List of top Mathematics Questions

The equation of the circle touching the x-axis at (5, 0) and the line y = 10 is

If $\beta=\displaystyle\lim _{x \rightarrow 0} \frac{e^{x^3}-\left(1-x^3\right)^{\frac{1}{3}}+\left(\left(1-x^2\right)^{\frac{1}{2}}-1\right) \sin x}{x \sin ^2 x}$ then the value of $6 \beta$ is ____.

Let \(\beta\) be a real number. Consider the matrix
\(A=\begin{pmatrix}\beta & 0 & 1 \\2 & 1 & -2 \\3 & 1 & -2\end{pmatrix}\)
If \(A^7-(\beta-1) A^6-\beta A^5\) is a singular matrix, then the value of \(9 \beta\) is __.

An integrating factor of the differential equation \( (x^2+1)\frac{dy}{dx} + xy = x^3 \) is

If \( f(x) = \sin(\tan^{-1} x) \), then \( \int_0^1 xf''(x)dx = \)

\( \int_{-\pi/4}^{\pi/4} \cos^8 x \ dx = \)

If \( \int \frac{x^8+4}{x^4-2x^2+2} dx = Ax^5+Bx^3+Cx+K \), then \(5A+3B+C = \)

If an open cylinder of given surface area has maximum volume then its radius is

If \(x+y=k, x>0, y>0\) then \(x^2+y^2\) is minimum if

The minimum distance of a point on the curve \( y = x^2 - 4 \) from the origin is

If \( f(x) = \begin{cases 4 & -\infty<x<-\sqrt{5}
x^2-1 & -\sqrt{5} \le x \le \sqrt{5}
4 & \sqrt{5}<x<\infty \end{cases} \). If k is the number of points where f(x) is not differentiable then k -- 2 =}

Assertion (A) : \( f(x)=|x| \) is differentiable at \( x=a \neq 0 \) and continuous but not differentiable at \( x=0 \) Reason (R) : If a function is differentiable at a point then it is continuous at that point. But converse is not true. .

A ray makes angles \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) with Y and Z-axes respectively. Then the value of the sine of the angle made by the ray with X-axis is

A plane meets the X, Y, Z -- axes in A, B, C respectively. If the centroid of the triangle ABC is \((2, -3, 5)\) then the perpendicular distance from origin to the given plane is

If the centroid of a triangle with vertices \((4, p, -3), (-1, -1, 2)\) and \((3, 5, -8)\) is given by mid point of \((1, 4, -2)\) and \((q, 2, -4)\), then \(p^2+q^2 = \)

\( \lim_{x \to \frac{\pi}{2}} \frac{1-\tan\frac{x}{2}}{1+\tan\frac{x}{2}} \cdot \frac{1-\sin x}{(\pi-2x)^3 = \)}

\( \lim_{x \to a} \frac{x^3+a^3}{x+a} = 7 \implies a = \)

The eccentricity of the ellipse \( 9x^2+16y^2=144 \) is

The length of the latus rectum of the parabola \( y^2-4x-4y+8=0 \) is

If \( ax^2 - 34xy - 5y^2 + 2x + 26y - 5 = 0 \) represents a pair of straight lines, then the value of a is

The equations of the lines perpendicular to \(x^2 - 5xy + 4y^2 = 0\) and passing through (2, 1) is

Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are \(3x+4y-4=0\) and \((2,2)\) respectively. Then, which of the following is another side of the triangle?

A point P on a line is at a distance of 4 units from the origin (0, 0). If the line makes 60\(^\circ\) with the negative direction of the x-axis, then P is

A point P(x, y) is such that the sum of squares of its distances from (a, 0) and (--a, 0) is \(2b^2\). The equation representing the locus of P is