List of top Mathematics Questions

If \(\overrightarrow F=y^2\hat{i}+xy\hat{j}+xz\hat{k}\) and C is the bounding curve of the hemisphere x2+y2+z2=9,z>0, oriented in the positive direction, then value of \(\int\limits_C \overrightarrow F\cdot d\hat{r}\) is
Which one of the following is not correct?
Find the sum of two consecutive numbers in which four times are first number is 12 more than the thrice of the second number
The orthogonal trajectory of the cardioid r = a(1+cos θ), a being the parameter is:
Evaluate the integral\(\oint\limits_C\frac{dz}{(z^2+4)^2},C:|z-i|=2\)
If there is no feasible region in LPP, then the problem has:
The maximum value of Z = x + 2y subjected to the constraints x+2y≥100, 2x-y≤0,2x + y≤ 200,x≥ 0, y≥0, is:
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The integral \(\int \int \int (x^2+y^2+z^2)dxdydz\) taken over the volume enclosed by the sphere x2+ y2+z2 = 1 is \(\frac{4\pi}{5}\)
Reason R: \(\int^{1}_{0}\int^{1}_{0}x\ dxdy=\frac{1}{2}\)
In the light of the above statements, choose the most appropriate answer from the options given below:
The value of the integral \(∮_c \frac{dz}{3-\bar z}, C:|z|=1\) is
Match List I with List II
Homogeneous function Degree
A.\(f(x,y)=\frac{x^\frac{1}{3}+y^\frac{1}{3}}{x^\frac{1}{2}+y^\frac{1}{2}}\)I.3
B.\(f(x,y)=\frac{x+y}{\sqrt{x}+\sqrt{y}}\)II.\(\frac{1}{2}\)
C.\(f(x,y)=\frac{x^4+y^4}{x+y}\)III.1
D.\(f(x,y)=\frac{\sqrt{x^3+y^3}}{\sqrt{x}+\sqrt{y}}\)IV.\(-\frac{1}{6}\)
Choose the correct answer from the options given below:
From the given system of constraints
A. 3x+5y≤90
B. x + 2y≤30
C. 2x + y≤30
D. x≥0, y≥0
The redundant constraint is :
The area bounded by the curves y = x2 and y = 4 - x2 is
The volume of the cylindrical column standing on the area common to the parabolas \(y^2 = x\), \(x^2 = y\) and cut off by the surface \(z = 12+y-x^2\) is:
If \(\vec{A} =(3x^2+6y)\hat{i}—14yz\hat{j} +20xz^2\hat{k}\), then the line integral \(\int\limits_{C} \vec{A}.d\bar{r}\) from (0.0, 0) to (1, 1.1), along the curve C ;x=t, y=t2. z=t3 is:
Which of the following set is convex?
If\(\int\limits_0^{1+i}(x^2 -iy) dz = α + iβ\) along the path \(y = x\), then value of \(α– β\) is:
If \(u = x^2 - y^2\) is real part of an analytic function f(z), then f(z) is:
Given below are two statements:
Statement I : If x2y" - 2xy' - 4y = x4, then \(C.F.=\frac{C_1}{x}+C_2x^4\)
Statement II: If (D2-8D+15) y = 0, then auxiliary equation has equal roots.
In the light of the above statements, choose the correct answer from the options given below
If \(\int \int\limits_{R} \int xyz\ dxdydz=\frac{m}{n}\) where, m,n, are coprime and R:0≤x≤1,1≤ y ≤2, 2 ≤ z ≤3 , then m.n is equal to:
If \(u=sin^{-1}[\frac{x+y}{\sqrt{x}+\sqrt{y}}]\) and \(x^2u_{xx}+2xyu_{xy}+y^2u_{yy}=-\frac{sinucos2u}{m^2cos^3u}\) then, m is equal to
If \(\int\int_R(x + y) dydx = A\), where R is the region bounded by x = 0, x = 2, y = x, y = x+2, then \(\frac{A}{12}\) is equal to:
Integrating factors of the equation y (2xy + ex) dx - ex dy = 0 is :
If a right circular cylinder a height 14cm is increased in a sphere of radius 8cm then volume of the cylinder (in cm3)- (use π = \(\frac{22}{7}\)).
The value of \(∫_c \frac{3z^2+7z+1}{z+1} dz\), where C is the circle |z|=\(\frac{1}{2}\) is:
Given below are two statements
Statement I: Draw back in Lagrange's method of undetermined multipliers is that nature of stationary point cannot be determined
Statement II: \(\displaystyle\sum_{n=1}^{∞} (-1)^{n-1}\frac{1}{n\sqrt n}\)convergent
In the light of the above statements, choose the correct answer from the options given below