List of top Mathematics Questions

\(V\) is the set of points on the curve \(y^3-3xy+2=0\) where the tangent is vertical, then \(V=\)

The equation of tangent of the curve \[ y=\sqrt{9-2x^2} \] at the point where the ordinate and abscissa are equal is

If \[ \frac{d}{dx} \left[ A\log\left(\frac{\sqrt{1-x^3}+B}{\sqrt{1-x^3}+1}\right) \right] = \frac{1}{x\sqrt{1-x^3}}, \] then \(AB=\)

If \(a\gt 0,\ b\gt 0\), then \[ \lim_{n\to\infty} \left( \frac{a+b^{1/n}-1}{a} \right)^n = \] is equal to:

If \[ f(x)=\frac{1-\sin x}{\log(1+\pi^2-4\pi x+4x^2)} \] is continuous at \(x=\frac{\pi}{2}\), then \(f\left(\frac{\pi}{2}\right)=\)

Evaluate \[ \lim_{n\to \infty}\sum_{r=1}^{n}\frac{r+2}{r(r+1)(r+3)} \] is equal to:

If \(a,b,c\) are the intercepts made by the plane passing through the point \((1,2,3)\) parallel to the plane \(3x+4y-5z=0\) on \(X,Y,Z\)-axes respectively, then \(3a+b+5c=\)

If \(a,b,c\) are the direction ratios of a line \(L\) and \(\ell,m,n\) are its direction cosines, then \[ \frac{a^2}{b^2+c^2}= \] is equal to:

Evaluate \[ \lim_{x\to \frac{\pi}{6}} \frac{3\sin x-\sqrt{3}\cos x}{6x-\pi} \]

If the latus rectum of an ellipse is equal to half of the minor axis, then its eccentricity is:

Let \(L(x_1,4)\) be the end of the latus rectum of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] lying in the first quadrant and let \(S(8,y_1)\) be the focus of the given hyperbola. Then the length of its transverse axis is:

If the line \(3x-my+5=0\) is a tangent to the hyperbola \(3x^2-4y^2=300\), then the square of the \(Y\)-intercept made by this tangent line is

The parabola with focus at \((4,-3)\) and vertex at \((4,-1)\) is

If the vertices of a triangle \(ABC\) are \(A(1,2,3)\), \(B(h,-3,0)\) and \(C(-4,k,-1)\) and the centroid of the triangle is \(\left(5,-1,\dfrac{2}{3}\right)\), then triangle \(ABC\) is:

The midpoint of the diagonal of a rectangle formed by \(x^2+5x-6=0\) and \(y^2-8y-20=0\) is

The slope of the normal to the circle \(x^2+y^2+2gx+2fy+c=0\) at \((x_1,y_1)\) is

The circle possessing \(y\)-axis as its tangent at \((0,2)\) and passing through \((-1,0)\), also passes through

Suppose the tangents drawn to the circle \(x^2+y^2-6x-4y-11=0\) from \(P(1,8)\) touch the circle at \(A\) and \(B\). Then the centre of the circle passing through \(P,A\) and \(B\) is

Suppose two tangents \(PA\) and \(PB\) are drawn to the circle centered at \(C(1,2)\) from the point \(P(16,7)\). If the area of the quadrilateral \(PACB\) is \(75\) square units, then the radius of the circle is

The centre of the circle that passes through the point \((0,1)\) and touches the curve \(y=x^2\) at \((2,4)\) is

The family of lines, forming an isosceles triangle with the lines \(3x-4y-2=0\) and \(12x-5y+6=0\), is

The straight line passing through \((-1,1)\) and remaining parallel to the line common to the pairs of lines provided by \(6x^2-xy-12y^2=0\) and \(15x^2+14xy-8y^2=0\), is

If a point \((\alpha,\beta)\) of \(3x+y=0\) and \((3,4)\) lie on the opposite sides of \(3x-4y-8=0\), then which of the following is correct?

If a particle moving along \[ x-2y-3=0 \] gets reflected in a perpendicular direction upon hitting the line \[ 3x-2y-5=0, \] then the line of movement of the particle after reflection is

A point \(P(x,y)\) is such that its distances from \((-1,0)\) and \((0,2)\) are in the ratio of \[ \sqrt{2}:1 \] Then the locus of \(P\) is