CUET UG Mathematics — Algebra previous year questions with solutions.
The maximum value of the objective function $Z = 2x + y$ of an LPP, subject to the constraints $x \leq 6, y \leq 2, x - y \leq 0$, $x \geq 0, y \geq 0$ is
A box contains 10 balls, each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, then the probability that none is marked with the digit 0 is:
A vector of magnitude 9, which is perpendicular to both the vectors $(4\hat{i} - \hat{j} + 8\hat{k})$ and $(-\hat{j} + \hat{k})$ is
The probabilities of occurrence of two events E and F are 0.25 and 0.50 respectively. The probability of their simultaneous occurrence is 0.14. The probability that neither E nor F occurs is
Let $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\vec{b} = -2\hat{i} + 3\hat{j} - 4\hat{k}$, then which of the following statements are correct? (A) $|\vec{a}| = \sqrt{14}$ (B) $|\vec{b}| = 29$ (C) $\vec{a} \cdot \vec{b} = 8$ (D) Angle between $\vec{a}$ and $\vec{b}$ is $\cos^{-1}\left(\frac{-8}{\sqrt{406}}\right)$ Choose the correct answer from the options given below:
An urn contains 5 red and 5 black balls. A ball is drawn at random, its color is noted and is returned to the urn. Moreover, 2 additional balls of the same color are put in the urn and then a ball is drawn at random. The probability that the second drawn ball is red, is:
Which of the following are correct about the linear programming problem(LPP)? (A) The objective function is always linear. (B) A corner point of a feasible region is a point in the region which is the intersection of two boundary lines. (C) The common region determined by all the linear constraints of a LPP is called the feasible region. (D) If an LPP admits optimal solution at two points then its optimal values occurs at an infinite number of points. Choose the correct answer from the options given below:
The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of Z = 11x + 7y is 
If A and B are independent events such that $P(A|B) = \frac{1}{3}$ and $P(B) = \frac{1}{2}$, then the value of $P(A \cap B)$ is equal to
Let $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + \hat{2j} + 3\hat{k}$ then a unit vector perpendicular to both vectors $(\vec{a} + \vec{b})$ and $(\vec{a} - \vec{b})$ is equal to
If A is any event associated with sample space and If $E_1, E_2, E_3$ are mutually exclusive and exhaustive events. Then which of the following are true? (A) $P(A) = P(E_1)P(E_2|A) + P(E_2)P(E_2|A) + P(E_3)P(E_3|A)$ (B) $P(A) = P(A|E_1)P(E_1) + P(A|E_2)P(E_2) + P(A|E_3)P(E_3)$ (C) $P(E_i|A) = \frac{P(A|E_i)P(E_i)}{\sum_{i=1}^3 P(A|E_i)P(E_i)}$, $i = 1,2,3$ (D) $P(A|E_i) = \frac{P(E_i|A)P(E_i)}{\sum_{i=1}^3 P(E_i|A)P(E_i)}$, $i = 1,2,3$ Choose the correct answer from the options given below:
If the system of equations $2x + 5y = 7, 6x + \lambda y = 28$ is inconsistent, then
Which of the following statements are correct? (A) Inverse of a matrix, if it exists, is unique (B) $(kA)' = -kA'$ (where k is any real number) (C) For an invertible matrix $A$, $(A^{-1})^{-1} = A$ (D) For an invertible matrix $A$, $(A')^{-1} = (A^{-1})'$ Choose the **correct** answer from the options given below:
Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is: [Given $e^{-2}=0.135$]
Which of the following statements are correct? (A) The mean and variance of the Poisson distribution are equal. (B) The mean and variance of a Binomial distribution are equal. (C) An unbiased die is thrown again and again until two sixes are obtained, then the probability of obtaining the second six in the 3rd throw is $\frac{5}{108}$. (D) If the variance of a Poisson distribution is 2, then P(X = 2) = $2e^{-2}$ Choose the **correct** answer from the options given below:
A Linear Programming Problem (LPP) consists of which of the following components? (A) Decision variables (B) The graphical compliment (C) The objective function (D) The linear constraints Choose the **correct** answer from the options given below:
The range of function $f(x) = 4x^2 + 12x + 7, x \in \mathbb{R}$ is
For a square matrix $A$ of order 3, if $|A| = 2$, then $|adj\ 2A| =$
The value of k for which the system of equations $x + y + z = 1$ $x - ky + z = 1$ $x - y + z = 1$ has more than one solutions is
60% members of a committee favour a certain proposal and 40% members oppose the proposal. A member is selected and let the random variable X = 0 if he opposes and X = 1 if he is in favour. Then the variance of the random variable X is
The objective function of an LPP is $z = ax + \beta y, (a, \beta > 0)$ in that has to be maximized/minimized subject to constraints $x + y \leq 2$, $x \geq 0$, $y \geq 0$. Then max (z) $-$ min (z) is equal to
For the relation $R = \{(a, b): a \leq b\}$ in $\mathbb{R}$, which of the following is correct?
Two persons A and B throw a die alternately till one of them gets a 'three' and wins the game. The probability of A's winning if A starts first is
A random variable X has the following probability distribution: | X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |---|---|---|---|---|---|---|---|---| | P(X) | 0 | k | 2k | 2k | 3k | k² | 2k² | 7k² + k | The value of $P(4 < x < 7)$ is equal to