List of top Mathematics Questions asked in KCET

The diagonals of a parallelogram are the vectors \(3\hat{i}+6\hat{j}-2\hat{k}\) and \(-\hat{i}-2\hat{j}-8\hat{k}\) then the length of the shorter side of parallelogram is

A vector \(\vec{a}\) makes equal acute angles on the coordinate axis.Then the projection of vector \(\vec{b}=5\hat{i}+7\hat{j}-\hat{k}\) on \(\vec{a}\) is

The number of solutions of \(\frac{dy}{dx}=\frac{y+1}{x-1}\) when y(1) = 2 is

Solution of Differential Equating xdy – ydx = 0 represents

If the area of the Ellipse is \(\frac{x^2}{25}+\frac{y^2}{\lambda^2}=1\) is 20π square units, then λ is

The area of the region bounded by \(y=\sqrt{16-x^2}\) and x-axis is

The value of \(\int\limits_0^{4042}\frac{\sqrt{x}\ dx}{\sqrt{x}+\sqrt{4042-x}}\) is equal to

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 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

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

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

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 ?