List of top Mathematics Questions asked in KCET

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

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

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

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

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

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

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

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

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

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

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

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

If \(a_1, a_2, a_3, \ldots, a_{10}\) is a geometric progression and \(\frac{a_3}{a_1} = 25\) then \(\frac{a_9}{a_5}\) equals

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

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

The value of cos 1200° + tan 1485° is

If x³ - 2x² - 9x + 18 = 0 and A = \(\begin{vmatrix}     1 & 2 & 3 \\     4 & x & 6 \\     7 & 8 & 9 \\ \end{vmatrix}\) then the maximum value of A is

The equation of the line joining the points $(-3,4,11)$ and $(1,-2,7)$ is

If y = (x - 1)² (x - 2)³ (x - 3)⁵ then \(\frac{dy}{dx}\) at x = 4 is equal to

Consider the following statements :
Statement 1 : If y = log₁₀x + log_ex then \(\frac{dy}{dx}=\frac{\log_{10}e}{x}+\frac{1}{x}\)
Statement 2 : \(\frac{d}{dx}(\log_{10}x)=\frac{\log x}{\log 10}\ \text{and}\ \frac{d}{dx}(\log_ex)=\frac{\log x}{\log e}\)