GATE Question Paper Maths

Question

If $\vec V$ is a differentiable vector function and ‘f’ is a sufficient differentiable scalar function, then curl(f $\vec V$ ) is equal to…

Possible Answers

Selected	Possible Answer
	fcurl( $\vec V$ )
	$\vec 0$
	(grad f)*( $\vec V$ )
	(grad f)*( $\vec V$ )+(fcurl $\vec V$ )

Question

the value of integral $\int_{-2} ^ {2} \frac{dx}{x^2}$ is

Possible Answers

Selected	Possible Answer
	1
	infinity
	0
	0.25

Question

The function f(x)=3x(x-2) has a…

Possible Answers

Selected	Possible Answer
	maximum at x=1
	maximum at x=2
	minimum at x=1
	minimum at x=2

Question

The value of $\int_{0} ^ {5*phi} (2-sinx)\, dx$ is ….

Possible Answers

Selected	Possible Answer
	undefined
	0
	0
	2

Question

The unit normal to the plane 2x+y+2z=6, can be expressed in the vector form as ….....

Possible Answers

Selected	Possible Answer
	i3+j2+k2
	i2/3+j1/3+k2/3
	i1/3+j1/2+k1/2

Question

The maximum slope of the curve -x^3+6x^2+2x+1 is …........

Possible Answers

Selected	Possible Answer
	19
	16
	-13
	14

Question

If the velocity vector in a two dimensional flow field is given by v=2xyi+(2y^2 - x^2)j, then vorticity vector, curl $\vec V$ will be….....

Possible Answers

Selected	Possible Answer
	$2y^2\vec j$
	zero
	$-4x\vec k$ )
	$6y\vec k$ )

Question

The triangle of maximum area inscribed in a circle of radius “r” is….......

Possible Answers

Selected	Possible Answer
	an equilateral triangle
	does not exist
	a right angled triangle with hypotenuse measuring 2r
	an isosceles triangle of height “r”

Question

let f(x)=x(x-1)(x-2), a=0, b=1/2. the value of ‘C’ in the Lagrange’s mean value theorem is….....

Possible Answers

Selected	Possible Answer
	$\frac{6+\sqrt{21}}{6}$
	$\frac{6+\sqrt{11}}{6}$
	$\frac{6-\sqrt{11}}{6}$
	$\frac{6-\sqrt{12}}{6}$

Question

The minimum value of |x^2-5x+21| is

Possible Answers

Selected	Possible Answer
	-5
	-1
	0
	-2

Question

The volume of an object expressed in sphericaal co-ordinates is given by $V=\int_{0} ^ {2phi}\int_{0} ^ {phi/3}\int_{0} ^ {1} r^2 sin\varnothingdrd\varnothingd\emptyset$ value of the integral is ….......

Possible Answers

Selected	Possible Answer
	2phi/3
	phi/6
	phi/4
	phi/3

Question

The third term in the Taylor series expansion of e^x about a would be….....

Possible Answers

Selected	Possible Answer
	$\frac{e^a}{2}$
	$\frac{e^a}{6} (x-a)^3$
	$\frac{x^2}{2}$

Question

If f(x)=|x|, then f(x) is …......

Possible Answers

Selected	Possible Answer
	discontinuous at x=1
	discontinuous at x=0
	continuous at x=0
	continuous at all values of x

Question

The temperature field in a body varies according to the equation T(x,y)= x^2 +xy .the direction of fastest variation in temperature at the point (1,0) is given by ….........

Possible Answers