List of top Mathematics Questions asked in KCET

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

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

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

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 \(I_n=^{\frac{\pi}{4}}_0\int\tan^n x\ dx\) where n is positive integer then I₁₀ + I₈ is equal to

The value of \(\int e^x[\frac{1+\sin x}{1+\cos x}]dx\) is equal to

The maximum slope of the curve y = -x³ + 3x² + 2x -27 is

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 + log_ex then \(\frac{dy}{dx}=\frac{\log_{10}e}{x}+\frac{1}{x}\)
Statement 2 : \(\frac{d}{dx}(\log_{10}x)=\frac{\log x}{\log 10}\ \text{and}\ \frac{d}{dx}(\log_ex)=\frac{\log x}{\log e}\)

For constant a, \(\frac{d}{dx}\)(x^x + x^a+ a^x + a^a) 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

Let M be 2 × 2 symmetric matrix with integer entries, then M is invertible if