List of top Mathematics Questions asked in KCET

The distance of the point (1, 2, -4) from the line \(\frac{x-3}{2}=\frac{y-3}{3}=\frac{z+5}{6}\) is
If a line makes an angle of \(\frac{\pi}{3}\) with each of x and y-axis, then the acute angle made by z-axis is
The point (1, -3, 4) lies in the octant
If \(|\vec{a}\times\vec{b}|+|\vec{a}.\vec{b}|^2\)=144 and \(|\vec{a}|\) = 6, then \(|\vec{b}|\) is equal to
If the vectors \(2\hat{i}-3\hat{j}+4\hat{k},2\hat{i}+\hat{j}-\hat{k}\) and \(\lambda\hat{i}-\hat{j}+2\hat{k}\) are coplanar, then the value of λ is
If \(\vec{a}\) and \(\vec{b}\) are unit vectors and θ is the angle between \(\vec{a}\) and \(\vec{b}\), then sin\(\frac{θ}{2}\) is
The two vectors \(\hat{i}+\hat{j}+\hat{k}\) and \(\hat{i}+3\hat{j}+5\hat{k}\) represent the two sides \(\vec{AB}\) and \(\vec{AC}\) respectively of a ΔABC. The length of the median through A is
The curve passing through the point (1, 2) given that the slope of the tangent at any point (x, y) is \(\frac{2x}{y}\) represents
The general solution of the differential equation x2dy - 2xydx = x4cosx dx is
The order of the differential equation obtained by eliminating arbitrary constants in the family of curves c1y = (c2 + c3)ex+c4 is
The area of the region bounded by the line y = 2x + 1, x-axis and the ordinates x = -1 and x = 1 is
The area of the region bounded by the curve y2=8x and the line y = 2x is
The value of \(\int\limits_0^1\frac{\log(1+x)}{1+x^2}\ dx\) is
The value of \(\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{\cos x}{1+e^x}\ dx\) is
The value of \(\int\limits^{\frac{1}{2}}_{-\frac{1}{2}}\cos^{-1}x\ dx\) is

The value of 

\[\int e^{\sin x}\sin 2x\ dx\]

 is

If 

\[\int\frac{3x+1}{(x-1)(x-2)(x-3)}dx\]

 

\[= A \;log |x - 1| + B \;log |x - 2| + C\; log |x - 3| + C\]

, then the values of A, B and C are respectively.

The value of \(\int\frac{1+x^4}{1+x^6}dx\) is
If the side of a cube is increased by 5%, then the surface area of a cube is increased by
The maximum value of \(\frac{\log_ex}{x}\), if x > 0 is
If the curves 2x = y2 and 2xy = K intersect perpendicularly, then the value of K2 is
If y = 2xn+1 + \(\frac{3}{x^n}\) then x2\(\frac{d^2y}{dx^2}\) is
If (xe)y = ex, then \(\frac{dy}{dx}\) is

If f(x) = sin-1 \((\frac{2x}{1+x^2})\), then f'\((\sqrt3)\) is\(\)

If 2x + 2y = 2x+y, then \(\frac{dy}{dx}\) is