List of top Mathematics Questions

\(\displaystyle \int \sin^2x\,dx=\)

For what value of \(x\), the function \(2x^3+3x^2-36x+10\) has minimum?

The derivative of \(x^x\) with respect to \(x\) is

\(\displaystyle \frac{d}{dx}\left(\tan^{-1}\frac{x}{a}\right)=\)

Slope of the normal to the curve \(x^{2/3}+y^{2/3}=2\) at the point \((1,1)\) is

If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots\infty}}}\), then \(\displaystyle \frac{dy}{dx}=\)

The equation of the tangent to the curve \(y=x^3\) at \((1,1)\) is

The equation of the parabola with focus \((2,0)\) and vertex \((1,0)\) is

If \((2,0)\) is the vertex and \(y\)-axis is the directrix of a parabola, then its focus is

The value of \(\displaystyle \lim_{x\to\infty}\frac{4x^3-x+1}{x^2-4x(1-x^2)\) is}

The value of \(\displaystyle \lim_{x\to 1}\left(\frac{x^3-1}{x-1}\right)\) is

The eccentricity of the ellipse \(16x^2+7y^2=112\) is

Modulus of the complex number \(\frac{(1+i)^{10{(2i-4)^4}\) is equal to}

The length of the tangent from the point \((5,1)\) to the circle \(x^2+y^2+6x-4y-3=0\) is

The real part of \(\frac{1+2i}{(2-i)^2\) is}

If length of the tangent is \(8\text{ cm}\) and the distance between the center of the circle and the external point is \(11\text{ cm}\), then the area of the circle is

In a circle with center \(O\), a \(6\text{ cm}\) long chord is at a distance \(4\text{ cm}\) from the center. Then the length of diameter is

If \(\sin5x+\sin3x+\sin x=0\), then the value of \(x\) other than zero lying between \(0\leq x\leq \frac{\pi}{2}\) is

The general solution of the equation \(\tan^2x=1\) is

The value of \(\cos\frac{5\pi}{17}+\cos\frac{7\pi}{17}+2\cos\frac{11\pi}{17}\cos\frac{\pi}{17}\) is

If \(\sin\theta-\cos\theta=\frac{4}{5}\), then the value of \(\sin\theta+\cos\theta=\)

The maximum value of \(3\cos\theta+4\sin\theta\) is

If \(5\sin\theta=4\), then the value of \(\frac{\cosec\theta-\cot\theta}{\cosec\theta+\cot\theta}\) is

For real \(x\), if \(x+\frac{1}{x}=2\cos\theta\), then \(\cos\theta\) is

\(\sin^6\theta+\cos^6\theta+3\sin^2\theta\cos^2\theta=\)