List of practice Questions

If the difference of the roots of the equation $x^2 - 7x + 10 = 0$ is same as the difference of the roots of the equation $x^2 - 17x + k = 0$, then a divisor of $k$ is
The product of all the real roots of the equation $|x^2 - 5||x| + 6 = 0$ is
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $5x^3 - 4x^2 + 3x - 2 = 0$, then $\alpha^3 + \beta^3 + \gamma^3$ equals
After the roots of the equation $6x^3 + 7x^2 - 4x - 2 = 0$ are diminished by $h$, if the transformed equation does not contain $x$ term, then the product of all possible values of $h$ is
The number of integers greater than 6000 that can be formed by using the digits 0, 5, 6, 7, 8 and 9 without repetition is
Evaluate \[ \frac{1}{3 . 5} + \frac{1}{5 . 7} + \frac{1}{7 . 9} + .s \text{ up to } 24 \text{ terms}. \]
If B is the inverse of a third order matrix A and det B = k, then $(\text{adj}(\text{adj} A))^{-1}=$
If $A = \begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix}$ and $\alpha, \beta, \gamma$ are the roots of the equation represented by $|A - xI| = 0$, then $\alpha^2 + \beta^2 + \gamma^2 =$
If the values of $x, y,$ and $z$ satisfy the equations \[ 2x - 3y + 2z + 15 = 0,
3x + y - z + 2 = 0,
x - 3y - 3z + 8 = 0 \] simultaneously are $\alpha, \beta,$ and $\gamma$ respectively, then
If $x = 3 - 2\sqrt{3}i$, then evaluate $x^4 - 12x^3 + 54x^2 - 108x - 54 = $
The product of the four values of the complex number $(1+i)^{3/4}$ is
Let $[x]$ represent the greatest integer less than or equal to $x$, $\{x\} = x - [x]$. Given \[ \sqrt{2} = 1.414
\text{and}
\sqrt{3} = 1.732. \] If \[ f(x) = x + \frac{x}{1 + x^2} \] is a real valued function, then find \[ f(\sqrt{2}) + f(-\sqrt{3}). \]
If the range of the function $f(x) = -3x - 3$ is $\{3, -6, -9, -18\}$, then which one of the following is not in the domain of $f$?
Which of the following is NOT a characteristic of cloud computing?
In a turning operation, the cutting speed is 120 m/min, and the diameter of the workpiece is 50 mm. What is the spindle speed in RPM?
Which of the following materials is most suitable for high-temperature applications in gas turbines?
A 3-phase, 400 V, 50 Hz induction motor runs at 1440 RPM. If the synchronous speed is 1500 RPM, what is the slip?
In a series RLC circuit, R = 10 $\Omega$, L = 0.1 H, and C = 100 $\mu$F. What is the resonance frequency (in Hz)?
Which of the following is a key advantage of a PID controller in control systems?
Which of the following sorting algorithms has the best average-case time complexity?
In a relational database, a table has 5 attributes and 1000 records. If a query returns 200 records after applying a condition, what is the selectivity of the query?
If the efficiency of a machine is 80% and it consumes 500 W of power, what is the useful output power?
Which of the following methods is most suitable for the design of flexible pavements in high-traffic areas?
A Carnot engine operates between a hot reservoir at 800 K and a cold reservoir at 300 K. What is its maximum theoretical efficiency?
The Supreme Court’s judgment in the case of Kesavananda Bharati v. State of Kerala (1973) is associated with which doctrine?