Algebra PYQ — Page 7

The graph given below represents which of the following function? 

The function $f: [-1, 1] \rightarrow R$ (set of real numbers) given by $f(x) = \frac{x}{x+3}$ is

The function $f: \mathbb{R} \rightarrow \mathbb{R}, f(x) = |x|$ ($\mathbb{R}$ is the set of real numbers) is

The function $f: [-1, 1] \rightarrow R$ is given by $f(x) = \frac{x}{x + 2}$

The function $f: \mathbb{R} \rightarrow [-1, 1]$ defined by $f(x) = \cos x$ is:

The function $f: [0, \infty) \rightarrow \mathbb{R}$ defined by, $f(x) = 2x^2 + 3$, is

The following system of equations $2x - y + 3z = 5, 3x + 2y - z = 7, 4x + 5y - \lambda z = \mu$ is consistent. Then

The following system of equations: $x + y - z = 7$ $4x + \lambda y - \lambda z = 3$ $3x + 2y - 4z = 5$ does not possess a solution if the value of $\lambda$ is:

The feasible region represented by the constraints $x + y \leq 50, 3x + y \leq 90, x \geq 0, y \geq 0$ of an LPP is 

The feasible region represented by the constraints: $x + 2y \geq 100$, $2x - y \leq 0$, $2x + y \leq 200$, $x \geq 0$, $y \geq 0$ of an LPP is: 

The feasible region of the linear programming problem is represented below:  The constraints of this LPP are

The feasible region of a LPP is bounded. The corresponding objective function is Z= 6x - 7y. Then objective function attains:

The feasible region of a linear programming problem is bounded. The corresponding objective function is Z= 3x-4y. The objective function attains

The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of Z = 11x + 7y is 

The feasible region corresponding to the linear constraints of a Linear Programming Problem (LPP) is represented by the shaded region in the given figure. Which of the following is not a constraint to the given LPP? 

The feasible region associated with the inequality $2x + 3y > 4$ is

The domain of the function $y = \sin^{-1}(x-1) + \cos^{-1}\sqrt{x-1}$ is:

The domain of the function $\cos^{-1}(2x - 3)$ is

The domain of $y = \cos^{-1}(x^2 - 4)$ is

The difference of two different skew-symmetric matrices is:

The diagonal elements of a skew symmetric matrix are all

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:

The corner points of the feasible region with the constraints $x + y \leq 30$, $x + y \geq 15$, $y \leq 20$, $x \leq 15$ and $x$, $y \geq 0$ are

The corner points of the feasible region of the LPP: Minimize $Z = -50x + 20y$ subject to $2x - y \geq -5$, $3x + y \geq 3$, $2x - 3y \leq 12$ and $x, y \geq 0$ are