List of practice Questions

In the human pancreas, which cell types secrete insulin and glucagon?
At time t, the cardiac dipole is oriented at - 45° (minus forty five degrees) to the horizontal axis. The magnitude of the dipole is 3 mV. Assuming Einthoven frontal plane configuration, what is the magnitude (in mV) of the electrical signal in lead II? (Round off the answer to two decimal places.)
A function f(x) is defined on the interval with values in R. It satisfies \( \int_0^2 f(x)[x-f(x)]dx = \frac{2}{3} \). Find the value of f(1).}
Bag-I contains 4 white and 6 black balls, Bag-II contains 4 white and 3 black balls. A ball is selected at random and it comes out to be a black ball. What is the probability that it is from Bag-I?
Consider the matrix \( A = \begin{pmatrix} 9 & 15 \\ 15 & 50 \end{pmatrix} \). The matrix A is decomposed using Cholesky decomposition. Determine the value of \(l_{22}\).
Given the following data: x: (-2, 1, 2), y: (28, 4, 16). Let \(P_2(x)\) be the quadratic interpolating polynomial passing through the above three points. Find the value of \(P_2(0)\).
Consider two infinitely long fins made of the same material and exposed to the same convective environment. One fin has a square cross-section of side \(a\), and the other has a circular cross-section of diameter \(d\). Assume \(a = d\). The ratio of the steady-state heat transfer rate from the square fin to that from the circular fin, \(\frac{\dot{Q}_{\text{square}}}{\dot{Q}_{\text{circular}}}\), is:
A cantilever beam of length \(L\) is fixed at the left end (\(x=0\)). It is subjected to a concentrated downward point load \(P\) and a concentrated clockwise moment \(M = \frac{PL}{2}\) at the midpoint (\(x = L/2\)). Which of the following descriptions correctly represents the Shear Force Diagram (SFD) for the beam?
A vibrating system has a critical damping coefficient \(C_c = 350 \, \text{N}\cdot\text{s/m}\) and an actual damping coefficient \(C = 35 \, \text{N}\cdot\text{s/m}\). The logarithmic decrement of the system is approximately:
Which of the following methods are used to check whether the flexural stresses in a prestressed concrete beam remain within permissible limits at transfer and final stages? Select all the correct option(s).
Let \( P = \begin{pmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{pmatrix} \). Which of the following statements is/are correct?
1. P\(^T\)P = I
2. P is skew-symmetric
3. The value of each eigenvalue of P is 1
4. The trace of P is equal to the sum of its eigenvalues
Consider the differential equation \( x^2 \frac{d^2y}{dx^2} = 6y \). The general solution of the above equation is
Consider the function \(f(x) = e^{-x} - x\). Using the Newton-Raphson method, obtain the first improved approximation starting from the initial guess \(x_0 = 0.5\). Enter the value of the second approximation, correct to two decimal places.}
\( (y + 3x - 13)^3 + (x + y - 7)^2 = 0 \) where x and y are integers. The value of \(x^3 + y^3\) is _____.
Consider the homogeneous system of linear equations: \( \begin{pmatrix} 1 & 1 & 1 \\ 1 & 0 & 2 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \end{pmatrix} \). What does the solution set of this system represent geometrically?
A portal frame has a span of 4 m (2 m + 2 m) and a height of 3 m. The left base is hinged and the right base is roller supported. A horizontal load of 50 kN acts at the top left joint. A vertical concentrated load of 90 kN acts at the midspan of the top beam. Determine the absolute value of the maximum bending moment in the frame.
A bridge has an expected design life of 50 years. It is designed for a flood discharge of 1000 m\(^3\)/s, which corresponds to a return period of 100 years. Determine the risk (probability) that the design flood will be equalled or exceeded at least once during the design life of the bridge. (Enter the numerical value of risk in decimal form, correct up to three decimal places.)
A rectangular catchment ABCD has an area of 7 hectares. The times of concentration from the four extreme points A, B, C and D to the outlet are 10, 20, 15 and 25 minutes, respectively. The rainfall intensity-duration relationship is given by \(I = \frac{25}{t+20}\), where I = rainfall intensity in cm/hr and t = time of concentration in minutes. The runoff coefficient of the catchment is 0.4. Determine the peak discharge from the catchment. (Enter the numerical value only in m\(^3\)/s.)
Long-term deformation of a material under sustained constant loading is primarily governed by:
In a reinforced concrete slab, 10 mm diameter bars are provided at a centre-to-centre spacing of 150 mm to resist a given design moment. If instead of 10 mm bars, 12 mm diameter bars of the same grade of steel are used, determine the required centre-to-centre spacing (in mm) so that the slab resists the same design moment. (Assume effective depth and other parameters remain unchanged. Enter the numerical value only in mm.)
A portal frame has a span of 4 m (2 m + 2 m) and a height of 3 m. The left base is hinged and the right base is roller supported. A horizontal load of 50 kN acts at the top left joint. A vertical concentrated load of 90 kN acts at the midspan of the top beam. Determine the absolute value of the maximum bending moment in the frame.

In a cold rolling process without front and back tensions, the required minimum coefficient of friction is 0.04. Assume large rolls. If the draft is doubled and roll diameters are halved, then the required minimum coefficient of friction is ___________. (Rounded off to two decimal places) 
 

Consider a linear time-invariant system represented by the state-space equation: \[ \dot{x} = \begin{bmatrix} a & b -a & 0 \end{bmatrix} x + \begin{bmatrix} 1 0 \end{bmatrix} u \] The closed-loop poles of the system are located at \(-2 \pm j3\). The value of the parameter \(b\) is: 

If P and Q are positive integers such that \(P^2 = Q^2 + 13\), find the value of the product \(PQ\).
Which one of the following casting defects is caused due to the supply of the molten metal through two gates?