ISRO Scientist or Engineer Civil 2019

Equation of a line normal to $$f(x) = (x + 4)^{\frac{1}{2}} + 1$$ at Q(0, 3) is:

Consider the shaded triangle P shown in the figure What is $$\int \int_{p} xy dx dy$$

Distance between the origin and the point nearest to it on the surface $$Z^{2}=1+xy$$ is :

At $$x = 0$$, the function $$f(x) = \mid x \mid$$ has

General solution of differential equation $$\frac{dy}{dx} = \cos(x + y)$$

A box contains 2 blue ,3 black, and 4 red balls are dreawn from the box at the random one at a time of replacement . The probability of drawing 2 blue balls first followed by 3
black balls and subsequently 4 red balls is:

Using the trapeZoidal rule and the dividing the interval of integration into three equal sub intervals ,the definite integral $$\int_{-1}^{+1} \mid x \mid dx$$ is :

Acircularring of radius 42 cm is cut and bentinto the form of a rectangle whose sides are in the ratio of 6:5. The small side of the rectangleis :

A tank is normally filled in 8 hours buttakes-2‘hours longer tofill because of a leak at the bottom. If the tankis full and due.*°leakagealone, the tank will get empty in ............... hours (Assume nofurther filling happens):

From a circular. sheet of paper having radius 50 cm, a sector of 40% area is removed in the shape of an arc section. If the remaining part is used to make a conical surface, then the ratio of the radius to height of the cone is: