List of top Mathematics Questions

The coordinates of the point of intersection of the lines \(\frac{x-3}{1} = \frac{y-5}{2} = \frac{z-1}{-1}\) and \(\frac{x-4}{2} = \frac{y-2}{-1} = \frac{z-4}{2}\) are...

If the plane \(2x+3y+z = 6\) cuts coordinate axes at A, B and C, then the volume of tetrahedron OABC (where O is the origin) is ......cubic units.

If the plane \(\overset{̄}{r} = (λ+μ)\hat{i}+(2+μ)\hat{j}+(3λ+2μ)\hat{k}\), where \(λ\) and \(μ\) are parameters, intersects coordinate axes at points \((a,0,0)\), \((0,b,0)\) and \((0,0,c)\) then \(a+b+c =\)...

Let \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) be three vectors of equal magnitude such that the angle between \(\overset{̄}{a}\) and \(\overset{̄}{b}\) is \(α\), \(\overset{̄}{b}\) and \(\overset{̄}{c}\) is \(β\), \(\overset{̄}{c}\) and \(\overset{̄}{a}\) is \(γ\).
Then the minimum value of \(cosα+cosβ+cosγ\) is ...

The acute angle \(θ\) between the \(xy\)-plane and the plane passing through the point \((1,2,4)\) and parallel to the vectors with direction ratios \(3,2,-1\) and \(1,-2,-2\) is...

A vector which is orthogonal to the vector \(\overset{̄}{a} = \hat{i}+2\hat{j}+3\hat{k}\) and coplanar with the vectors \(\overset{̄}{b} = 3\hat{i}+2\hat{j}\) and \(\overset{̄}{c} = 2\hat{i}+\hat{j}+3\hat{k}\) is

If \(\overset{̄}{a} = \hat{i}-\hat{k}\), \(\overset{̄}{b} = x\hat{i}+\hat{j}+(1-x)\hat{k}\) and \(\overset{̄}{c} = y\hat{i}+x\hat{j}+(1+x-y)\hat{k}\) then \([\overset{̄}{a} \overset{̄}{b} \overset{̄}{c}]\) depends on

The line \(\ell\) passes through the point \((2,1,1)\) and is parallel to the plane \(x+y+2z = 18\). If line \(\ell\) intersects the line \(\frac{x+2}{3} = \frac{y+1}{-1} = \frac{z-2}{1}\), then equation of the line \(\ell\) is...

Let \(\overset{̄}{u},\overset{̄}{v},\overset{̄}{w}\) be three vectors such that \(|\overset{̄}{u}| = 1,|\overset{̄}{v}| = 2,|\overset{̄}{w}| = 3\). If the projection of \(\overset{̄}{v}\) along \(\overset{̄}{u}\) is equal to the projection of \(\overset{̄}{w}\) along \(\overset{̄}{u}\) and \(\overset{̄}{v},\overset{̄}{w}\) are perpendicular to each other, then \(|\overset{̄}{u}-\overset{̄}{v}+\overset{̄}{w}| =\)...

The area (in square units) bounded by the line \(y = x\), the X-axis and the lines \(x = -2\) and \(x = 4\) is...

The value of the definite integral \(\int _0^{log_e5}\frac{e^x\sqrt{e^x-1}}{e^x+3}\,dx\) is equal to...

A body cools from \(100^{\circ}\text{C}\) to \(60^{\circ}\text{C}\) in 20 minutes, the temperature of the surroundings being \(20^{\circ}\text{C}\). The total time taken (in minutes) for the body to cool down to \(40^{\circ}\text{C}\) is ...

If \([\cdot ]\) denotes the greatest integer function, then \(\int _0^{π/3}[tanx]\,dx =\)

The general solution of the differential equation \(xsinx\frac{dy}{dx}+(xcosx+sinx)y = sinx\) is

The equation of the curve whose slope is \(\frac{y-1}{x^2+x}\) and which passes through the point \((1,0)\) is

If the tangent to the curve \(xy+ax+by = 0\) at \((1,1)\) makes an angle of \(tan^{-1}2\) with positive direction of the \(x\)-axis, then the value of \(\frac{ab}{a+b}\) is...

If the line \(x+By+C = 0\) is the normal to the curve given by \(x = asin^3t\), \(y = bcos^3t\), (where \(a,b\neq 0\)) at a point \(t = \frac{π}{2}\), then \(B-C =\)

\(\int \frac{(x+1)\,dx}{x(1+xe^x)} = \ldots \ldots\)

The value of \(\int \frac{n\sqrt{\text{cosec}^2x^n-1}}{x^{(1-n)}}\,dx\) is ...

\(\int sin(logx)\,dx =\)

If the side of an equilateral triangle increases at the rate of \(\sqrt{3} \text{cm/sec}\), then the rate of change of increase of its area when the side is \(12 \text{cm}\) is ____

Let \(f(x) = ax+b\) and \(g(x) = cx+d\). The condition \(f(g(x)) = g(f(x))\) holds for all \(x\) if and only if ...

If \(0\leq x\leq 1\) and \((sin^{-1}x)^3+(cos^{-1}x)^3 = aπ^3\) then

If \(x\,e^{xy} = y+sin^2x\), then the value of \(\frac{dy}{dx}\) at \(x = 0\) is equal to

If \(g(x) = (x^2+2x+1)\cdot f(x)\) such that \(f(0) = 5\) and \(\underset{x\rightarrow 0}{lim}\frac{f(x)-5}{x} = 4\) then \(g^'(0) =\)