List of top Mathematics Questions

If $ asin^{-1}x - bcos^{-1} x = c $ , $ a sin^{-1}x + b cos^{-1} x $ is equal to

The length of the perpendicular distance of the point $ (-1,\,4,\,0) $ from the line $ \frac{x}{1}=\frac{y}{3}=\frac{z}{1} $ is equal to

The number of lines making equal angles with the coordinate axes in three dimensional geometry is equal to

The projection of a line segment $OP$ through origin $O$, on the coordinate axes are $8, 5, 6$. Then, the length of the line segment $OP$ is equal to

The numerically greatest term in the expansion of \((3-5x)^{11}\) when \(x=\dfrac{1}{5}\), is

If \(f(x)=\sqrt{\log_{10}(x^2)}\), the set of all values of \(x\) for which \(f(x)\) is real, is

The principal value of \(\sin^{-1}\left\{\sin\left(\frac{5\pi}{6}\right)\right\}\) is

The two curves \(y=3^x\) and \(y=5^x\) intersect at an angle

The distance between the line \(\vec{r}=2\hat{i}-2\hat{j}+3\hat{k}+\lambda(\hat{i}-\hat{j}+4\hat{k})\) and the plane \(\vec{r}\cdot(\hat{i}+5\hat{j}+\hat{k})=5\), is

The equation of sphere concentric with the sphere \(x^2+y^2+z^2-4x-6y-8z-5=0\) and which passes through the origin, is

If the lines \(\dfrac{x-1}{2}=\dfrac{y+1}{3}=\dfrac{z-1}{4}\) and \(\dfrac{x-3}{1}=\dfrac{y-k}{2}=\dfrac{z}{1}\) intersect, then the value of \(k\) is

If \(A(-2,1)\), \(B(2,3)\) and \(C(-2,-4)\) are three points. Then, the angle between \(BA\) and \(BC\) is

The equation \(\lambda x^2+4xy+y^2+\lambda x+3y+2=0\) represents a parabola, if \(\lambda\) is

If two circles \(2x^2+2y^2-3x+6y+k=0\) and \(x^2+y^2-4x+10y+16=0\) cut orthogonally, then the value of \(k\) is

The degree of differential equation of all curves having normal of constant length \(c\) is

If \(\displaystyle \int_{1}^{x}\frac{dt}{t\sqrt{t^2-1}}=\frac{\pi}{6}\), then \(x\) can be equal to

The area bounded by the curve \(y=|\sin x|\), \(x\)-axis and the lines \(x=\pi\), is

If \(\vec{a}=2\hat{i}+2\hat{j}+3\hat{k}\), \(\vec{b}=-\hat{i}+2\hat{j}+\hat{k}\) and \(\vec{c}=3\hat{i}+\hat{j}\), then \(\vec{a}+\vec{b}\) is perpendicular to \(\vec{c}\), if \(t\) is equal to

If \(x=\sec\theta-\cos\theta,\ y=\sec^n\theta-\cos^n\theta\), then \((x^2+4)\left(\dfrac{dy}{dx}\right)\) is equal to

If \(y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+\cdots}}}}\), then \(\dfrac{dy}{dx}\) is equal to

\(\displaystyle \int \sin^{-1}\left(\frac{2x+2}{\sqrt{4x^2+8x+13}}\right)dx\) is equal to

Domain of the function \(f(x)=\log_x(\cos x)\), is

Range of the function \(y=\sin^{-1}\left(\dfrac{x^2}{1+x^2}\right)\), is

If \(\{f(x)\dx=f(x)\), then \(\int \{f(x)\}^2 dx\) is equal to}

The condition that the line \(lx+my=1\) may be normal to the curve \(y^2=4ax\), is