CUET Mathematics Mock Test - 2

If $A$ is a singular matrix, then $\text{adj }A$ is:

What is the degree of the following differential equation?
$$x=\sqrt{1+\frac{d^{2}y}{d{x}^2}}$$

The variance ${\sigma }^2$ of a random variable $X$ is given by:

What is the interval over which the function $f(x)=6x-x^2,x>0$ is increasing?

A coin is tossed $5$ times. The probability of head is $\frac{1}{2}$. The probability of exactly $2$ heads is:

Which of the following is correct regarding the analysis of four components of time series analysis?

If $4\hat{i}+\hat{j}-3\hat{k}$ and $p\hat{i}+q\hat{j}-2\hat{k}$ are collinear vectors, then what are the possible values of $p$ and $q$ respectively?

If $a\mathbb{N}=\{ax:x\in \mathbb{N}\}$, then $2\mathbb{N}\cap 5\mathbb{N}$ is:

What is the general solution of $(1+e^x)ydy=e^{x}dx$? (where $c$ is a constant of integration)

If $I_3$ is the identity matrix of order $3$, then $I_3^{-1}$ is:

Maximize $z=4x_1+3x_2$ subject to constraints:$2x_1+x_2\le 1000$$x_1+x_2\le 800$$x_1\le 400$$x_2\le 700$$x_1,x_2\ge 0$ Find the optimum units of $x_1$ and $x_2$ to be used.

Let $f(x)=x+x^{-1}$. Then which of the following is correct?

Rate of growth of bacteria is proportional to the number of bacteria present at time. If $x$ is the number of bacteria present at any instant $t$, then which one of the following is correct? (Let the proportional constant equal to $2$)

Find the condition on $k$, so that the system of equations: $x+3y=5$ and $2x+ky=8$ has a unique solution.

If $\theta$ is the acute angle between the diagonals of a cube, then which one of the following is correct?

The value of $[\vec{a}+2\vec{b}-\vec{c},\vec{a}-\vec{b},\vec{a}-\vec{b}-\vec{c}]$ is:

If $f(x)=|x+1|+|x+10|$, then find the minimum value of $f(x)$.

The length of the perpendicular drawn from the origin to the plane $2x-3y+6z-42=0$ is:

If a line has direction ratios $⟨a+b,b+c,c+a⟩$, then what is the sum of the squares of its direction cosines?

If $x^e=e^{x^2+y^2}$, then find $\frac{dy}{dx}$.

Consider the Linear Programming problem:Maximize: $7X_1+6X_2+4X_3$ subject to:$X_1+X_2+X_3\le 5$$2X_1+X_2+3X_3\le 10$$X_1,X_2,X_3\ge 0$ The number of basic solutions is:

A manufacturing firm has its variable cost given by $C(x)=x(12-x^3)$. The price per unit is $p(x)=6x-2$. Find the marginal revenue when $3$ units were in demand.

A solution of $100\text{L}$ contains $75\%$ water and the rest liquid sugar. How much liquid sugar must be added to make it a $50\%$ sugar solution?

A card is drawn at random from a pack of $52$ cards. What is the probability that the card drawn is either an Ace or a King?

The mean of the probability distribution function given by the following table will be:\begin{center}\begin{tabular}{|c|c|c|c|c|c|}\hline$x$ & 1 & 2 & 3 & 4 & 5 \ \hline$P(x)$ & 0.2 & 0.35 & 0.25 & 0.15 & 0.05 \ \hline\end{tabular}\end{center}

Maximize $z=5x_1+3x_2$ subject to the following constraints:$x_1+x_2\ge 3$$x_1-x_2\le 2$ and the solution is in the first quadrant ($x_1,x_2\ge 0$). What can be said about the solution of this LPP?

If $f$ and $g$ are differentiable functions in $(0,1)$ satisfying $f(0)=2=g(1)$, $g(0)=0$ and $f(1)=6$, then for some $c\in (0,1)$:

Given that $x$ is a random variable in the range $[0,\infty )$ with a probability density function $f(x)=\frac{e^{-x/2}}{K}$, the value of the constant $K$ is:

Find the present value of a sequence of payments of $Rs.432$ made at the end of each $5$ months and continuing forever if money is worth $5\%$ compounded at the end of each $5$ months.

A cricket bat manufacturing firm assesses its variable cost to be $2x(x-40)$, where $x$ is the number of bats produced, and the fixed cost incurred on storage is $Rs.1200$. How many bats should be manufactured for the minimum total cost?

The value of $k$ for which the system of equations $x+ky+3z=0$, $4x+3y+kz=0$, $2x+y+2z=0$ has a non-trivial solution is:

Using the base year 1985, the index number calculated by the simple aggregate method for four items (A, B, C, D) is $125$. Given:Prices in 1985: $75,85,\alpha ,100$ Prices in 1986: $90,115,75,\beta$ Find the value of $(4\beta -5\alpha )$.

Let $k$ be the order of $a(\mathrm{mod}n)$, then $a^b\equiv 1(\mathrm{mod}n)$ if and only if:

Which of the following statement is true regarding sinking fund and saving account?

If $|3x-5|\le 2$, then:

For a continuous random variable $X$ distributed in the interval $[0,10]$, the probability $P(X=2)$ is:

Calculate the value of:
$${\int }_{1/2}^2\frac{1}{x}\sin \left(x-\frac{1}{x}\right)dx$$

Let $R=\{(a,b):a,b\in \mathbb{N}\text{ and }{a}^2=b\}$. Which property does the relation $R$ satisfy?

Evaluate:
$$\int \frac{1}{e^x+e^{-x}}dx$$

Find the area under the curve $y=\cos x$ in the interval $0\le x\le \pi /2$.

Consider the following statements:I. The derivative, where the function attains maxima or minima, is zero.II. If a function is differentiable at a point, then it must be continuous at that point.Which of the above statement(s) is/are correct?

If $a_{ij}=\frac{1}{2}(3i-2j)$ and $A=[a_{ij}{]}_{2\times 2}$, then $A$ is equal to:

Find the area of the region (in sq. units) bounded by the curve $y=x,y=x^2+2$ for $x\in (-1,1)$.

Let $A=\left[\begin{array}{ccc}4& 6& -1\\ 3& 0& 2\\ 1& -2& 5\end{array}\right]$, $B=\left[\begin{array}{cc}2& 0\\ -1& 4\\ 1& 2\end{array}\right]$, and $C=[312]$. The expression which is not defined is:

The area bounded by the curve $x^2=ky,k>0$, and the line $y=3$ is $12{\text{ units}}^2$. Then $k$ is:

Find the value of $f(x)$ when:
$$f(x)={\int }_0^x\frac{dt}{t^2+9}$$

If ${\tan }^{-1}(2)$ and ${\tan }^{-1}(3)$ are two angles of a triangle, then what is the third angle?

What is the domain of the function $f(x)=\cos ({\sin }^{-1}(x+1))$?

If the area of a triangle with vertices $(-3,0),(3,0)$ and $(0,k)$ is $9$ square units, then what is the value of $k$?

If $y=\cos ({\sin }^{2}x)$, then find the value of $\frac{dy}{dx}$ at $x=\pi /2$.