CUET Mathematics Mock Test - 4

The order of a matrix is defined as:

Solve the differential equation $xdy-2ydx=0$.

If $\frac{4}{x}<\frac{1}{3}$, what is the possible range of values for $x$?

The vector $\vec{a}\times (\vec{b}\times \vec{a})$ is coplanar with:

The order and degree of the differential equation ${\left[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)\right]}^{3/4}=\frac{d^{2}y}{d{x}^2}$ are:

For the given ordinary differential equation, $\frac{dx}{dy}+x{\sec }^{2}y=e^{-\tan y}$, the integrating factor will be equal to:

If $A=\left[\begin{array}{ccc}2& 0& 0\\ 0& 2& 0\\ 0& 0& 2\end{array}\right]$, then $A^5$ is equal to:

What will be the weekday on 15th of August if 15th of July on the same year was Sunday?

A tap can fill a tank in 8 hrs. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

A LED TV costs $₹25000$ and is expected to have a life of 8 years. Its final scrap value is $₹5000$. The annual depreciation according to the linear method of depreciation is:

If the expected value of a random variable $X$ is 2 and its variance is 1, then what will be the variance of $3X+4$?

The principal value of ${\sin }^{-1}\left(\frac{1}{\sqrt{17}}\right)+{\cos }^{-1}\left(\frac{5}{\sqrt{34}}\right)$ is:

A manufacturing company has its variable cost given by $C(x)=x(80-x^2)$ where $x$ is the number of quantities produced. The price per unit is $p(x)=5x$. The ratio of marginal cost and marginal revenue when 5 units were both produced and in demand is:

On the set of positive rational numbers, a binary operation $\ast$ is defined by $a\ast b=|a-b|$. If $5\ast p\le 5$, then the maximum value of $p$ is:

Let $S$ denote all integers. Define a relation $R$ on $S$ as $aRb$ if $ab\ge 0$ where $a,b\in S$. Then $R$ is:

The system of equations $7x+9y=15$ and $14x+18y=30$ has:

Find the area of a triangle with vertices at points $A(1,1)$, $B(6,0)$, and $C(3,2)$.

Mrs. Shivani takes a loan of $₹10,00,000$ with a $10\%$ annual rate of interest for 5 years. The EMI under the flat rate system is:

Find the value of $\det (2^{2}A)$ for the following matrix:
$$A=\left[\begin{array}{ccc}2& 3& 1\\ -1& 0& 2\\ -3& 1& 2\end{array}\right]$$

The index number calculated for the data below by simple weighted aggregate method is 110.| Item | Price (Current) | Price (Base) | Weights || :--- | :--- | :--- | :--- || A | $p$ | 4 | 60 || B | 3 | 2 | $q$ || C | 2 | 3 | 40 |Given $60p+3q=360$, then the value of $p$ will be:

A boat takes 2 hours to go 16 km downstream; while covering the same distance upstream, it takes 4 hours. What is the speed of the current?

If Rolle's theorem holds for the function $f(x)=x^3-a{x}^2+bx-4,x\in [1,2]$ with $f^{\prime }(4/3)=0$, then the ordered pair $(a,b)$ is equal to:

If $\sum p_0{q}_0=160$, $\sum p_0{q}_1=250$, $\sum p_1{q}_0=200$ and $\sum p_1{q}_1=288$, then Fisher's ideal index number is:

If $y=4x-5$ is tangent to the curve $y^2=p{x}^3+q$ at $(2,3)$, then:

The maximum slope of the curve $y=\frac{1}{2}{x}^4-5x^3+18x^2-19x$ occurs at the point:

In a $500\text{m}$ race, the ratio of the speeds of $P$ and $Q$ is $3:4$. When the race starts, $P$ is $140\text{m}$ ahead. What is the distance between $P$ and $Q$ when $P$ wins the race?

A piecewise-defined function is defined as:
$$f(x)=\{\begin{array}{ll}-1& \text{if }x\le 0\\ ax+b& \text{if }0<x<1\\ 1& \text{if }x\ge 1\end{array}$$
Where $a$ and $b$ are constants. If the function is continuous everywhere, what is the value of $a$?

If $x=3\tan t$ and $y=3\sec t$, then the value of $\frac{d^{2}y}{d{x}^2}$ at $t=\frac{\pi }{4}$ is:

For the linear programming problem:$\text{Maximize }Z=3X_1+2X_2$ Subject to:$-2X_1+3X_2\le 9$$X_1-5X_2\ge -20$$X_1,X_2\ge 0$ The above problem has:

Let $f:(0,+\infty )\to \mathbb{R}$ and $F(x)={\int }_0^{x}f(t)dt$. If $F(x^2)=x^2(1+x)$, then $f(4)$ equals:

If $A$ is a skew-symmetric matrix, then its transpose $A^T$ is equal to:

Correct evaluation of $\int \frac{x}{(x-2)(x-1)}dx$ (where $p$ is an arbitrary constant) is:

If ${\lim }_{n\to \infty }{\sum }_{k=1}^n\left[{\left(\frac{3k}{n}\right)}^2+2\right]\frac{3}{n}={\int }_0^{6}f(x)dx$, then:

A coin is tossed twice. If $E$ and $F$ denote the occurrence of a head on the first toss and second toss respectively, then what is $P(E\cup F)$ equal to?

What is $\int e^x\left(\sqrt{x}+\frac{1}{2\sqrt{x}}\right)dx$ equal to?

The area enclosed between the curves $y^2=x$ and $y=|x|$ is:

Let $f$ be a differentiable function such that $f(1)=2$ and $f^{\prime }(x)=f(x)$ for all $x\in \mathbb{R}$. If $h(x)=f(f(x))$, then $h^{\prime }(1)$ is equal to:

The plane $2x-3y+6z-11=0$ makes an angle ${\sin }^{-1}(\alpha )$ with the X-axis. The value of $\alpha$ is equal to:

The magnitude of the projection of the vector $2\hat{i}+3\hat{j}+\hat{k}$ on the vector perpendicular to the plane containing the vectors $\hat{i}+\hat{j}+\hat{k}$ and $\hat{i}+2\hat{j}+3\hat{k}$ is:

Find the distance between the straight line $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{1}$ and the plane $x-y+z-5=0$.

The minimum value of $3x+5y$ such that:$3x+5y\le 15$$4x+9y\le 18$$13x+2y\le 2$$x\ge 0,y\ge 0$ is:

What is the area of one of the loops between the curve $y=c\sin x$ and the x-axis?

Two models, $P$ and $Q$, of a product earn profits of $₹100$ and $₹80$ per piece, respectively. Production times for $P$ and $Q$ are $5$ hours and $3$ hours, respectively, while the total production time available is $150$ hours. For a total batch size of $40$, the objective function $Z$ is subjected to the constraints:

Find the area under the curve $y=x+2$, bounded by the x-axis and the y-axis.

What is the probability that the roots of the equation $x^2+x+n=0$ are real, where $n\in \mathbb{N}$ and $n<4$?

Five coins are tossed at a time. The probability of obtaining at least one head is:

$X$ is a random variable with probability density function:
$$f(x)=\{\begin{array}{ll}\frac{1}{2\pi }& -\pi \le x\le \pi \\ 0& \text{elsewhere}\end{array}$$
Then $E[\sin x]$ is:

If the lines $\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$ and $\frac{x-x_2}{p}=\frac{y-y_2}{q}=\frac{z-z_2}{r}$ lie on the same plane, then:

Let $X$ be a random variable that is uniformly chosen from the set of positive odd numbers less than $100$. The expectation $E[X]$ is: