CUET UG Mathematics — Algebra previous year questions with solutions.
The probability that a student is not a swimmer is $\frac{1}{5}$. Then the probability that out of five students, four are swimmers is :
Let A = PQ. The elementary operation on A, that produces the same effect as it does on applying on P and keeping Q unchanged is : (A) $R_i \leftrightarrow R_j$ (B) $R_i \to R_i + KR_j$ (C) $C_i \to KC_i$ (D) $C_i \to C_i + KC_j$ Choose the **correct** answer from the options given below :
If matrix $A = \begin{bmatrix} 3 & x \\ y & 0 \end{bmatrix}$ and $A' = A$, then :
The value of $\begin{vmatrix} \sqrt{3}/2 & 1/2 \\ \sqrt{3}/2 & 1/2 \end{vmatrix}$
The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are :
Let $f : R \to R$ defined by $f(x) = 2x^3 - 7$ for $x \in R$. Then : (A) $f$ is one-one function (B) $f$ is many to one function (C) $f$ is bijective function (D) $f$ is into function Choose the correct answer from the options given below :
The area of the parallelogram determined by the vectors $\hat{i} + 2\hat{j} + 3\hat{k}$ and $3\hat{i} - 2\hat{j} + \hat{k}$ is
Let $A = \begin{bmatrix} 3 & -1 \\ 2 & 4 \end{bmatrix}$, then adjoint (A) is:
Owner of a whole sale computers shop plans to sell 2 types of computers. A desktop and portable model. If $x$ is the number of desktops and $y$ is the number of portable model and the shop's capacity cannot exceed 250 units. Which of the following is correct ?
The inverse of the function $f : R \to R$ given by $f(x) = 2x + 7$ is :
The random variable X has a probability distribution P(X) of the following form, where k is some number. $P(X=x) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$ Then $P(x \leq 2)$ is :
The solution of a LPP with basic feasible solutions (0, 0), (10, 0), (0, 20), (10, 15) and objective function Max $Z = 2x + 3y$ is :
The matrix $A = \begin{bmatrix} 0 & 1 & -3 \\ -1 & 0 & 0 \\ 3 & 0 & 0 \end{bmatrix}$ is a
In a box containing 100 bulbs, 10 are defective. Then the probability, that out of a sample of 5 bulbs none is defective, is:
Let A = {1,2,3}. Consider the relation R = {(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}. Then R is
A manufacturer can sell $x$ items at a price of Rs $3x+5$ each. The cost price of $x$ items is Rs $x^2 + 5x$. If x is the number of items she should sell to get no profit and no loss, then:
If the matrix $A = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$, then $A^2$ is equal to:
Match List I with List II | LIST I | LIST II | |---|---| | A. The area of parallelogram determined by vectors $2\hat{i}$ and $3\hat{j}$ | I. 2 | | B. The value of $(\hat{i} \times \hat{j}) \cdot \hat{k} + (\hat{j} \times \hat{k}) \cdot \hat{i}$ | II. 4 | | C. The value of a for which the vectors $2\hat{i} - 3\hat{j} + 4\hat{k}$ and $a\hat{i} - 6\hat{j} + 8\hat{k}$ are collinear. | III. 0 | | D. The value of $\lambda$ for which the vectors $2\hat{i} + \hat{j} + \hat{k}$ and $2\hat{i} - 4\hat{j} + \lambda\hat{k}$ are perpendicular | IV. 6 | Choose the correct answer from the options given below:
If three points $A(a_1, b_1), B(a_2, b_2)$ and $C(a_3, b_3)$ are collinear and $D = \begin{vmatrix} a_1 & b_1 & 1 \\ a_2 & b_2 & 1 \\ a_3 & b_3 & 1 \end{vmatrix}$, then:
Which of the following statements is NOT CORRECT.
The range of the function $f(x) = \frac{1}{3 - \sin 4x}$ is:
A coin is tossed 7 times. The probability of getting at least 4 heads is:
The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is $z = 4x + 3y$. Compare the quantity in Column - A and Column - B. | Column - A | Column - B | |---|---| | Maximum value of z | 350 |
A and B throw a die alternatively till one of them gets a number more than 4 and wins the game. Then the probability of winning the game by B, if A starts first :