CUET UG Mathematics — Algebra previous year questions with solutions.
The function $f: \mathbb{R} \rightarrow [-1, 1]$ defined by $f(x) = \cos x$ is:
For $I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, if $X$ and $Y$ are square matrices of order $2$ such that $X Y=X$ and $Y X=Y$, then $\left(\mathrm{Y}^{2}+2 \mathrm{Y}\right)$ equals to :
If $A$ and $B$ are symmetric matrices of the same order, then $A B-B A$ is a :
Match the options of **List-I** to **List-II** : | List-I | List-II | | --- | --- | | (A) $ k $ | (I) $ \frac{7}{10} $ | | (B) $ P(X < 3) $ | (II) $ \frac{53}{100} $ | | (C) $ P(X > 2) $ | (III) $ \frac{1}{10} $ | | (D) $ P(2 < X <7 ) $ | (IV) $ \frac{3}{10} $ | Choose the **correct** answer from the options given below :
If $A$ is a square matrix and $I$ is an identity matrix such that $A^{2}=A$, then $A(I-2 A)^{3}+2 A^{3}$ is equal to :
The corner points of the feasible region determined by $x+y \leq 8, 2 x+y \geq 8, x \geq 0, y \geq 0$ are $A(0,8), B(4,0)$ and $C(8,0)$. If the objective function $Z=a x+$ by has its maximum value on the line segment $A B$, then the relation between $a$ and $b$ is :
If $\mathrm{A}=\left[\begin{array}{ll}2 & 4 \\ 4 & 3\end{array}\right], \mathrm{X}=\left[\begin{array}{l}\mathrm{n} \\ 1\end{array}\right], \mathrm{B}=\left[\begin{array}{c}8 \\ 11\end{array}\right]$ and $A X=B$, then the value of $n$ will be :
If $P=\left[\begin{array}{r}-1 \\ 2 \\ 1\end{array}\right]$ and $Q=\left[\begin{array}{lll}2 & -4 & 1\end{array}\right]$ are two matrices, then $(P Q)^{\prime}$ will be :
The probability of a shooter hitting a target is $\frac34$. How many minimum number of times must he fire so that the probability of hitting the target at least once is more than $90 \%$ ?
Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be :
For a square matrix $A_{n \times n}$ (A) $|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{\mathrm{n}-1}$ (B) $|\mathrm{A}|=|\operatorname{adj} \mathrm{A}|^{\mathrm{n}-1}$ (C) $\mathrm{A}(\operatorname{adj} \mathrm{A})=|\mathrm{A}|$ (D) $\left|\mathrm{A}^{-1}\right|=\frac{1}{|\mathrm{~A}|}$
Let R be the relation over the set A of all straight lines in a plane such that $l_{1} \mathrm{R} l_{2} \Leftrightarrow l_{1}$ is parallel to $l_{2}$. Then R is :
If the matrix $\left[\begin{array}{rrr}0 & -1 & 3 x \\ 1 & y & -5 \\ -6 & 5 & 0\end{array}\right]$ is skew-symmetric, then the value of $5 x-y$ is:
The corner points of the feasible region for an L.P.P. are $(0,10),(5,5),(5,15)$ and $(0,30)$. If the objective function is $Z=\alpha x+\beta y, \alpha, \beta>0$, the condition on $\alpha$ and $\beta$ so that maximum of $Z$ occurs at corner points $(5,5)$ and $(0,20)$ is :
Choose the **correct** answer from the options given below :
If f(x) = x² + 2x + 1, then f(3) equals
If $A$ is a square matrix of order $4$ and $|A|=4$, then $|2 A|$ will be :
A die is rolled thrice. What is the probability of getting a number greater than $4$ in the first and the second throw of dice and a number less than $4$ in the third throw ?
If $[\mathrm{A}]_{3 \times 2}[\mathrm{~B}]_{\mathrm{x} \times \mathrm{y}}=[\mathrm{C}]_{3 \times 1}$, then :
A person wants to invest an amount of ₹ $75,000$. He has two options A and B yielding $8 \%$ and $9 \%$ return respectively on the invested amount. He plans to invest at least ₹ $15,000$ in Plan A and at least ₹ $25,000$ in Plan B. Also he wants that his investment in Plan A is less than or equal to his investment in Plan B. Which of the following options describes the given LPP to maximize the return (where $x$ and $y$ are investments in Plan A and Plan B respectively) ?
The solution set of the inequality $|3 x| \geq|6-3 x|$ is :
Three defective bulbs are mixed with $8$ good ones. If three bulbs are drawn one by one with replacement, the probabilities of getting exactly $1$ defective, more than $2$ defective, no defective and more than $1$ defective respectively are:
There are $6$ cards numbered $1$ to $6$, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two cards drawn. Then $\mathrm{P}(\mathrm{X}>3)$ is :
If $\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors such that $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$, where $\vec{a}$ and $\vec{b}$ are unit vectors and $|\vec{c}|=2$, then the angle between the vectors $\vec{b}$ and $\vec{c}$ is :