List of top Mathematics Questions

The angle between the line \(x-1 = 2-y = \frac{2z-6}{4}\) and the plane \(\overset{⃗}{r}\cdot (2\hat{i}+\hat{j}+\hat{k}) = 10\) is

Let \(\overset{⃗}{a} = λ\hat{i}+\hat{j}+\hat{k},\overset{⃗}{b} = 2\hat{i}+4\hat{j}+4\hat{k},\overset{⃗}{c} = \hat{i}+μ\hat{j}+\hat{k}\)
If \(\overset{⃗}{a}\) is parallel to \(\overset{⃗}{b}\) and \(\overset{⃗}{b}\) is perpendicular to \(\overset{⃗}{c}\) then \(λ-μ = \ldots\)

If \(|\overset{⃗}{a}\cdot \overset{⃗}{b}| = |\overset{⃗}{a}\times \overset{⃗}{b}|\), \(\overset{⃗}{a}\cdot \overset{⃗}{b} < 0\) and \(θ\) is the angle between \(\overset{⃗}{a}\) and \(\overset{⃗}{b}\), then the value of \(sinθ+tanθ\) is...

The value of \(b\) such that the scalar product of the vector \(\hat{i}+\hat{j}+\hat{k}\) with the unit vector parallel to the sum of the vectors \(2\hat{i}+4\hat{j}-5\hat{k}\) and \(b\hat{i}+2\hat{j}+3\hat{k}\) is one, is...

The general solution of the differential equations \(\frac{dy}{dx} = (9x+y+5)^2\) is...

Let \(\overset{⃗}{a}\) and \(\overset{⃗}{b}\) be linearly independent vectors such that
\(|\overset{⃗}{a}| = \sqrt{3},|\overset{⃗}{b}| = 3\) and \(|\overset{⃗}{a}-\overset{⃗}{b}| = 4\).
If \(\overset{⃗}{a}\times (2\hat{i}+2\hat{j}-\hat{k}) = (2\hat{i}+2\hat{j}-\hat{k})\times \overset{⃗}{b}\) and \(|(\overset{⃗}{a}+\overset{⃗}{b})\cdot (3\hat{i}+4\hat{j}+2\hat{k})| = \sqrt{λ}\), then \(λ = \ldots\)

The general solution of the differential equation \(secy+(x-e^{siny})\frac{dy}{dx} = 0\) is...

If \(\int _a^b(x^2-x)\,dx = 18,\int _a^bx^3\,dx = 0\), then \(a+b\) is equal to

If \(f(x) = \frac{sin^{-1}x}{\sqrt{1-x^2}}\) and \(g(x) = e^{sin^{-1}x}\), then the value of \(\int f(x)g(x)\,dx = \ldots\)

The function \(f(x) = \int _0^x\frac{dt}{1+cost}\) satisfies which of the following differential equations?

The value of the definite integral \(\int _0^π\frac{1}{5+4cosx}\,dx\) is equal to ...

Let \(f(x) = x-[x]\) for every real number \(x\), where \([x]\) is integral part of \(x\). then \(\int _{-1}^1f(x)\,dx\) is

The area of the region bounded by curves \(y = sinx,y = cosx\) and the lines \(x = 0\), \(x = \frac{π}{4}\) is

The equation of the tangent to the curve \(y = \sqrt{9-3x^2}\) at the point where the ordinate and abscissa equal is...

If \(\int f(x)\,dx = g(x)\) then \(\int x^3f(x^2)\,dx\) is equal to

The coordinates of the points on the curve \(4y = x^2\) that are nearest to the point \((0,5)\) are ...

If the line \(y = 4x-5\) is tangent to the curve \(y^2 = ax^3+b\) at the point \((2,3)\), then the value of \(7a-2b\) is...

If \(\int \frac{3x+7}{x^2-3x+2}\,dx = mlog(\frac{x-2}{x-1})+nlog(x-2)+c\), where \(m,n\in R\) and \(c\) is an integration constant, then \(m+n =\)

If \(\int \frac{sinx}{sin4x}\,dx = αlog\frac{1+sinx}{1-sinx}+βlog\frac{1+\sqrt{2}sinx}{1-\sqrt{2}sinx}+c\), then the value of \(32(α+β^2) =\)

If \(y = \frac{1}{3x+5}\), then the value of \(\frac{d^9y}{dx^9}\) is..

If the function \(f(x) = \frac{4\sqrt{2}(sin3x+sinx)}{2sin2xsin\frac{3x}{2}+cos\frac{5x}{2}-cos\frac{3x}{2}}\) for \(x\neq \frac{π}{2}\) is continuous at \(x = \frac{π}{2}\), then the value of \(f(\frac{π}{2})\) is equal to

If \(f(x) = cosx\,cos2x\,cos4x\,cos8x\,cos16x\), then \(f^'(\frac{π}{4}) =\)

If \(y = \sqrt{cosx^2+\sqrt{cosx^2+\sqrt{cosx^2+\ldots \infty }}}\) and \(\frac{dy}{dx} = \frac{f(x)}{2y-1}\) then, \(\int f(x)\,dx = \ldots\)

If \(f(x) = cot^{-1}(\frac{3x-x^3}{1-3x^2})\) and \(g(x) = cos^{-1}(\frac{1-x^2}{1+x^2})\), then \(\underset{x\rightarrow a}{lim}\frac{f(x)-f(a)}{g(x)-g(a)}\), \((0 < a < \frac{1}{2})\) is

The derivative of \(tan^{-1}(\frac{\sqrt{1+x^2}-1}{x})\) with respect to \(tan^{-1}(\frac{x}{\sqrt{1-x^2}})\) at \(x = \frac{1}{2}\) is