List of top Mathematics Questions asked in KEAM

The domain of the function \(f(x) = (x^2-2x-63)^{\frac{3}{2}}\), x ∈ R is
The centre of the ellipse x2+7y2-14x+28y+49=0 is
If the line y = mx + c is perpendicular to y=1+x and passes through the point (1, 2), then the value of c is equal to
\(\displaystyle\lim_{x\rightarrow-2}\frac{3x^2+ax-2}{x^2-x-6}\) is a finite number, then the value of a is equal to
The value of \(\left[ \frac{5i}{(1-i)(2-i)(3-i)} \right]^{50}\)is equal to
If \(z=\frac{(3+i)(7-i)^2}{3-i}\), then the value of |z| is equal to
If the lines 2x-3y+5=0, 9x-5y+14=0 and 3x-7y+λ=0 are concurrent, then the value of λ is equal to
Let \(\begin{vmatrix} 2&1&-2\\1&1&-1\\1&0&\ \ 3 \end{vmatrix}\)and let B=|A|adj(A). Then |B|=
\(\displaystyle\lim_{t\rightarrow0}\frac{sin(t^2)}{tsin(5t)} \ is\ equal\ to\)
Let A = {x∈Z: -1 ≤ x < 4} and let B = {x ∈ Z:0 < \(\frac{x}{2}\) ≤ 3}. Then A∩B is equal to
The number of subsets containing exactly 4 elements of the set {2, 4, 6, 8, 10, 12, 14, 16, 18) is equal to
If A is non-singular matrix and if \(A^{-1}=\frac{1}{2}\begin{bmatrix} -10&-4\\2&1\end{bmatrix}\), then adj(A)=
Let \(f(x) =   \begin{cases}     3x+6,       & if\ x\geq c \\       x^2-3x-1,       & if\ x\lt c   \end{cases}\), where x∈R and c is a constant. The values of c for which f is continuous on R are
If \(\cos\theta=\frac{5}{11}\) and \(\tan\theta\lt0\), then the value of \(\sin\theta\) is equal to
There are 4 red, 3 blue and 3 yellow marbles in an urn. If three marbles are drawn simultaneously, then the probability that the number of yellow marbles will be less than 2 is equal to
The range of the function f(x) = 2sin(3x) +1 is equal to
Let A = {1,2,3,4,5} and let B={1,2,3,4}. If the relation R : A → B is given by (a, b) ∈ R if and only if a+b is even, then n(R) is equal to
The period of the function \(g(x)=5\cot(\frac{\pi}{3}x+\frac{\pi}{6})+2\) is equal to
If \(z^4=7-5i\), then \(\text{Im}((\bar{z})^4)\) is equal to
If the radius of the circle x2+y2+ax+by+3=0 is 2, then the point (a, b) lies on the circle
\(\cos \left( \sin^{-1}(\frac{\sqrt{3}}{200})+\cos^{-1}(\frac{\sqrt{3}}{200}) \right)=\)
The eccentricity of the hyperbola \(\frac{(x-3)^2}{9}+\frac{4(y-1)^2}{45}=1\) is equal to
The solutions of the equation \(cos\theta=2-3sin(\frac{\theta}{2})\ in\ the\ interval\ 0\leq\theta\leq\pi\ are\)
The modulus of \((\frac{1+i}{1-i})^{75}-(\frac{1-i}{1+i})^{75}\)is
If \(|\bar{a}|=\sqrt{14},|\bar{b}|=\sqrt{10},|\bar{a}-\bar{b}|=\sqrt{24}\ and\ \theta\) is angle between \(\bar{a}\ and\ \bar{b}\), then \(\cos\theta=\)