Recent questions in Engineering Mathematics

19 votes
4 answers
8922
The function $f(x) =x \sin x$ satisfies the following equation: $$f''(x) + f(x) +t \cos x = 0$$The value of $t$ is______.
43 votes
4 answers
8925
Let the function$$f(\theta) = \begin{vmatrix} \sin\theta & \cos\theta & \tan\theta \\ \sin(\frac{\pi}{6}) & \cos(\frac{\pi}{6}) & \tan(\frac{\pi}{6}) & \\ \sin(\frac{\pi...
60 votes
4 answers
8926
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________
41 votes
5 answers
8927
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set?$ 2^{n}$$2^{n} – 1$$2^{n} – 2$$2(2^{n} – 2)$
35 votes
6 answers
8928
Consider the following system of equations: $3x + 2y = 1 $$4x + 7z = 1 $$x + y + z = 3$$x - 2y + 7z = 0$The number of solutions for this system is ______________
32 votes
3 answers
8930
20 votes
6 answers
8932
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n-3)}{2}$
5 votes
1 answer
8933
13 votes
1 answer
8934
Find the points of local maxima and minima, if any, of the following function defined in $0\leq x\leq 6$. $$x^3-6x^2+9x+15$$Integrate $$\int_{-\pi}^{\pi} x \cos x dx$$
61 votes
3 answers
8935
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
25 votes
5 answers
8939
Consider the following determinant $\Delta = \begin{vmatrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \end{vmatrix}$Which of the following is a factor of $\Delta$?$a+b$$a-b...
20 votes
4 answers
8940
The rank of the matrix given below is:$$\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &21 \end{bmatrix}$$$3$$1$$2$$4$