CUET UG Mathematics — Algebra previous year questions with solutions.
If the area of a triangle with vertices $(-3,0)$, $(3, 0)$ and $(0, k)$ is 9 sq. units, then k equals
If A is a square matrix of order 3 such that $|A| = 3$, then $|adj(adj A)|$ is equal to:
The corner points of the bounded feasible region for an LPP are (0,4), (4,4), (6,6), (0,12). If the objective function is $Z = px + qy, p > 0, q > 0$, then the condition on p and q so that maximum of Z occurs at (6,6) and (0,12) is
Which of the following terms are associated with a linear programming problem? (A) Constraints (B) Independent events (C) Feasible region (D) Objective function Choose the correct answer from the options given below:
Match List-I with List-II | List-I | List-II | |---|---| | (A) The vectors $\lambda\hat{i}$ $ + \hat{j} + 2\hat{k}$ and $\vec{i} + \lambda\hat{j} + \hat{k}$ are perpendicular if λ is equal to | (I) 1 | | (B) The vectors $3\hat{i} + 6\hat{j} - \hat{k}$ and $2\hat{i} + 4\hat{j} - \lambda\hat{k}$ are collinear if λ is equal to | (II) -1 | | (C) The number of vectors of unit-length which are perpendicular to both the vectors $\vec{a}$ = $\hat{i} + \hat{j} + 2\hat{k}$ and $\vec{b}$ = $3\hat{i} - \hat{j} + 5\hat{k}$ is | (III) 2/3 | | (D) If $\lvert \vec{a} \rvert = 1$ and $\vec{a} + \vec{b} = \vec{0}$, then $\lvert \vec{b} \rvert$ is equal to | (IV) 2 | Choose the correct answer from the options given below:
For independent events $A_1, A_2, A_3, ..., A_n$ if $P(A_i) = \frac{1}{i+1}$, $i = 1, 2, 3, ..., n$, then the probability that none of the events occur is:
Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success, then the probability of at most 3 successes is
If, in a pair of consecutive positive integers, both numbers are greater than 5 and their sum is less than 23, then the number of such pairs are:
If $A$ is a square matrix such that $A^2 = A$ and $I$ is the identity matrix of the same order as $A$, then $(I + 2A)^2 - 5A$ is equal to
For the objective function $Z = 3x + 5y$ subject to constraints $x + 3y \geq 3$, $x + y \geq 2$, $x \geq 0$, $y \geq 0$:
The corner points of the bounded feasible region of the LPP: Maximize $z = x + y$ subject to constraints $2x + 5y \leq 100$, $8x + 5y \leq 200$, $x \geq 0$, $y \geq 0$ are
The corner points of a bounded feasible region determined by the following system of linear inequalities $x + 3y \leq 60, x + y \geq 10$, $x \leq y$, $x \geq 0$, $y \geq 0$ are (0,10), (5,5), (15, 15) and (0, 20). Let $z = 2px + qy$, $p, q > 0$. If maximum of z occurs at both (15, 15) and (0, 20), then the relation between p and q is
if $A = \begin{bmatrix}1 & 0\\3 & 1\end{bmatrix}$ and $A^4 = \begin{bmatrix}1 & 0\\k & 1\end{bmatrix}$ then value of $k$ is
The corner points of the bounded feasible region determined by a set of constraints in an LPP are $P(0, 5)$, $Q(3, 5)$, $R(5, 0)$ and $S(4, 1)$. If the objective function is $z = ax + 2by$, where, $a, b > 0$, then the condition on $a$ and $b$ such that the maximum value of $z$ occurs at $Q$ and $S$ is
The probability distribution of a random variable X is given by | X | 0 | 1 | 2 | |---|---|---|---| | P(X) | $1 - 7a^2$ | $\frac{1}{2}a + \frac{1}{4}$ | $a^2$ | If $a > 0$, then $P(0 < x \leq 2)$ is equal to
If the difference between mean and variance of a Binomial distribution is 1 and the difference of their squares is 5, then the probability of success is
The corner points of the bounded feasible region determined by the system of linear constraints are (15,0), (40,0), (4,18) and (6, 12). If objective function is Z = 30x + 20y, then the sum of the maximum and the minimum values of Z is
The value of $\begin{vmatrix} 1 & bc & bc(b+c) \\ 1 & ca & ca(c+a) \\ 1 & ab & ab(a+b) \end{vmatrix}$ is
If $\vec{a}$ is any vector, then $|\vec{a} \times \hat{i}|^2 + |\vec{a} \times \hat{j}|^2 + |\vec{a} \times \hat{k}|^2$ is equal to
The curve $y = f(x)$ is normal probability curve, then which of the following statements are correct? (A) mean, median and mode of the distribution coincide. (B) the area bounded by the curve $y = f(x)$ and $x$-axis is one unit. (C) The curve is symmetrical about the line $x = \mu$, where $\mu$ is the mean. (D) $y$-axis is an asymptote to the curve. Choose the correct answer from the options given below:
Match List-I with List-II Let A & B are two events such that P(A)=0.8, P(B)=0.5, P(B|A)=0.4 | List-I | List-II | | :--- | :--- | | (A) $P(A \cap B)$ | (I) 0.2 | | (B) $P(A \mid B)$ | (II) 0.32 | | (C) $P(A \cup B)$ | (III) 0.64 | | (D) $P(A')$ | (IV) 0.98 | Choose the correct answer from the options given below:
If the system of equations $kx + y + z = 0$, $x + ky - z = 0$, $x - y + z = 0$ has a non-zero solution, then the possible values of $k$ are:
Let f: $\mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = 10x$. Then (Where $\mathbb{R}$ is the set of real numbers)
A die is tossed 6 times and getting "1 or 5" is considered a success. The probability of getting at least one success in six tosses is: