List of practice Questions

While solving a system of linear equations \( AX = B \) using Cramer’s rule, if \includegraphics[]{6.png}
In a class of 10 girls and 20 boys, Jaya’s rank is ‘4’ among the girls and ‘18’ in the class. What is Jaya’s rank among boys in the class?

In a Carnot engine, the absolute temperature of the source is 25% more than the absolute temperature of the sink. The efficiency of the engine is

5 boys and 6 girls are arranged in all possible ways. Let \(X\) denote the number of linear arrangements in which no two boys sit together, and \(Y\) denote the number of linear arrangements in which no two girls sit together. If \(Z\) denotes the number of ways of arranging all of them around a circular table such that no two boys sit together, then \(X:Y:Z\) = ?
If the number of real roots of \( x^9 - x^5 + x^4 - 1 = 0 \) is \( n \), the number of complex roots having argument on imaginary axis is \( m \), and the number of complex roots having argument in the second quadrant is \( k \), then \( m.n.k \) is:
If \( \alpha \) and \( \beta \) are two distinct negative roots of the equation \( x^5 - 5x^3 + 5x^2 - 1 = 0 \), then the equation of least degree with integer coefficients having \( \sqrt{-\alpha} \) and \( \sqrt{-\beta} \) as its roots is:
If \( \alpha, \beta \) are the roots of the equation \( x^2 - 6x - 2 = 0 \), \( \alpha > \beta \), and \( a_n = \alpha^n - \beta^n, n \geq 1 \), then the value of \( \frac{a_{10} - 2 a_8}{2 a_9} \) is:
The smallest change in measurant that will result in a measurable change in the transducer output is called
Which of the following instrument is used for recording the movements imparted to the body with each beat of the heart cycle?
The amplitude of EMG signals depend upon which of the following factor?
The external interrupts of 8051 microcontroller are
A 4-bit R/2R digital-to-analog (DAC) converter has a reference of 5 V. What is the analog output for the input code 0101?
Determine the output frequency of a frequency division circuit which contains 12 flip-flops with an input clock frequency of 20.48 MHz.
An amplifier has an open loop voltage gain of -500. This gain is reduced to -100 when negative feedback is applied. The reverse transmission factor, \( \beta \), of the system is
The equation $x^4 - x - 10 = 0$ is to be solved using the Newton-Raphson method. If $x = 2$ is taken as the initial approximation of the equation, then the next approximation of the solution is
For two events A and B, let $P(A)=\frac{1}{3}$, $P(B)=\frac{1}{4}$ and $P(A \cup B)=\frac{1}{2}$ then $P(A/B)$ is
A biased coin was thrown 300 times and the tail turned up 120 times, then the standard error of the observed proportion of tails is
The rank of the matrix A = $ \begin{bmatrix} 1 & 3 & 4 & 3 \\ 3 & 9 & 12 & 9 \\ -1 & -3 & -4 & -3 \end{bmatrix} $ is
If $u = \frac{x+y}{x-y}$ and $v = \frac{xy}{(x-y)^2}$ are functionally dependent, then the relation between $u$ & $v$ is
If $f(x) = \begin{cases} -\pi, & \text{in } -\pi<x<0 \\ x, & \text{in } 0<x<\pi \end{cases}$ then the constant term of the Fourier series is
If 60\(\%\) of students in a class are female, and 40\(\%\) of the females wear glasses, what percentage of the class wears glasses?
A charge is kept at the central point \( P \) of a cylindrical region. The two edges subtend a half-angle \(\theta\) at \( P \), as shown in the figure. When \(\theta = 30^\circ\), then the electric flux through the curved surface of the cylinder is \(\Phi\). If \(\theta = 60^\circ\), then the electric flux through the curved surface becomes \(\frac{\Phi}{\sqrt{n}}\), where the value of \(n\) is \_\_\_\_. \includegraphics[width=0.3\linewidth]{ph8.png}
Tetracycline undergoes epimerization at C4 between pH 4-8 to give:
5-Fluorouracil, an anti-metabolite used in cancer treatment, is activated to:
When 25 is subtracted from 50% of a number, the result is 25. Find the number.