CUET UG 2022 — Applied-Mathematics

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

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

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

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

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

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 :

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

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 :

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.

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 :

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

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

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

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

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 :

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

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

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 :

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

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

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 :

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

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

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

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 $(1.1)^6 = 1.771$)

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

Which of the following is a statistic ?

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 :

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 :

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 :

Objective function of a LPP represent

Irregular variation in a time series are not caused by :

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

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

The area bounded by the curve $y = x^2$ between $x = 0$ and $x = \pi$ in the first quadrant 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 general solution of the differential equation $(1 + y) dx - 2x dy = 0$ is :

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

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

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

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

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

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

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