CUET UG Mathematics — Algebra previous year questions with solutions.
If $\theta$ is the acute angle between two unit vectors $\vec{a}$ and $\vec{b}$, then $\cos\frac{\theta}{2} =$
The type of feasible region and its corner points are. A. bounded B. unbounded C. (0,5), (2,4), (10,0) D. (0,8), (2,4), (4,0) E. (0,8), (2,4), (10,0) Choose the correct answer from the options given below:
The feasible solution to the LPP is-
The value of $P(E)$ is
The probability of 'the student knows the answer given that he answered it correctly' is
The vertices of a closed convex polygon representing the feasible region of the LPP with, objective function $z = 5x + 3y$ are $(0, 0)$, $(3, 1)$, $(1, 3)$ and $(0, 2)$. The maximum value of $z$ is
If $2 \begin{bmatrix} a & d \\ b & c \end{bmatrix} + 3 \begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix} = 3 \begin{bmatrix} 3 & 5 \\ 4 & 6 \end{bmatrix}$, then the value of $|a + b - c - d|$ is
Which of the following is true on the basis of above diagram?
The probability that exactly two of them complete the task on time is
The length ($x$) and breadth ($y$) of plot satisfy equations:
The linear equation involving $x$ and $y$ are written in matrix form as:
Value(s) of $x$ for which, $\begin{vmatrix} x & 1 \\ 5 & x \end{vmatrix} = \begin{vmatrix} 8 & 2 \\ 2 & 1 \end{vmatrix}$ is:
If R is a relation on $A = \{a, b, c\}$ such that $R = \{(a,a), (b,b)\}$, which element/elements should be included to make R an equivalence relation. A. (c, c) B. (c, c), (a, c), (c, a) C. (a, b), (b, c), (a, c) D. (b, c), (c, c), (c, a), (b, a) Choose the correct answer from the options given below:
A function f: R $\to$ R is given by $f(x) = x^3 + 3$. If $f(x) = -24$, then the value of x is:
Match List I with List II: Given that A and B are invertible matrices of size $3 \times 3$ | List I | List II | |---|---| | A. $\lvert AB \rvert$ | I. $\frac{1}{\lvert A \rvert}$ | | B. $\lvert \operatorname{Adj} A \rvert$ | II. $\lvert A \rvert \lvert B \rvert$ | | C. $\lvert A^{-1} \rvert$ | III. $B^{-1} \cdot A^{-1}$ | | D. $(AB)^{-1}$ | IV. $\lvert A \rvert^2$ | Choose the correct answer from the options given below:
When the doctor arrives late, what is the probability that he comes by metro?
If the system of linear equations $x + 2y - 3z = 1$ $(2p+1)y + z = 2$ $3x + 3z = 5$ has a unique solution, then p can not be equal to
Match List I with List II | List I | List II | |---|---| | A. Range of $\lvert x\rvert$ | I. $(-5, \infty)$ | | B. Range of $9x^2 + 6x - 5$ for all $x \geq 0$ | II. $[0, \infty)$ | | C. Domain of $\dfrac{1}{\sqrt{x+5}}$ | III. $\{(1,1), (2,2), (3,3)\}$ | | D. Smallest equivalence relation on Set $\{1,2,3\}$ | IV. $[-5, \infty)$ | Choose the correct answer from the options given below:
If A is a square matrix of order 3 and $|adj A| = 49$, then $|7A^{-1}|^2$
If $3A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ x & 2 & y \end{bmatrix}$ and $AA^T = I$, then $x + y$ is equal to
In a triangle, $\triangle ABC$, the sides AB and AC are represented by vectors $\hat{i} + \hat{j} + \hat{k}$ and $2\hat{i} - \hat{k}$ respectively. The length of median drawn from vertex A to BC is:
Let $\vec{OA} = 2\hat{i} - \hat{j} + \hat{k}$ and $\vec{OB} = \hat{i} + \hat{j} - \hat{k}$. Then A. The magnitude of vector $\vec{OA}$ is 6 B. The magnitude of vector $\vec{OB}$ is $\sqrt{3}$ C. The vector $\vec{AB}$ is $(-\hat{i} + 2\hat{j} - 2\hat{k})$ D. $\vec{OA} \cdot \vec{OB} = 0$ E. $\vec{OA} \parallel \vec{OB}$ Choose the correct answer from the options given below:
If A and B are two independent events such that $P(A) = 0.4$, and $P(B) = 0.5$, then P (neither A nor B) is
The probability that the study time of students is at least 3 hours