CUET UG Mathematics — Algebra previous year questions with solutions.
If $|\vec{a}| = |\vec{b}| = |\vec{a} + \vec{b}| = 1$, then $|\vec{a} - \vec{b}|$ is equal to:
Arrange the vectors in descending order of their magnitudes. (A) $\hat{i} + \hat{j} + \hat{k}$ (B) $2\hat{i} - 3\hat{j}$ (C) $\frac{1}{2}\hat{i} - \frac{1}{3}\hat{j}$ (D) $2\hat{i} - \hat{k}$ Choose the correct answer from the options given below :
The probability that the study time of students is exactly 2 hours
If $f:\mathbb{R} \to [-5, \infty)$ is defined as $f(x) = x^2 - 5$, then the function f is A. one-one B. many-one C. onto D. into Which of the above statements are true? Choose the correct answer from the options given below:
If $-3 \leq k \leq 1$ and $|\vec{a}| = 2$ then $|k\vec{a}|$ is
The probability that he copied it given that his answer is correct :
In linear programming, the optimal value of the objective function is attained at the points given by
A die is tossed four times. The probability of getting an odd number at least once, is
The minimum cost of the mixture is-
If $|\vec{a}| = 8$, $|\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 12$, then the value of $\vec{a} \cdot \vec{b}$ is
The area of rectangular field is:
If the points $(2, -3)$, $(\lambda, -1)$ and $(0, 4)$ are collinear, then the value of $\lambda$ is :
In Binomial distribution with parameters $n = 12$ and $p = \frac{1}{3}$, value of $E(X^2) + E(X)$ is :
A letter is expected to come either from city 'SURAT' or from city 'RAMPUR' through post office. If on the way, envelope containing the letter is damaged and only two consecutive alphabets RA are visible on it, then the probability that letter comes from the city 'SURAT' is :
If A and B are square matrices of same order n, then identify correct statements from the statements given below: A. $|adj\ A| = |A|^{n-1}$ B. $|A \cdot B| = |B| \cdot |A|$ C. $adj\ A' = (adj\ A)'$ D. $adj\ AB = (adj\ A) \cdot (adj\ B)$ E. $|A^n| = |A|^n$ Choose the correct answer from the options given below:
The Relation $R = \{(x, y) : x \leq y^2\}$ defined on the set $\mathbf{R}$ of Real numbers is : (A) reflexive but not symmetric (B) neither reflexive nor symmetric (C) neither reflexive nor transitive (D) reflexive but not transitive (E) not reflexive but symmetric Choose the correct answer from the options given below :
The matrix $\begin{bmatrix} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{bmatrix}$ is: A. a square matrix B. a scalar matrix C. a diagonal matrix D. an identity matrix Which of the above statements are true? Choose the correct answer from the options given below:
The probability that task is completed on time by at least one of them is:
The 10th term of AP: 3, 7, 11, 15, ... is
The equations in terms of $x$ and $y$ are:
The value of the expression $\frac{x^2 + y^2}{x - y}$ is:
The number of all different possible matrices of order $2 \times 2$ with each entry $-1$, $0$ or $1$ is :
The constraints to the LPP are: A. $3x + 2y \leq 720$ B. $2x + 3y \leq 720$ C. $x + y \leq 300$ D. $x \geq 0$ and $y \geq 0$ E. $x + y \geq 300$ Choose the correct answer from the options given below:
If the objective function for an LPP is max.$(z) = 300x + 700y$ and the corner points for the bounded feasible region are $(6,0)$ $(5,0)$ $(0,6)$ $(4,4)$ and $(0,4)$, then the maximum values of z occurs at :