List of top Mathematics Questions

The value of \(θ\in (0,\frac{π}{2})\) for which vectors \(\overset{̄}{a} = (sinθ)\hat{i}+(cosθ)\hat{j}\) and \(\overset{̄}{b} = \hat{i}-\sqrt{3}\hat{j}+2\hat{k}\) are perpendicular is

The angle between the line \(\overset{̄}{r} = (\hat{i}+2\hat{j}+\hat{k})+λ(\hat{i}+\hat{j}+\hat{k})\) and the plane \(\overset{̄}{r}\cdot (2\hat{i}-\hat{j}+\hat{k}) = 8\) is \(\ldots\)

If \(|\overset{̄}{a}| = |\overset{̄}{b}| = 1,|\overset{̄}{c}| = 2\) and \(\overset{̄}{a}\times (\overset{̄}{a}\times \overset{̄}{c})+\overset{̄}{b} = \overset{̄}{0}\), then the acute angle between \(\overset{̄}{a}\) and \(\overset{̄}{c}\) is \(\ldots\)

The equation of the plane passing through the points having position vectors \((\overset{̄}{a}+\overset{̄}{b}),(\overset{̄}{b}+\overset{̄}{c})\) and \((\overset{̄}{a}+\overset{̄}{c})\) is \(\ldots\)

The order and degree of the differential equation \(\sqrt{⎷1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}\) are \(\ldots\)

The integrating factor of the differential equation \(x\frac{dy}{dx}+2y = x^2logx\) is

If the volume of the tetrahedron whose coterminous edges are given by the vectors \(\overset{̄}{a} = -2\hat{i}+3\hat{j}-3\hat{k}\), \(\overset{̄}{b} = 4\hat{i}+5\hat{j}+(λ-10)\hat{k}\), \(\overset{̄}{c} = 6\hat{i}+2\hat{j}-3\hat{k}\) is 11 cubic units, then the sum of the possible values of \(λ\) is \(\ldots\)

The differential equation of the family of all parabolas whose axis is the \(y\)-axis is \(\ldots\)

A spherical raindrop evaporates at a rate proportional to its surface area. The differential equation involving the rate of change of its radius \(r\) with time '\(t\)' is \(\ldots\) (where \(k\) is a positive constant)

Let \(f(x) = x\), \(f_1(x) = f(logx)\), \(f_2(x) = f_1(logx)\), \(f_3(x) = f_2(logx)\), \(\ldots\) and so on. Then \(\int \frac{1}{f(x)\,f_1(x)\,f_2(x)\,\ldots f_{2026}(x)}\,dx = \ldots\)

\(\int _0^2|4x-5|\,dx = \ldots\)

If \(\int e^{x+tan^{-1}x}(\frac{x^2+2}{sec^2(tan^{-1}x)})dx = e^{f(x)}+c\), then \(\ldots\)

The rate of disintegration of a radioactive element at any time is proportional to its mass at that time, where \(k\) \((k > 0)\) is the constant of proportionality. The time during which an original mass of 1.5 gm will disintegrate to a mass of 0.5 gm is \(\ldots\)

If the area bounded by \(y = x^3+ax\) (where \(a > 0\)), the \(x\)-axis and the lines \(x = -2\) and \(x = 1\) is \(\frac{37}{4}\) square units, then \(\ldots\)

If \(\int _0^2x(2-x)^b\,dx = \frac{32}{7}\), where \(b\in N\) then \(b =\)

If \(f:R\rightarrow R\) is an even function then

If the function \(f(x) = ax^2+bx+sinx\) satisfies all the conditions of Rolle's theorem on \([0,π]\) and the slope of the tangent to the curve \(y = f(x)\) at \(x = \frac{π}{4}\) is zero, then \(a-b =\)

Let \(g(x) = f(x)+f(1-x)\) and \(f^{''}(x) < 0,0\leq x\leq 1\), then \(\ldots\)

If \(f^'(x) = sin^2x\) and \(y = f(\frac{2x-1}{x^2+1})\), then \(\frac{dy}{dx}\) at \(x = 1\) is

If a particle moves such that the displacement (s) is proportional to the square of the velocity (v), then its acceleration (a) is

Let \(y = \sqrt[p]{x^3y}\). If \(\frac{dy}{dx} = \frac{3}{2}\) when \(y = 1\), then the value of \(p\) is equal to \(\ldots\)

If \(tan^{-1}ax+tan^{-1}3x = \frac{π}{4}\), where \(3ax^2 < 1\), then value of \(a\) for \(x = \frac{1}{6}\) is \(\ldots\)

\(sec^2(tan^{-1}3)-tan^2(sec^{-1}3) =\)

If \(f(x) = \frac{3^x+3^{-x}-2}{tanx\cdot log(1+x)}\) for \(x\neq 0\), is continuous at \(x = 0\), then the value of \(f(0)\) is equal to \(\ldots\)

The domain of the function \(f(x) = \sqrt{\frac{x}{1+x}}\) is \(\ldots\)