List of top Questions asked in KEAM

If the angular speed of a particle moving in a circular path of radius \(1.2\) m is increased from \(2\ \text{rad s}^{-1}\) to \(4\ \text{rad s}^{-1}\) keeping its radius constant, then its linear speed is increased by

The function \(y = be^x + ae^{-x}\), \(a\) and \(b\) are constants, is a solution of

\(\int_{0}^{\pi/3} \frac{dx}{1 + \sqrt{\tan x}} =\)

\(\int_{0}^{\pi/4} \sqrt{1 + \sin 2x}\,dx =\)

The area of the region bounded by the lines, $y = x + 2$, $x = 0$, $x = 1$ and $y = 0$ is

The solution of $(e^y + 1)\cos x\,dx + e^y \sin x\,dy = 0$ is

If \(\int_a^b x^3 \, dx = 0\) and \(\int_a^b x^2 \, dx = \frac{2}{3}\), then the values of \(a\) and \(b\) respectively are

\(\int \sin^3 x \, e^{\log \cos x} \, dx =\)

If $u = \int e^x \cos x \, dx,\; v = \int e^x \sin x \, dx$, then $u + v =$

If $\int \left(3t^2\sin\left(\frac{1}{t}\right) - t\cos\left(\frac{1}{t}\right)\right) dt = f(t)\sin\left(\frac{1}{t}\right) + c$ then $f(2)$ is equal to

$\int e^x \left(\frac{1 - \sin x}{1 - \cos x}\right) dx =$

If \(\int \frac{2^{1/x}}{x^2} \, dx = k\,2^{1/x} + c\) then \(k\) is equal to

If the rate of increase of the radius of a circle is $5$ cm/sec, then the rate of increase of its area when the radius is $20$ cm, will be

If \(y = \sin x + e^x\), then \(\frac{d^2 x}{dy^2}\) is equal to

The function $f(x) = x^4 - 2x^2$ is strictly increasing on

The absolute maximum value of the function $f(x) = x^3 - 3x + 2$ in $[0,2]$ is

If \(y = \log_{10} x + \log_e x\), then \(\frac{dy}{dx}\) is equal to

If the function $f(x) = x^2 + ax + 1$ is increasing on $[1,2]$, then $a$ is greater than or equal to

If \(f(1)=2,\ f'(1)=1\), then \(\lim_{x \to 1} \frac{x f(1) - f(x)}{x-1}\) is

Let \(\lim_{x \to a} f(x)g(x) = 16\) and \(\lim_{x \to a} \frac{f(x)}{g(x)} = 4\). If both \(\lim_{x \to a} f(x)\) and \(\lim_{x \to a} g(x)\) exist, then \(\lim_{x \to a} [f(x)+g(x)]\) is

The positive integer \(n\), such that \(\lim_{x \to 3} \frac{x^n - 3^n}{x - 3} = 108\)

If \(y = 3^x + e^x + x^x + x^3\), then \(\frac{dy}{dx}\) at \(x=3\) is equal to

If \(y = \log \sqrt{\frac{x-1}{x+2}}\), then \(\frac{dy}{dx}\) is

Let \(f(x)\) and \(g(x)\) be twice differentiable functions defined on \([0,2]\) such that \(f''(x) - g''(x) = 0\), \(f'(1)=4,\ g'(1)=2,\ f(2)=9,\ g(2)=3\). At \(x=\frac{3}{2}\), \(f(x)-g(x)\) is

The value of \(\lim_{x \to 0} \frac{\sqrt{1 - \cos 2x}}{|x|}\) is equal to