List of top Mathematics Questions

The shaded region is the solution set of the inequalities
Shaded Region
The area of the quadrilateral ABCD, when A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to
If a plane meets the coordinate axes at A, B and C in such a way that the centroid of triangle ABC is at the point (1, 2, 3) then the equation of the plane is
The angle between the lines whose direction cosines are \((\frac{\sqrt3}{4},\frac{1}{4},\frac{\sqrt3}{2})\) and \((\frac{3}{4},\frac{1}{4},\frac{-\sqrt3}{2})\) is
The equation of the line joining the points (-3, 4, 11) and (1, -2, 7) is
If \(\vec{a}.\vec{b}=0\) and \(\vec{a}+\vec{b}\) makes an angle 60° with \(\vec{a}\) then
The diagonals of a parallelogram are the vectors \(3\hat{i}+6\hat{j}-2\hat{k}\) and \(-\hat{i}-2\hat{j}-8\hat{k}\) then the length of the shorter side of parallelogram is
A vector \(\vec{a}\) makes equal acute angles on the coordinate axis.Then the projection of vector \(\vec{b}=5\hat{i}+7\hat{j}-\hat{k}\) on \(\vec{a}\) is
The number of solutions of \(\frac{dy}{dx}=\frac{y+1}{x-1}\) when y(1) = 2 is
Solution of Differential Equating xdy – ydx = 0 represents
If the area of the Ellipse is \(\frac{x^2}{25}+\frac{y^2}{\lambda^2}=1\) is 20π square units, then λ is
The area of the region bounded by \(y=\sqrt{16-x^2}\) and x-axis is
The value of \(\int\limits_0^{4042}\frac{\sqrt{x}\ dx}{\sqrt{x}+\sqrt{4042-x}}\) is equal to
If \(I_n=^{\frac{\pi}{4}}_0\int\tan^n x\ dx\) where n is positive integer then I10 + I8 is equal to
The value of \(\int e^x[\frac{1+\sin x}{1+\cos x}]dx\) is equal to
The value of \(\int\frac{xe^x dx}{(1+x)^2}\) is equal to
The value of \(\int\frac{x^2dx}{\sqrt{x^6+a^6}}\) is equal to
\(\int\frac{x^3\sin(\tan^{-1}(x^4))}{1+x^8}dx\) is equal to
The maximum slope of the curve y = -x3 + 3x2 + 2x -27 is
The function f(x) = x2 - 2x is strictly decreasing in the interval
If the parabola y = αx2 - 6x + β passes through the point (0, 2) and has its tangent at x = \(\frac{3}{2}\) parellel to x axis, then
A particle starts form rest and its angular displacement (in radians) is given by \(\theta=\frac{t^2}{20}+\frac{t}{5}\). If the angular velocity at the end of t = 4 is k, then the value of 5k is
If y = (x - 1)2 (x - 2)3 (x - 3)5 then \(\frac{dy}{dx}\) at x = 4 is equal to
If the parametric equation of curve is given by x = cosθ + log tan \(\frac{θ}{2}\) and y = sinθ, then the points for which \(\frac{dy}{dx}=0\) are given by
For constant a, \(\frac{d}{dx}\)(xx + xa+ ax + aa) is