List of top Questions asked in KCET

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

If A = \(\begin{bmatrix} 0 & 1 \\ 0 & 0 \\ \end{bmatrix}\) then \((aI + bA)^n\) is (where I is the identity matrix of order 2)

If A=\([\begin{smallmatrix} 2 & -1 \\ 3 & -2 \end{smallmatrix}]\) ,then the inverse of the matrix A³ is

If A is matrix of order 3x3, then \((A^2)^{-1}\) is equal to

\(\lim_{{y \to 0}} \frac{\sqrt{3} + y^3 - \sqrt{3}}{y^3}\)

Let the relation R is defined in N by \(a \mathbb{R} b\), if \(3a+2b = 27\) , then R is

If \(f: \mathbb{R} \rightarrow \mathbb{R}\) be defined by \(f(x) = \begin{cases}  2x & \text{if } x > 3 \\ x^2 & \text{if } 1 < x \leq 3 \\ 3x & \text{if } x \leq 1 \end{cases}\). Then \(f(-1) + f (2) + f(4)\) is

If the set x contains 7 elements and set y contains 8 elements, then the number of bijections from x to y is

If the standard deviations of the numbers - 1, 0, 1, K is \(\sqrt5\), where \(k>0\), then k is equal to

If 3x + i(4x-y) = 6-i, where x and y are real numbers, then the value of x and y are respectively

The octant in which the point (2,-4,-7) lies is

If the straight line 2x-3y+17 = 0 is perpendicular to the line passing through the points (7,17) and (15,β), then β equals