ISRO Scientist or Engineer Civil 2017

The value of $$\lim_{x \rightarrow 0} (\tan x \log x)$$ is

The general solution of the differential equation $$9yy'+4x = 0$$ is, $$( y' = \frac{dy}{dx}$$, C= constant ) 

The Laplace transform $$L(e^{at})$$ is, [Note : $$L(f(t)) = \overline f(s)$$]

The number of sub matrices $$(1 \times 2)$$ of a matrix $$(2 \times 3)$$ is

if $$A = \begin{bmatrix}3 & 2 & -1 \\0 & 4 & 6 \end{bmatrix}$$ and $$B = \begin{bmatrix}1 & 0 & 2 \\5 & 3 & 1\\ 6 &4 & 2 \end{bmatrix}$$ Then the product of the matrices $$AB$$ is

If 2 is root of the equation $$2X^{2}+X^{2}-13X+6=0$$, then the equation is exactly divisible by the factor

A determinant $$(\delta)$$ of 3 rows $$(R_{1}, R_{2},R_{3})$$ and 3 columns $$(C_{1}, C_{2},C_{3})$$ has a value $$\delta$$ = 15 . If two columns $$C_{2} and C_{3}$$ of the determinant $$(\delta)$$ are interchanged, then the value of determinant will be

If $$u = \sin^{-1} \frac{x + y}{\sqrt{x} + \sqrt{y}}$$ then by Euler’s theorem, $$x. \frac{\partial u}{\partial x}+y .\frac{\partial u}{\partial y}$$ will be

While calculating the cost of a pile of bricks measured as $$2 m \times 15 m \times 1.2 m$$, the tape is stretched 1% beyond the standard length. If the count is 450 bricks per cubic meter and cost of bricks is Rs. 5,000 per 1000 no’s, the approximate error in the cost is

The series $$1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+..............$$ is