Algebra PYQ — Page 37

The relation $R = \{(a, b) : a \leq b^2\}$ on the set of real numbers is:

Let $f(x) = x^3$ be a function with domain {0, 1, 2, 3} then domain of $f^{-1}$ is :

A manufacturing company makes two models M$_1$ and M$_2$ of a product. Each piece of M$_1$ requires 9 labour hours for fabricating and one labour hour for finishing. Each piece of M$_2$ require 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs.800 on each piece of M$_1$ and Rs.1200 on each piece of M$_2$ The maximum profit will be at the point

If $5x + y \leq 100$, $x + y \leq 60$, $x \geq 0$, $y \geq 0$. Then one of the corner points of the feasible region is :

If a, b and c are all different from zero and $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = 0$, then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ is :

If a fair coin is tossed 10 times the probability of atleast 6 heads is:

Which one of the following options is incorrect? For a square matrix A in the matrix equation AX = B.

If $P = \begin{bmatrix} 1 & x & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of 3x3 matrix A and $|A|$ is 4, then $x$ is equal to :

The value of $\begin{vmatrix} 1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b \end{vmatrix}$ is

For the LPP Maximise $z = x + y$ subject to $x - y \leq -1$, $-x + y \leq 2$, $x, y \geq 0$, $z$ has :

If in a binomial distribution $n = 4$, $P(X=0) = \frac{16}{81}$, then $P(X=4)$ equals :

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 :

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 :

If the probability distribution of a random variable X is as given below : | X | -1 | 0 | 1 | 2 | 3 | |---|---|---|---|---|---| | P(X) | K | $\frac{1}{5}$ | 2K | $\frac{3}{10}$ | K | Then the value of K 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 order of a null matrix is :

A doctor is to visit a patient. It is known that the probabilities that he will come by train, bus, scooter or by other means of transport are respectively $\frac{3}{10}, \frac{1}{5}, \frac{1}{10}$ and $\frac{2}{5}$. The probabilities that he will be late are $\frac{1}{4}, \frac{1}{3}$ and $\frac{1}{12}$, if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he arrives late. The probability that he comes by bus is:

Probabilities to solve a specific problem by A, B and C are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. Probability that at least one will solve the problem is:

Given relation $R = \{(x, y) : y = x + 5, x < 4, x, y \in N\}$. Where N is a set of natural numbers then :

Match List - I with List - II. If $A = \begin{vmatrix} 3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2 \end{vmatrix}$ | List - I | List - II | |----------|-----------| | (A) $M_{23}$ | (I) $-17$ | | (B) $A_{32} + a_{13}$ | (II) $-1$ | | (C) A | (III) 0 | | (D) $a_{13}A_{12} + a_{23}A_{22} + a_{33}A_{32}$ | (IV) 12 | Choose the correct answer from the options given below :

Let $A = \begin{bmatrix} 3 & -1 \\ 2 & 4 \end{bmatrix}$, then adjoint (A) is:

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

A coin is tossed 7 times. The probability of getting at least 4 heads is:

If $f(x) = \sqrt{x}$, $g(x) = 2x - 3$, then domain of $fog(x)$ is :