CUET Mathematics Mock Test - 3

The projection of a vector on another vector is:

The solution of $\int \frac{\log x}{x^2}dx$ is:

The degree of the given equation is $\frac{dy}{dx}-x={\left(y-x\frac{dy}{dx}\right)}^{-6}$

The function $y=f(x)$ has relative minima where:

What is the principal value of ${\text{cosec}}^{-1}(-\sqrt{2})$?

The line with direction ratios $1,0,-1$ is inclined with the $z$ -axis at an angle of:

If $\left[\begin{array}{ccc}1& x& 1\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 3& 2& 5\end{array}\right]\left[\begin{array}{c}1\\ -2\\ 3\end{array}\right]=0$, then the value of $x$ is:

Let $f(x)=\{\begin{array}{ll}3x-4,& 0\le x\le 2\\ 2x+l,& 2<x\le 3\end{array}$. If $f$ is continuous at $x=2$, then what is the value of $l$?

The number that exceeds its square by the greatest amount is:

If $c$ is a point at which Rolle's theorem holds for the function $f(x)={\log }_e\left(\frac{x^2+\alpha }{7x}\right)$ in the interval $[3,4]$, then the value of $c$ is:

If the curve $y=a{x}^2+bx+c$ passes through $(1,2)$ and the tangent to this curve at the origin is $y=x$, then the possible values of $a,b,c$ are:

The mean of the numbers obtained on throwing a die having written $5$ on four faces, $4$ on three faces, $3$ on two faces and $2$ on one face is?

A continuous random variable $X$ has a probability density function $f(x)=e^{-x},0<x<\infty$. Then $P(X>1)$ is:

A discrete random variable $X$ has the following probability function:$X:0,1,2,3,4,5,6,7,8$$f(x):k,2k,3k,5k,5k,4k,3k,2k,k$ The value of $E(X)$ is:

A continuous random variable $X$ has uncountably many values in the interval $[a,b]$. If $C$ is a value in the interval $[a,b]$, then $P(X=C)$ is:

Let $R$ be a relation on the set of natural numbers defined by $xRy⟺x\le y$. Which one of the following is correct?

If a function is defined as $f:\mathbb{N}\to \mathbb{N},f(x)=\frac{x-1}{2}$, then which of the following is true regarding this function?

For a Linear Programming Problem, $Z=2x+4y$. Feasible corner points are $O(0,0),A(0,2.5),B(3,1),C(4,0)$. What is the optimal maximized value of $Z$?

$M$ is a square matrix of order $n$ and $|M|=5$. If all elements of $M$ are multiplied by $2$, the determinant becomes $40$. The value of $n$ is:

Evaluate: ${\tan }^{-1}(1)+{\cos }^{-1}(-1/2)+{\sin }^{-1}(-1/2)$

The differential coefficient of $f(\log x)$ when $f(x)=\log x$ is:

The system of equations $x+2y+z=0,x-z=k,x+y=0$ has infinitely many solutions. If $\text{adj}(A)=\left[\begin{array}{ccc}1& 1& -2\\ -1& -1& 2\\ 1& 1& -2\end{array}\right]$, then the possible value of $k$ is:

The points $(5,-2),(8,-3)$ and $(a,-12)$ are collinear if the value of $a$ is:

Given $\vec{a}=2\hat{i}$, $\vec{b}=\hat{i}+\hat{j}+\hat{k}$, $\vec{c}=2\hat{k}$ and $\vec{x}-\vec{w}=\vec{v}$ where $\vec{w}=\vec{b}-\vec{a}$ and $\vec{v}=\vec{b}-\vec{c}$. Then $\vec{x}$ is:

The lines $\frac{x+3}{-4}=\frac{y-6}{3}=\frac{z}{2}$ and $\frac{x+2}{-4}=\frac{y}{1}=\frac{z-7}{1}$ are:

Find ${\lim }_{n\to \infty }\left(\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+\cdots +\frac{1}{3n}\right)$

If a matrix $A$ is such that $3A^3+2A^2+5A+I=O$, then what is $A^{-1}$ equal to?

Let $A$ and $B$ be two events such that $P(\overline{A\cup B})=\frac{1}{6}$, $P(A\cap B)=\frac{1}{4}$ and $P(\bar{A})=\frac{1}{4}$. Then, events $A$ and $B$ are:

Maximize $Z=2X_1+3X_2$ subject to $2X_1+X_2\le 6$, $X_1-X_2\ge 3$, $X_1,X_2\ge 0$. The solution to the LPP is:

Which of the following is NOT true for matrices $A,B,C$ (assuming dimensions allow operations)?

What is the area bounded by the curves $|y|=1-x^2$?

If $I_1=\int \frac{e^x}{e^x+e^{-x}}dx$ and $I_2=\int \frac{dx}{e^{2x}+1}$, then what is $I_1+I_2$ equal to?

If $f(x)=2\ln (e^{x/2})$, what is the area bounded by $f(x)$ for the interval $[0,2]$ on the x-axis?

Find the area of the parabola $y^2=4ax$ bounded by its latus rectum.

Ram is a fruit seller. Apples cost Rs 80/kg and Mangoes Rs 120/kg. Profits are Rs 10/kg and Rs 12/kg respectively. Let $x$ be kgs of apples and $y$ be kgs of mangoes. If Ram wants to maximize profit, the objective function $Z$ is:

The function $y=e^{-4x}$ is a solution to the differential equation:

The value of ${\int }_{-1}^3[{\tan }^{-1}(\frac{x}{x^2+1})+{\tan }^{-1}(\frac{x^2+1}{x})]dx$ is:

Solve $\frac{dy}{dx}=e^{x-y}(e^x-e^y)$

The function $f(x)=8{\log }_{e}x-x^2+3$ attains its global minimum over the interval $[1,e]$ at $x=\dots$

For a point of inflection of $y=f(x)$, which one of the following is correct?

The identity element for the binary operation $\ast$ defined on $\mathbb{Q}-\{0\}$ as $a\ast b=\frac{ab}{2}$ is:

What is the cosine of the angle between the planes $x+y+z+1=0$ and $2x-2y+2z+1=0$?

If $P=\hat{i}+3\hat{j}-2\hat{k}$ and $Q=3\hat{i}+\hat{j}-2\hat{k}$, then what is the position vector of the bisector of $\angle POQ$?

If $x$ is a real number, the function $f(x)=x^3+x^2+x+1$ has:

Find the absolute minimum value of the function $y=3x^2-4$ in the interval $[-1,5]$.

Find the solution set of $y$ for the system: $10x+8y\le 80$, $x\ge 0$, $y\ge 6$.

If $A$ is the identity matrix of order 3 and $B$ is its transpose, then what is the value of the determinant of the matrix $C=A+B$?

What is the area under the curve $f(x)=x{e}^x$ above the x-axis and between $x=0$ and $x=1$?

Find the value of $\sin \left(\frac{\pi }{3}-{\sin }^{-1}(-\frac{1}{2})\right)$

A pair of fair dice is thrown. What is the probability of getting a six on both, given at least one die gets six?