Engineering Mat...

If A is a 3 × 3 real matrix with eigen values 1, 2, 3, then the matrix A satisfies

For the given boundary conditions:

y(0) = 3; \(\frac{{dy}}{{dx}} = 5\) at x = 5 and \(\frac{{{d^2}y}}{{d{x^2}}} = 0,\) then y(3) = ______

Let P(E) denote the probability of the event E. If P(A) = \(\frac{3}{4}\) and P(B) = \(\frac{1}{2}\) and A and B are mutually exhaustive events then P(A’ ∪ B’) is equal to _____.

If \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {4 - x}&{x \le 2}\\ {kx - 4}&{x > 2} \end{array}} \right.\) is a continuous function for all real values of x, then f(8) is equal to ________.

If V̅ = (x + 2y + az) i̅ + (bx – 3y – z) j̅ + (4x + cy + 2z) k̅ is irrotational, then which of the following is/are correct?

If the Laplace transform of e^ωt is \(\frac{1}{{s - \omega }}\), the Laplace transform of \(t\cosh t\) is

\(I = \mathop \smallint \limits_0^\infty \frac{{dx}}{{{{\left( {{x^2} + 1} \right)}^2}}}\) has the value

The value of \(\mathop \smallint \limits_c \frac{{{e^z}dz}}{{{{\left( {z - 3} \right)}^2}}}\) c being |z| = 2 is

Which of the following recursion relation to solve x = e^-x using Newton – Raphson method is/are incorrect?

If particle moves along a straight line with velocity given by \(\frac{{dy}}{{dt}} = 1 + y\), where ‘y’ is distance travelled, that time taken by a particle to travel distance of 999 metres is

The partial differential equation has degree and order respectively,

\(\frac{{{\partial ^2}\phi }}{{\partial {x^2}}} + \frac{{{\partial ^2}\phi }}{{\partial {y^2}}} + \frac{{\partial \phi }}{{\partial x}} + \frac{{\partial \phi }}{{\partial y}} = 0\)

 The value of \(\mathop {\lim }\limits_{x \to \infty } {\left( {1 + \frac{1}{x}} \right)^x}\)

If f(x) = x. |x| then at x = 0 which of the following statements is/are false?

Let u(x,y) = x³ + a x² y + b x y² + 2y³ be a harmonic function and v(x, y) its harmonic conjugate. If v(0, 0) = 1, then |a + b + v(1, 1)| is equal to _____

Consider \(\frac{{dy}}{{dx}} = x + y\) with y(0) = 0 using Euler’s method with step size of 0.1. The value of y(0.3) is

A fair dice is thrown twice what is the probability that the sum of the numbers on dice is divisible by 2 if 4 appear on one of the dice(answer up to two decimal place)?

The minimum value of the function \(f\left( x \right) = \frac{1}{3}x\left( {{x^2} - 3} \right)\) in the interval - 100 ≤ x ≤ 100 occurs at x = __________.

Consider the differential equation and choose the correct statements

For \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {x,\;0 \le t \le 3}\\ {4,\;3 \le t \le 6} \end{array}} \right.\) 

The value of (x + y + z) for the following set of linear equations

5x + 3y + 7z = 4, 3x + 26y + 2z = 9, 7x + 2y + 10z = 5

If S is the surface of the sphere x² + y² + z² = a², then the value of

If the matrix A_{3 × 3} has three linearly independent eigen vectors, then which of the following statements is true?

The value of \(\mathop \oint \nolimits_C \left( {{x^2} - x{y^3}} \right)dx + \left( {{y^2} - 2xy} \right)dy\), where C, is the square with vertices (0, 0), (2, 0), (2, 2), (0, 2) is ________

In sampling a large number of parts manufactured by a machine, the mean number of defectives in a sample of 20 is 2 out of 1000 such samples. How many would be expected to contain at least 3 defective parts.

The value of integral \(\mathop \smallint \limits_0^{\frac{\pi }{2}} \sec x\;dx\) is: