List of top Mathematics Questions

The acute angle between the vector \(2\hat{i}+\hat{j}-3\hat{k}\) and the plane containing the vectors \(2\hat{i}+3\hat{j}-\hat{k}\) and \(\hat{i}-\hat{j}+2\hat{k}\) is

The lines \(\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k}\) and \(\frac{x-1}{k} = \frac{y-4}{2} = \frac{z-5}{1}\) are coplanar if

A parallelogram is constructed on \(5\overset{̄}{a}+2\overset{̄}{b}\) and \(\overset{̄}{a}-3\overset{̄}{b}\) as its adjacent sides, with \(|\overset{̄}{a}| = 2\sqrt{2},|\overset{̄}{b}| = 3\) . The angle between \(\overset{̄}{a}\) and \(\overset{̄}{b}\) is \(\frac{π}{4}\) . Then the length of the diagonals of the parallelogram are

The lines \(\frac{x-1}{-1} = \frac{y+2}{1} = \frac{z-3}{-2}\) and \(\frac{x-1}{1} = \frac{y+2}{1} = \frac{z+1}{-2}\) are

If the product of the distances of the point (1, 2, 3) from the origin and the plane \(2x-3y+z+k = 0\) is 7, then the value of k is

The degree of the differential equation obtained from the equation \((y-a)^2 = 4(x-b)\) [where \(a\) and b are arbitrary constants] is

The solution of the differential equation \((x+2y^3)\frac{dy}{dx}-y = 0\) is

The rate of reduction is proportional to the square root of a persons existing assets at that moment. If his assets at the beginning are 10000 and they dwindle down to 5625 in 2 years, then the person will be bankrupt in

Let A, B, C, D be the points in the plane with position vectors \(-2\hat{i}-\hat{j}\), \(4\hat{i}\), \(3\hat{i}+3\hat{j}\) and \(-3\hat{i}+2\hat{j}\) respectively, then \(◻\)ABCD is

Let \(\overset{̄}{a} = \hat{i}+\hat{j}\), \(\overset{̄}{c} = \hat{i}-\hat{j}\) and a vector \(\overset{̄}{b}\) be such that \(\overset{̄}{a}\times \overset{̄}{b} = \overset{̄}{c}\) and \(\overset{̄}{a}\cdot \overset{̄}{b} = 3\) then \(|\overset{̄}{b}| =\)

If a vector \(3\hat{i}+4\hat{j}-5\hat{k}\) is rotated through a certain angle about the origin in the anti-clockwise direction, then the components of the new vector are \(a+1,-3,5\) . The possible values of \(a\) is

\(\int \frac{cos^3x}{sin^2x+sinx}\,dx =\)

\(\int cot^4x\,dx\) is equal to

\(\int _0^{log5}\frac{e^x\sqrt{e^x-1}}{e^x+3}\,dx =\)

\(\int _{π/6}^{π/3}\frac{sinx-cosx}{1+sinxcosx}\,dx =\)

The integrating factor of the differential equation \((1+t^2)+(x-e^{tan^{-1}t})\frac{dt}{dx} = 0\) is

\(\int \frac{(x+1)(x+logx)^2}{x}\,dx =\)

If the derivative of the function \(f(x) = \{\begin{array}{cc}ax^2+b & \text{if }x < -1 \\ bx^2+ax+4 & \text{if }x\geq -1\end{array}\) is continuous everywhere then

A triangle has two fixed vertices A \((a,0)\) and B\((0,b)\) . Let its third vertex C is moving along the line \(x = y\). If \(s\) is the area of triangle ABC, then \(\frac{ds}{dx} =\)

The derivative of \(log_8(log_5x)\) w. r. t. \(x\) is

The minimum value of \(\frac{logx}{x}\) in the interval \((2,\infty )\) is

The function \(f(x) = tan^{-1}(sinx+cosx)\) is an increasing function in the interval.....

If \(y^{\frac{1}{m}}+y^{\frac{-1}{m}} = 2x\) , then \((x^2-1)y_1^2 =\)

If \(y = tan^{-1}[\frac{x-\sqrt{1-x^2}}{x+\sqrt{1-x^2}}]\) , then \(\frac{dy}{dx} =\)

Inverse of \([\begin{array}{cc}3 & -2 \\ 1 & 4\end{array}]\) is