 10, 3x + 4y \leq 24$, $x \geq 0, y \geq 0$ - (iii), the minimum value of Z is :

The value of the integral $\int_{-3}^{3} (x^3 - x) dx$ is :

Given a linear programming problem, Max $Z = 22x + 18y$, Subject to constraints $x + y \leq 20, 360x + 240y \leq 5760, x \geq 0, y \geq 0$. Its corner points are :

10 works hard drawn successively with replacement from a lot containing 10% defective bulb. The probability that there is at least one defective bulb is :

The corner points of feasible region determined by the following system of linear inequalities $2x + y \leq 10, x + 3y \leq 15, x \geq 0, y \geq 0$ are $(0,0), (5,0), (3,4)$ and $(0,5)$, then the relation between p and Q so that minimum of Z occurs both points $(3,4)$ and $(0,5)$ is :

$\int \frac{dx}{x^{n+1} - x}\,dx$

If $P = \begin{bmatrix} -2 & 2 & 0 \\ 3 & 1 & 4 \end{bmatrix}$ and $Q = \begin{bmatrix} 2 & 0 & -2 \\ 7 & 1 & 6 \end{bmatrix}$, If $5Q - 3P + 2R = 0$, then the matrix R is

The second order derivative of which of the following functions is $5^x$ ?

As a factory owner, you have decided to purchase a heavy machinery after 10 years. It's expected price will be Rs. 1,00,00,000. For this you set aside a certain amount at the end of every year. Which of the following financial tool fits best for this purpose ?

The probability distribution of a discrete random variable X is given by : | X | 30 | 10 | -10 | |---|---|---|---| | P(X) | 1/5 | 3/10 | 1/2 | then E(X) is equals to

Solution for the inequality $|3x - 7| \leq 2$ is :

<img src="https://balti.afterboards.in/p9DwD9JrEuGMwjM" width="300px"/>Which of the following are true for the given graph. (A) Break even point is at x = 10 (B) Break even point is at x = 8 (C) Break even point is at x = 6 (D) Fixed cost is 20 (E) Fixed cost is 0 Choose the correct answer from the options :

A vessel contains 56 litres of mixture of milk and water in the ratio 5:2. How much water should be mixed with it so that the milk to water ratio becomes 4:5

2 voices dice are thrown together. For the first die $P(6) = \frac{1}{2}$, other scores are equally likely. While for the second die $P(1) = \frac{2}{5}$ and other scores are equally likely than the Mean for the probability distribution of the number of one score will be

If $\begin{bmatrix} 2x & -7 \\ 5y & 8 \end{bmatrix} = \begin{bmatrix} 6 & -7 \\ -5 & 3x + y \end{bmatrix}$, then value of $5x - 3y$ is :

Irregular variation in a time series are not caused by :

The least positive integer X satisfying $28 \equiv x (\mod 6)$ is :

For the given 7 values 5, 7, 9, 2, 2, 3, 4 the five year moving averages are

For the LPP, Min $Z = 6x + 10y$ subject to $x \geq 6, y \geq 3, 2x + y \geq 10, x \geq 0, y \geq 0$, redundant constraint is :

A person started giving aside Rs. 10,000 each year for his child college education in a sinking fund the amount he will receive after 6 years. if the rate of interest is 10% per annum is : (Use $(1.1)^6 = 1.771$)

If $A = \begin{bmatrix} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{bmatrix}$ and $B = \begin{bmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{bmatrix}$, then AB is equals to :

Which of the following is a correct set of constraint for a LPP ?

In a binomial distribution the probability of getting success is $\frac{1}{4}$ And standard deviation is 3 then its mean is ?

For the feasible reason of a LPP as shown, if the equation of OA and BC are $y - 2x = 0$ and $y - 2x = 4$ respectively than constraints for LPP are

A Simple random sample consists of four observation 1, 3, 5, 7. The point estimate of population standard deviation is

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

Objective function of a LPP represent

At 8% converted quarterly the present value of perpetuity of Rs. 8000 payable at the end of each quarter ( in rupees) is :

If $C(x) = x^3 - \frac{5}{2} x^2 + 10$ represents the total cost of producing x unit by car manufacturing company. The slope of the marginal cost curve at $x = 3$, will be

If a matrix A is both symmetric and skew symmetric then :

Which of the following is a statistic ?

If x is real, the minimum value of $f(x) = x^2 - 8x + 20$ is :

$P(X = x) = \begin{cases} 2k & \text{if } x = 0 \\ kx & \text{if } x = 1 \\ k(x - 1) & \text{if } x = 2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}$ The value of k is

If a person goes 20 kilometre downstream in 5 hours and returns against the stream in 15 hours, then the speed of the stream in kilometre per hour is :

If $y = x^3 \log x$, then $\frac{d^2 y}{dx^2}$ is equal to :

A random variable X has a probability distribution P(X) of the following form, where k is some unknown constant: P(X = 0) = k P(X = 1) = 2k P(X = 2) = 3k P(X = other values) = 0 Then, find the value of 1/k.

the least non-negative remainder when $3^{17}$ is divided by 7 is :

An asset costing Rs. 1,50,000 has a final scrap value of Rs. 25,000. If annual depreciation charge is Rs. 25,000, then useful life of the asset is :

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