List of top Mathematics Questions asked in KCET

The sum of the degree and order of differential equation \(\left(1 + y_1^2\right)^{\frac{2}{3}} = y_2\) is

If \(|\vec{a}\times\vec{b}|\) + \(|\vec{a}.\vec{b}|^2=36\) and \(|\vec{a}|=3\) then \(|\vec{b}|\) is equal to

If y(x) be the solution of the differential equation \(x \log(x) \frac{dy}{dx} + y = 2x \log(x), \quad y(e)\) is equal to

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

If \(\frac{dy}{dx} + \frac{y}{x} = x^2\) then \(2y (2) - y (1) =\)

\(\int\limits_{0}^{\frac{\pi}{2}}\frac{\cos x\sin x}{1+\sin x}\ dx\) is equal to

Evaluate \(\int\limits_{2}^3x^2\ dx\) as the limit of a sum

Area of the region bounded by the curve \(y = tan x\), the x- axis and the line \(x = \frac{\pi}{3}\) is

If \(\int \frac{dx}{(x+2)(x^2 + 1)} = a \log |1+x^2| + b \tan^{-1} x + \frac{1}{5} \log |x+2| + c\), then

\(\int \frac{\cos(2x) - \cos(2\alpha)}{\cos(x) - \cos(\alpha)} \, dx\) is equal to

If \(e^y + xy = e\) the ordered pair \(\left(\frac{dy}{dx},  \frac{d^2y}{dx^2}\right)\) at \(x = 0\) is equal to

\(\int\limits_{0}^{\frac{\pi}{2}}\sqrt{\sin \theta}\cos^3\theta\ d\theta\) is equal to

The function \(f(x) = 4 \sin^3 x - 6 \sin^2 x + 12 \sin x + 100\) is strictly

The co-ordinates of the point on the \(\sqrt{x} + \sqrt{y} = 6\) at which the tangent is equally inclined to the axes is

The function \(f(x) = \log(1+x) - \frac{2x}{2+x}\) is increasing on

If A_n = \(\begin{bmatrix} 1-n & n \\ n & 1-n \\ \end{bmatrix}\) then | A₁ | + | A₂ | + ….. + | A₂₀₂₁ | =

If \(y = x^{\sin(x)} + (\sin(x))^x\), then \(\left. \frac{dy}{dx} \right|_{x = \frac{\pi}{2}}\) is

If \(f(1) = 1, \quad f'(1) = 3\) then the derivative of \(f(f(f(x))) + (f(x))^2\) at \(x= 1\) is

If \(y =\)\(e^{\sqrt{x\sqrt{x\sqrt{x\ldots}}}}\) \(x>1,\) then \(\left. \frac{{d^2y}}{{dx^2}} \right|_{x = \log_e 3}\) is

If \(x = e^\theta \sin \theta, \quad y = e^\theta \cos \theta\), where \(θ\) is a parameter , then \(\left. \frac{dy}{dx} \right|_{(1,1)}\) is equal to

If \(y = (1+x^2) \tan^{-1}(x) - x\). Then \(\frac{dy}{dx}\) is

Domain of \(cos^{-1} [x]\), where \([. ]\) denotes a greatest integer function

If the vertices of triangle are (-2,6), (3,-6) and (1,5), then the area of the triangle is

If there are two values of ‘a’ which makes determinant
\(\Delta=\begin{bmatrix} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a \\ \end{bmatrix}=86\)
Then the sum of these numbers

If A is a 3x3 Matrix such that \(|5 \cdot \text{adj}(A)| = 5, \text{ then } |A|\) is equal to