List of top Mathematics Questions asked in KCET

The value of \(\int\frac{xe^x dx}{(1+x)^2}\) is equal to
The value of \(\int\frac{x^2dx}{\sqrt{x^6+a^6}}\) is equal to
\(\int\frac{x^3\sin(\tan^{-1}(x^4))}{1+x^8}dx\) is equal to
If y = (x - 1)2 (x - 2)3 (x - 3)5 then \(\frac{dy}{dx}\) at x = 4 is equal to
The function f(x) = x2 - 2x is strictly decreasing in the interval
If the parabola y = αx2 - 6x + β passes through the point (0, 2) and has its tangent at x = \(\frac{3}{2}\) parellel to x axis, then
A particle starts form rest and its angular displacement (in radians) is given by \(\theta=\frac{t^2}{20}+\frac{t}{5}\). If the angular velocity at the end of t = 4 is k, then the value of 5k is
If the parametric equation of curve is given by x = cosθ + log tan \(\frac{θ}{2}\) and y = sinθ, then the points for which \(\frac{dy}{dx}=0\) are given by
Consider the following statements :
Statement 1 : If y = log10x + logex then \(\frac{dy}{dx}=\frac{\log_{10}e}{x}+\frac{1}{x}\)
Statement 2 : \(\frac{d}{dx}(\log_{10}x)=\frac{\log x}{\log 10}\ \text{and}\ \frac{d}{dx}(\log_ex)=\frac{\log x}{\log e}\)
For constant a, \(\frac{d}{dx}\)(xx + xa+ ax + aa) is
If y = (cosx2)2, then \(\frac{dy}{dx}\) is equal to
At x = 1, the function f(x) = \(\left\{ \begin{aligned}     & x^3-1\ \ \ \ \ \ 1<x<\infin \\     & x-1\ \ \ \ \ -\infin<x≤1 \\      \end{aligned} \right.\) 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
If f(x) = \(\begin{vmatrix}     cosx & 1 & 0 \\     0 & 2cosx & 3 \\     0 & 1 & 2cosx \\ \end{vmatrix}\) then \(\lim\limits_{x\rightarrow\pi} f(x)=\)
If A and B are invertible matrices then which of the following is not correct ?
If A and B are matrices of order 3 and |A| = 5, |B| = 3 then |3AB| is
\(\tan^{-1}[\frac{1}{\sqrt3}\sin\frac{5\pi}{2}]\sin^{-1}[\cos(\sin^{-1}\frac{\sqrt3}{2})]=\)
Let M be 2 × 2 symmetric matrix with integer entries, then M is invertible if
If \(A=\begin{bmatrix}     1 & -2 & 1 \\     2 & 1 & 3 \\ \end{bmatrix}\ B=\begin{bmatrix}     2 & 1 \\     3 & 2 \\     1 & 1 \\ \end{bmatrix}\) then (AB)' is equal to
\(\cos[\cot^{-1}(-\sqrt3)+\frac{\pi}{6}]=\)
Let A = { x : x ∈ R; x is not a positive integer } Define f : A → R as f(x) = \(\frac{2x}{x-1}\), then f is
Domain of the function f(x) = \(\frac{1}{\sqrt{[x]^2-[x]-6}}\) where [x] is greatest integer ≤ x is
The function f(x) = \(\sqrt3\) sin2x - cos2x + 4 is one-one in the interval
f : R → R defined by f(x) = \(\left\{ \begin{aligned}     & 2x;x>3 \\     &x^2;1<x≤3\\     & 3x;x≤1 \end{aligned} \right.\) then f(-2) + f(3) + f(4) is
If P(A) = 0.59, P(B) = 0.30 and P(A ∩ B) = 0.21 then P( A' ∩ B') =