List of top Mathematics Questions

\(\int e^{\tan x}(\tan^{7}x+5\tan^{6}x+\tan^{5}x+5\tan^{4}x)\,dx=\)

\(\int \sin^3 2x \sin^{26}x \, dx=\)

\(\int \frac{1}{2\cot x-3\tan x}dx =\)

If P and Q are the points of intersection of the straight line $x=1$ and the curve $x^{2}+xy+y^{2}=7$ then the acute angle between the normals drawn at P and Q is}

If the nearest point on the parabola $y^{2}=4x$ to the given point $P(-1,4)$ is $Q(h,k)$ and $PQ=d$, then $h^{2}+k^{2}+d^{2}=$}

$[\frac{d}{dx}((sin~x)^{cos~x})]_{x=7/4}=$}

If $y=e^{2x}+sin~x$, then $2y^{\prime\prime}-5y^{\prime}+2y=$}

If $x=Sin^{-1}(cos~t)$ and $y=Tan^{-1}(cos~t)$ then $\frac{dy}{dx}=$}

The area of a triangle is obtained with lengths of two sides and included angle between them. If the angle is measured as $60^{\circ}20^{\prime}$ instead of $60^{\circ}$, then the percentage error in its area is}

If the rate of change of volume of a cube and that of its surface area are numerically equal, then the length of its diagonal is

If $f(x)=\begin{cases}\frac{x}{|x|}when~x\ne0\\ |x|when~x=0\end{cases}$ is a real valued function, then}

If A(1,2,-3), B(2,3,-1), C(3,1,-2) are vertices of triangle ABC, then area is

If the function $\Gamma(x)=\begin{cases}\frac{sin^{2}ax-sin^{2}bx}{x^{2}} & x<0 \\ x & x=0 \\ \frac{(s+2x^{2})^{\frac{1}{2}}-x^{\frac{3}{2}}}{sin^{2}x} & 0<x<\pi\end{cases}$ is continuous at $x=0$, then $a^{2}+b=$}

Plane through (3,5,7), (7,-5,3) parallel to line joining (1,-2,-4) and (4,2,-1) is \(ax+by+cz+80=0\). Then \(a+b+c=\)

Direction cosines satisfy \(l-2m+n=0\), \(2l^2-3m^2+n^2=0\). Angle between lines is

For parabola \(y^2=5x\), normal at P meets x-axis at Q. If PQ subtends \(60^\circ\) at vertex, slope of normal is

For an ellipse, distance between centre and focus is \(\sqrt7\) and semi-latus rectum is \(\frac{9}{4}\). Area of triangle formed by foci and one end of minor axis is

For ellipse \(9x^2+25y^2=225\), focal chord \(L_1\) makes equal intercepts on axes. Intersection with tangent at end of latus rectum lies in

If \((h,k)\) is the centre of a circle cutting three circles orthogonally, then \(\frac{3}{h}+\frac{1}{k}=\)

Line \(x+y+k=0\) touches hyperbola \(x^2-5y^2=5\). Point of contact is

Common tangent to circle \(x^2+y^2=4\) and parabola \(y^2=8\sqrt2 x\) is \(y=mx+c\). Then \(\sqrt{m+c^2}=\)

For circle \(x^2+y^2+12x-4y-9=0\), line \(x+2y-3=0\) represents

If \((h,k)\) is external centre of similitude of circles \[ x^2+y^2-6x-10y+9=0 \] and \[ x^2+y^2+6x+6y+2=0, \] then \(k-h=\)

If line \(2y-3=0\) bisects angle between \(x+2y-k=0\) and \(x-2y+k=0\), then a point on the bisector of other angle is

Tangent to circle \(x^2+y^2-4x-8y-5=0\) equally inclined to axes is \(x+by+c=0\), \(b0\). Find \(2b+c\).